23 Jul 1991 - 0 free electron lasers, requiring intense electron linacs. ...... CRNL study for PNC - costs were reviewed by Nissan HV to meet manufacturing ...
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I A C P - 9 1-272
SCALING AND OPTIMIZATION Irv HIGH-INTENSITY LINEAR ACCELERATORS
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Stllcty for the J npan Atomic Energy Resenrch Institute (JAEII I) ‘l’okxi IWearch Establishnient ‘l’okai, Ibaraki 319- 11, Japan
I’e1-fOmed by
R A . Jameson, Principal Investigator, AT-DO P.J. ‘I’alXerico,AT-5 (Sec.IV) W.K. FOX,AT-4 (Sec.V) N. Bultrnan, AT-4 T.H. L,arkin, AT-4 I
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K.L. Martineau, AT-4 S.J, Black, IP, Grurnman ‘‘ It
A:celcmtor ‘Technology Division I,os klanios National Laboratory Los t\lamos, N M 87545, USA J d y 1991
Work pcrforriied iiricler tlic .iuspices of the US Ueputnient o f Energy t i i i d c r l;unds In Agrecirient No. LlE-FIO4-91AL73477 bctwccn tlie LX)fI anti 11ie Japan Atomic Energy Kcsearch tnstitute. May t x rc:pr.oduceil or distributed only by pc:miission of the authors or IAEKl
LA-CP-91-272
SCALING AND OPTIMIZATION IN HIGH-INTENSITY LINEAR ACCELERATORS
Study for the
Japan Atomic Energy Research Institute (JAERI)
Tokai Research Establishment Tokai, Ibaraki 319-11, Japan
Performed by R.A. Jameson, Principal Investigator, AT-DO P.J.Tallerico, AT-5 (Sec.IV) W.E. Fox, AT-4 (Sec.V) N. Bultman, AT-4 T.H. Larkin, AT-4 R.L.Martineau, AT-4 " S.J. Black, IP,Gnunman " It
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AccelcratmTechnology Division
Los Alamos National Laboratory Los Alamos, NM 87545, USA July 1991
May be r e p r o d d or dbuibuted only by pamission of the authors or JAERI
TABLE OF CONTENTS
I. Background 11. Purpose of This Study, Executive Summary of Results, and Recommended
Future Work
III. Framework for Codification
A. TheLINACS Code 1. Introduction 2. How to Run the Code 3. Inputs 4. outputs 5. LevelOModel a. Minimum Cost Model b. Level 0 Graphs 6. Level 1 Model a. Accelerator Technical Model b. Cost Models c. Define linacLev1 Function d. Examples e. Bridge between Level 0 and Level 1 7. Levet2Model a. Linac Beam Dynamics (see Section III.B.) b. Accelerator Physics & Engineering Constraints
B. Linac Beam Dynamics, LINACS Level 2 Model 1. Introduction 2. Inputs, Defaults, Reset Functions 3. Formulas C. Linac Beam Dynamics Examples and Comparisons With Simulation Results 1. CURLIMode 1 2. CURLIMode2 3. Example - JAEWSHJ DTL 4. Example - FMIT80 MHz case 5. Example - 425 M H z case 6. A p e m factor example 7. Make table, plot graphs 8. Minimum ellipse beta vs phase advance? 9. Check using APT material from LANL point design 10. Check using 4/91 BTA design 11. Check using 13 Dec 80 RAJ equipartitioned run, 12. Studies
IV.RF Power Considerations for Transmutation-DriverLinacs A. Introduction B . Optimizing the Acceleratar to Minimize RF Costs C. Reliability
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31 35
35 III.B. 1
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8 9 12 13
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19 24 27 30
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D. Power Efficiency E. QuantityDiscounts F. Power Substation G. Power Supply H.Power Conditioning I. Power Amplifier J. Cost Estimates K . Design Examples L. CW Klystron Results 1. CW Klystron Summary M. Pulsed Klystron System Results N. Appendix for Cost Spreadsheets 1. 1 MW CW Klystrons at 352 MHz 2. 1 MW CW Klystrons at 704 MHZ 3. 2 MW CW Klystrons at 704 MHZ 4. 0.5 MW, 50% Efficient CW Klystrons at 850 MHZ 5. 0.5 MW, 60%Efficient CW Klystrons at 850 M H z 6. 1 MW, 50% Efficient CW Klystrons at 850 MHz 7. 1 MW, 62% Efficient CW Klystrons at 850 MHz 8. 4 MW Peak, 1 MW Average Klystrons at 433 MHz 9. 1.25 MW Peak, 0.1 MW Average Klystrons at 850 M H z
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V. Coupled-CavityLinac Characterization and Costing A. Introduction
B . Couplcd-CavityDesign Optimization C. Thermal, Stress and Frequency Detuning Sensitivity Considerations D. Cavity Frequency Tuner Considerations E. Sumtkuy 6f Coipled-Cavity Parameter Study and Cost Models VI. Linac and Transport Design Using the Envelope and Equipartitioning
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30 34
Equations
A. Introduction B . The Basic Relationships C. The Ratio of Transverse to Longitudinal Tune Shifts 1. Hofmann Stability Charts D. Expressions far LongitudinalQuantities in Terms of Transverse . Beams E. Requhmnts for Bright and Volume-F. AperhveRatioa 1. Tmsvtrse aputure factor a. Tfrt flumr factor b. Simple forms 2. Longitudinal aperture factor 3. Solutionsfor beam ellipsoid radii 4. Analysis of beam radius solutions under matched and equipartitionedconditions: derivation of constraints. 5. "Conventional" equipartitioned example 6. Examples exploring (Q&) and ( c J ~ ~ / G ~ * ) 7. Discussion
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VI. 1 2 3
7 9 10 10
13 14 16 17 19 25
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I. Background High-intensity linear accelerators (linacs) are those in which the beam being accelerated is of sufficient intensity that the beam’s self- or induced-fields interact with the externally applied electromagnetic fields to substantially affect the transport and acceleration characteristics of the system. For electron beams, beam-induced wakefields are the phenomena of interest; for ion beams (not completely relativistic), the beam’s space charge fields are important. In this report, we concentrate on ion beams. Operating and potential applications include: 0
0
physics research facilities; for example, the Los Alamos Meson Physics Facility (LAMPF) is the world’s most intense ion linac, 1 km long, with an 800 MeV, 1 mA average current proton beam. materials testing facilities; the proposed JAERI Energy Selective Neutron Irradiation Test facility requires a deuteron beam at 35-40 MeV with 50 mA average current.
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free electron lasers, requiring intense electron linacs.
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intense neutral particle beams for fusion heating and strategic defense.
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heavy-ion driven inertial confinement fusion. In addition is an application with very strong contemporary and future interest:
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the possibility for using intense ion beams (protons) to enable the transmutation of radioactive wastes, and to generate electricity from plentifully available thorium fuel with accompanying waste burnup, so as not to leave a waste legacy behind. [Kaneko 1990, Bowman et al 19911
Research on accelerator-driven transmutation technology is beginning in earnest, with the Japanese OMEGA program at JAERI, and on a presently smaller scale at Los Alamos. The linacs required are in the 800-1600 MeV, 30-250 rnA cw proton current class - many times the operational capability of LAMPF. The beam physics basis for such linacs is in hand, and much of the engineering has been demonstrated at the component level [ERAB,19901. Construction of a complete, full-scale facility is nevertheless a major challenge, to produce a system-optimized, fully-engineered facility capable of very high availability (>85%) over a sustained period (>30 years) at minimal capital and operating cost.
This study addresses the conceptual design of high-intensity linacs from the point of view of selecting the major parameters. The selection is accomplished partly by scaling to the operating regime for the problem at hand; sometimes scaling is possible using a theoretical framework, and sometimes by extrapolation from established practice and data. Orice the parameters for the operating regime have been roughly established, optimization to finer-grained criteria must be undertaken, with due regard for constraints. 171
11. Purpose of This Study, Executive Summary of Results, and Recommendations For Future W o r k The purpose of this study is to consider, for the JAERI OMEGA radioactive waste transmutation program, how an optimal 1.6 GeV high-current linac would be configured. Adequate conceptual physics and engineering designs have already been developed for the applications of interest [Lawrence,l991],[Varsamis, G.L.,et al, 19901. However, the underlying design principles are usually held by more-or-less interlocking groups, with beam physicists doing the beam dynamics design, mechanical engineers designing the accelerating structures, rf engineers building the rf equipment, and so on. The projects are so large that such specialization is inevitable; the problem is how to make decisions regarding system optimization. Everyone agrees that determining trade-offs between groups is a serious and often contentious business, requiring strong direction with broad-based competence. The criteria and considerations by which a design is brought together are not at all well codified; thus the result is highly dependent on “expert” knowledge in the design team and its coordinator. Even within each design area, the number of parameter trade-offs and optimization considerations is so large and diverse that the best designers are “experts” whose criteria may be largely unwritten. The effort required to change design directions is so large that there is a tendency to “lock-in” on familiar or well-used criteria even when new requirements would benefit from new approaches. It would have been easiest, within the small scale of this study, to provide an “expert” conceptual design based on a best judgment, after consideration of the parameter ranges of interest to JAEItI and ourselves. Indeed, we have already provided such information, in the cited references. However, we do not claim that the conceptual point designs in these reports are fully optimized. We believe they are not far from optimum, but would require much more work before being ready to commit to construction. In many cases, the possible trade-offs are broad and insensitive, so the designer has leeway and can emphasize some considerations over others. In particular, for example, JAERI is interested in whether or not operation at lower rf frequencies, in the 200 MHz range for the radiofrequency quadrupole (rfq)/drift-tube linac (dtl) part of the linac, is desirable. In fact, after consideration of the differences between primary machine specifications where the main criterion is very low beam loss along the linac (to afford hands-on maintenance over the facility’s operating life), instead of a high-brightness output beam, Los Alamos agrees that the question of lower frequency operation is worthy of exploration. As will be seen in this report, we have made progress toward resolution of this question, but the answer is not yet clear. The present way to look at different frequencies would be to do a “point design” at each frequency. The basic linac would be laid out according to general practice and the beam performance evaluated from multiparticle computer simulation runs. This approach is tedious, and while such simulations indeed verify adequate performance, they do not elucidate optimization. Similarly, engineering to point specifications may overlook broader considerations. A basis for a different approach was laid a decade ago [Jameson, 19811 when the basic requirements for avoiding emittance growth through proper handling of various factors was
11.-1
shown and exploited using analytic methods for non-relativistic linacs. If this basis were to be further developed, and accompanying constraints clarified, a much clearer picture of the underlying relationships might be expected to emerge. Therefore, it was decided to attempt a more systematic undertaking, with the eventual goal of synthesizing and codifying more of the expertise involved in linear accelerator system design. While this goal could not be, and has not been, attained in this small study, the immediate objectives proposed and achieved are as follows: 1. Provide a n overall framework for codification of linear accelerator system design.
- The framework must be powerful enough to afford significant capability for information organization and interactive manipulation by mathematical, logical and graphical techniques, but also supportive of good documentation and readable. The Mathematica programming system was chosen. - The framework code, names LINACS, is Section I11 of this report. It is a Mat hematica document. As such, it represents an unusual report, but representative of what many reports will be like in the future. If actuated by the Mathematica program, the technical information resides in live code statements that can immediately be used by the reader. Other information in this report, yet in conventional form, will be converted to live code in future versions. 2. Organize the system description at several conceptual levels, with more detail at each lower level.
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Each level will contain an accelerator technical model and a cost model, and may contain a set of constraints and rules under which the model must operate.
- LINACS presently contains Levels 0, 1, and 2. Level 0 has a very simple “customer-view”;the accelerator is only a black-box providing a specified ion beam at the desired energy and current, along with an optimized cost based on a set of basic fixed and variable cost figures and the fundamental trade-off between the length of a linac and its rate of acceleration. Level 1 expands the technical model to include separate injector, rfq, dtl and coupledcavity-linac (ccl) sections and the rf system in more detail, and, in its present form,includes as examples three different cost models from separate sources. Upon further study, these cost models would be merged into one.
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At Level 1, we also intended to explore two considerations believed to be of major importance in deciding an optimal system configuration:
- the question of pulsed vs. fully continuous-wave (cw) operation to achieve the required average current - what are the technical and cost tradeoffs involved? See item 4. below.
- the effect of requiring specified “stay-clear”factors between the actual beam size and
the physical or dynamic aperture limits of the machine. Such factors, or ”aperture ratios” are of basic importance in achieving very low particle loss along the machine and hands-on maintenance capability. See item 6. below.
At Level 2, the level of detail expands greatly. This level contains the full and operational analytical beam dynamics modeling package (item 3. below) and a beginning toward codification of the many beam dynamics and engineering constraints. The constraints package is in very preliminary form. No cost modeling at Level 2 has been developed yet, although considerable information is in hand. A specific effort of this study, to begin codifying the mechanical engineering design of accelerator structures, is discussed in item 5. below. 3. Improve the fundamental analytic modeling of ion linac beam dynamics
involving space-charge phenomena:
- Include the coupled-phase-spacecharacteristics of the beam itself as well as machineacceptance characteristics, and the relationships between the beam and the accelerating structure. - Extend the model to a fully relativistic treatment, as required for high-energy applica,tions to 1-1.6 GeV and above.
- Include the capability to handle the various types of accelerator structures needed at different beam energies -- the rfq, dtl’s of various types, coupled-cavity high-beta linacs, arid other types in the future. - This package, in operational Muthematica code, is the Linac Dynamics section in LINACS at Level 2. 4. Explore two basic rf system questions:
- The rf system dominates the economics of linacs in the transmutation driver or materials test facility class. We intended in this study to explore two questions:
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Under what conditions would one choose a pulsed rf system or a fully cw system? Significant progress wati made on this issue as detailed in Section IV, which outlines the multitude of necessary considerations and includes up-to-date cost information. Generally, a cw system will be considerably cheaper than a pulsed system, and, the overall primary cost reduction factor available will be the economy-of-scale effect that a substantial market would have on prices.
11.-3
- Are larger or smaller rf amplifiers to be preferred? Larger amplifiers appear to give lower rf power costs per watt, and possibly reliability advantages. However, the question is complex, and must be integrated with the accelerator structure layout and the envisioned administrative procedures for machine operation and maintenance. A good start has been made toward gathering information in Section V, but further work is needed. 5. Define mechanical engineering constraints on accelerator
structure design.
- The mechanical engineering considerations in accelerator structures place constraints, sometimes severe, on the beam dynamics design and also factor heavily into costs. The large number of variables and heavy geometrical dependencies have made codification of design practice very difficult; however, this study intended to start toward such a goal, and the Los Alamos accelerator engineering group believes that a more systematic set of criteria and constraints can eventually be worked out. Section V outlines a preliminary definition of a procedure followed in cavity optimization where shunt impedance, aperture size, and frequency detuning sensitivity are balanced against thermal and stress limitations, and provides initial data for ccl cavities at different frequencies and beam energies. Considerably more work will be required to discover how this codification should be cunipleted for other types of structures and reduced to convenient design practice. 6.
Explore the design aspects of “stay-clear” o r “apert ure-ratio” factors.
- It was proposed to study the “stay-clear” or “aperture-ratio” factors as an optimization issue. This requires first of all that an underlying philosophy of design be chosen. The “natural equilibrium” state along a linac is now rather well understood as the simultaneous satisfaction of matching and energy balance conditions. In this study, for the first time, this premise is selected as the design philosophy, and elaboration of this approach is initiated. - Section VI outlines the work to date. The algebraic analytical form based on the
“smooth approximation”, used in the present beam dynamics model (LINACS Level 2) allows manipulation and solution by Mathematica. By casting the equations in a form requiring matching, and matching plus equipartitioning, new relationships among the variables become apparent. Some of these are explored. Preliminary conclusions are:
- Results from the equations agree well with multiparticle simulation results.
- At the present level of approximation, the transverse aperture factor appears to vary
monotonically as other key factors are varied, and does not reveal a clear optimization path. However, a more accurate model, employing trigonometric functions, would show an optimum phase advance for maximizing the transverse aperture factor. Adding the matrix modeling option is recommended for future work
- The longitudinal aperture factor is a complicated quantity, but does indicate an optimum value.
11.-4
- Other useful relationships have been derived, between the variables, and showing
why this design philosophy avoids regimes where coherent instabilities might occur.
Summarizing and projecting:
- The results presented are new, and are presented in an innovative format. The work benefitted considerably from earlier work on the LINACS code formulation by its author while a Foreign Visiting Researcher at JAERI during 1990 and 1991. - The work is still preliminary and incomplete, without clear summarization or succinct directions to the accelerator designer, and may contain e m o w . The Mathematicu code sections axe, however, in usable form and afford a new and very flexible tool for exploring system design and beam dynamics modeling of transverse/longitudinal space-charge coupled systems. - Some patterns begin to emerge in the framework: - the clear major impact of the rf system on system cost and the urgent requirement for significant R&D in this area. - the accuracy, usefulness and convenience of the coupled matching and equipaftitioning beam dynamics equations for the beam dynamics conceptual design.
- the role of constraints and rules, and the potential benefit of organizing them to be used directly in the mathematical framework for design solutions.
- Future, next-step activities would include:
- further work on defining the mechanical engineering considerations. - further clarification on the question of large vs. small rf amplifiers and ramifications on accelerator modularization, operations and maintenance.
- address of the future possibilities of superconducting technology. We believe this is an urgent issue that, with proper analysis, attention, and supportive R&D,might substantially lower costs for production-level transmutation/power generation systems [Lawrence,l991].
- continued development of the design philosophy; addition of the chain-matrix model option to the beam dynamics package, to improve accuracy, and to afford enhanced optimization criteria.
- considerable further development and analysis of the cost models.
II.-5
References
Bowman, C.D., et al, “Nuclear Energy Generation and Waste Transmutation Using An Accelerator-Driven Intense Thermal Neutron Source”, Los Alamos National Laboratory, to be published. “Accelerator Production of Tritium (APT)”, Report of the Energy Research Advisory Panel to the US DOE, February 1990, DOE/s-0074/ Jameson, R.A., “Equipartitioning in Linear Accelerators”, Proc. 1981 Linear Accelerator Conference, LA-9234-C, Los Alamos Natl. Lab., p. 125. Kaneko, Y . , “The Intense Proton Accelerator Program”,The 2nd Intl. Symp. on Advanced Nuclear Energy Research - Evolution by Accelerators, January 24-26, 1990, Mito, Japan, Proc. by JAERI.
Lawrence, G.P., “High-Power Proton Linac for Transmuting the Long-Lived Fission Products in Nuclear Waste”, IEEE Particle Accelerator Cod., May 6-9, 1991, San Francisco, CA. et .ala,“Conceptual Design of a High-Performance Deuterium-Lithium NeuVarsamis, G.L., tron Source for Fusion Materials and Technology Testing”, Nucl. Sci. & Eng., Vol. 106, No. 2, October 1990, p. 160.
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111. Framework for Codification
A. The LINACS Code
LINACS Linear accelerator system code for conceptual design work and to perform parametric trades on various types of linacs. D e t e d n e s technical requirements and cost for accelerator.
Written by R.A. Jameson including inputs acknowledged. Accelerator Technology Division AT-DO MSH817 Los Alamos National Laboratory Los Alamos, New Mexico, 87545 USA
505-665-2275 505-667-0919fax jameson@lampf
Copyright 1991 University of California
1XI.A. -1-
H Introduction The LINACS code is a physics, engineering, and cost model for linear accelerators. A variety of particles - electrons, protons, deuterons, and heavier ions that may be single or multiple charged - are needed for a variety of applications. The particle to be accelerated, its charge state, electrical current, and the energy desired, are assumed known and provided as input. An actual linac is comprised of a number of subsystems - injector, radio-frequency-quadrupole "rfq" preaccelerator, drift-tube-linac "dtl" section up to 20 - 100 MeV, and the coupled-cavity-linac "ccl" up to the final energy, the rf system, and other subsystems. The code is organized in "Levels". Each Level contains an accelerator technical model, that may have accelerator physics and engineering aspects and a set of rules and constraints, and a cost model. The amount of detail increases with the Level number. At the LINACS top level, Level 0, the accelerator is just the customer's black box, described only by the beam output energy "w" (MeV) and electrical c m n t "i" (A), and an impedance "z" (Mohms/m) to enable power calculations. It is assumed that the customer wants a minimum cost accelerator, so given the cost factors "s"(M$/m) for costs that depend on the length of the accelerator, and "r" (M$/MW) for costs that depend on the amount of rf power required, the accelerator length and accelerating gradient (MeV/m) are adjusted to give a cost minimum. Fixed costs "f'@ areIadded, $)and the whole is multiplied by an overhead factor "0".Scalings of these Level 0 factors with important parameters such as frequency, duty factor and other constraintsare built up in the lower levels of this code. At the next more detailed level, Level 1, the major inputs an? the following eight quantities: the final energy "ener" in MeV, the peak electrical current "curr" in amps,the rf frequency "frq" in MHz for the low-energy part of the accelerator, the duty factor "df" as fraction of one, the rf pulse length "pl" in usec, and, either (the ccl real-estate accelerating gradient "cclregrad", in MeV/m, or the ccl beam-loading "bmload", as a fraction of one,for the main high-energy, coupled-cavity part of the linac), the desired transverse ratio of aperture to rms beam size "tranapratio", and the longitudinal ratio of phase acceptance to beam phase size "longapratio"). At Level 2, considerable detail will eventually reside. The beam dynamics aspects of the accelerator technical model use the smooth approximation of Wangler for a variety of linac types, including the RFQ, Alvarez and Widerlle drift-tube linacs, and coupled cavity linacs. This approximation is well suited to execution by Muthematica;however, it lacks accuracy for larger phase advances and also does not reveal some of the subtler features of more accurate models with respect to optimization; therefore the option to use other models is planned for future versions. Engineering aspects are being developed as a set of constraints and rules under which the beam dynamics equations are solved. This part of the code is at a very early stage at this point. Cost detail modules at Level 2 am not included yet. Bridging between the Levels of the code is to be provided. The bridging between Level 0 and Level 1 has been completed, as shown in the section "Bridge between Level 0 and Level 1". Cost factors as built up in Level 1 can be plugged into the cost equation of Level 0, or the Level 1 factors can be used to compute the Level 0 optima.
Units are given in the statement comments, generally as above, with costs in $M. The code is not finished, nor thoroughly tested beyond the examples given, and bugs may exist. The mer is hereby warned.
1II.A. -2-
H o w to Run the Code
The LINACS code, written in Muthemuticu, runs on a Macintosh.
The LINACS code can be run either on a case by case basis with printed output, or as a series of cases with output in the form of plots, or reconfigured as desired by the advanced user. R.J.LeClaire, Los Alamos A-4, in his APT Systems Code, August 1989, first set up the Lawrence and Grumman cost models in Murhematica; some of his exact words live on, e.g. in these instructions. The programming style used hen is different.
Muthematica allows many programming styles. The environment chosen here is relatively "open" at present, with named groups of definitions and a few functions, and without separate "blocks" with local variables, or "packages" or "contexts". Different accelerator types (rfq, dtl, ccl, etc.) are treated as "objects" by declaring attributes relative to the type,e.g. a[dtl], using the assignment ; in the environment presently being used, this seems to have no apparent advantages, and some disadvantages (e.g. when used in fmctions). The main code statements are printed in Courier Bold. Examples often contain live code, but it is given in Times bold font.
To begin a session, the user opens this notebook and clicks "yes" when the system asks if initialization cells should be evaluated (this essentially compiles the code). If the user answered "no" at this time, then the user will have to click on "evaluate initialization" under the action menu in order to ready the code for use. Note that a default can be set through which initialization cells can be evaluated automatically and thus the code made ready for use without user input (see the action settings under the edit menu).
The code reads in numerous default input values for the various routines when it is first compiled. A complete list of these variables, an explanation and their units is given in the section on Inputs. In use, to change a value of one of these input variables, the user types the variable name followed by an equal sign and the desired value, and executes the code. For example, a user concerned about the assumption for availability might consult the section on Inputs to see that this variable is called "avail", type "avail" (and enter) to see that the default value is 0.75 and then decide to change availability to 0.6 by typing "avail46" (and enter). Then a routine can be xun using this newly defined input. The variable can also be changed to symbolic form by typing, for example, "avail This is useful for solving for that variable, or for exploring the analytic form of the equations. The user can always reset all inputs back to their default values by typing "defaults" (and enter). The user can also change the default value for any variable by editing the code itself. Typing the appropriate reset command ("resetLevO', "resetLevl", etc.) sets the inputs to their symbolic form. =.It
To run the code at Level 0 on a case-by-case basis, the user executes the main routine, by typing (without the quotes) " l i ~ c L e v O [i,~z, , s, r, f, 01" and executing (by hitting the "enter" key), where the seven values inside the square brackets are user input numbers or variables from the lower level routines. At Level 1, cases are run by typing "linacLevl[ener, WIT, frq, df, pl, cclregrad, bmload, tranapratio, longapratio]" and executing. At Level 1, the user can specify all of the first five and last two of these inputs as ~iumbers,or can leave some as variables. One of cclregrad or bmload can be a number or itself as a symbolic variable; the other is entered as -1 in the argument list and willbe solved for. In the beam dynamics section at Level 2, an input set is defined and groups of definitions are executed. Then equations are solved for the desired relationships.
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Examples are included to demonstrate how the code is used. Because an interactive code like this is so versatile, it is difficult to prepare instructions for every possibility, so the examples are intended to provide the instructional vehicle,
'she code and the examples shown are "locked" using the Locked command in the Cell Menu, to prevent accidental changes, The user can re-execute any step, and w ill see a new output block appear, which should agree with the locked block if the code is operating properly. 1II.A. -3-
InDutS Input variables are initialized at the beginning of a session because not all would ordinarily be changed in routine use. Also, the code will execute faster when as many variables as possible are assigned values as early as possible.
a Constants p i = N[Pi,6] ; c = 2.997925*10*8 ;(* speed of light, m/s *) erest = 9 3 1 . 5 0 1 6 ;(* rest mass, MeV *) z0 = 377 ;(* free space impedance *)
a Level 0 InDutS levOinputs := ( w = 1600. ;(* final energy, MeV *) i = 0.1 ;(* beam current, A *) z = 23.8 ;(* ccl shunt impedance, M0hm.m *) s = 0 . 1 5 0 ;(* /m cost factor, M$/m *) r = 3.0 ;(* /watt cost factor, M$/MW *) f = 500. ;(* fixed costs, M$ *) 0 = 2. ;(* overhead factor *)
1 ; 0
Level 1 InDuts
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accLevlinputs := ( ;(* final energy, MeV *) e = w crnt i ;(* beam current, A *) f l = 200 ;(* front end frequency, MHz *) einj = 0.100 ;(* injection energy, MeV *) erfq = 2 .O ;(* rfq output energy, MeV *) rfqxmsn = 0 . 9 0 ;(* rfq current transmission *) edtl = 20. ;(* dtl output energy, MeV *) dtlgrad = 4 . ;(* dtl accelerating gradient *) d t l z t 2 = 50. ;(* dtl shunt impedance, Mohms/m *) CClXeale8tgt8d = 1. ;(* ccl real estate gradient *) cclgradfacrt = 1 . 2 7 ;(* ccl structure to real-estate gradient, room temp *) cclzt2 = 23.8 ;(* ccl shunt impedance, ZTA2, Mohms/m *) bmldg =. ;(* ccl beamloading factor *) tapr =. ;(* ratio of transverse aperture to rms beam size *) lapr =. ;(* ratio of longitudinal phase acceptance to beam rms phase width *)
1 ;
1II.A. -4-
e
A(2.DC.and RF Power
acdcrf Levlinputs := ( du = 1. ;(* dutyfactor *) pu = 10000. ;(* pulse length, usec; assumed cw if > 5000 *) avail = 0.75 ;(* accelerator availability factor *) frontenddctorf = 0.65 ;(* dc to rf conversion efficiency, rfq & dtl *) ccldctorf = 0 . 7 ;(* dc to rf conversion efficiency in ccl *) actodc = 0.855 ;(* ac to dc conversion efficiency *) extrapower = 20. ;(* balance of ac power for accelerator, MWe *) klystronpower = 4 . ;(* power per klystron, MW gpl routine *) rfunitpower = 1. ;(* power per klystron, MW grumman routine *) klystronlife = 50000. ;(* klystron life, hrs *)
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1 ;
e
CCIst factors: General. LANL Overheads. EastWest costLevlinputs := ( scalerf = 0 rfunitcost = 3.0 cclcost = 0.15 frontendcost = 50. powerprice = 0.035 klyunitcost = 0.5 accelstaff * 200. manunitcost = 0.14 otheroperating = 0 . edandi = 0.25 management = 0 . 4 contingency = 0.35 cclnre = 2.250 dtlnre = 1.730 rfqnre = 0.570 in jnre = 0.300 injmtl = 0.590 injinst = 0 . 2 0 0 rfpnre = 1.500 llrfnra = 0.500 lamlovrhd lab = 1 div
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=
:=
scale klystron unit size in RF costing; kyes, ()=no *) ;(* rf capital unit cost, $/watt *) ;(* ccl structure cost per unit length, $M/m *) ;(* cost for equipment other than ccl, $M *) ;(* power unit cost, $/kW-hr *) ;(* unit cost of klystron, $M *) ;(* staff needed for accelerator *) ;(* annual cost per staff member, $M *) ;(* other annual costs, $M *) ;(* engineering, development and inspection factor *) ;(* management factor *) ;(* contingency factor *) ;(* ccl non-recurring-engineeringcost, $M +) ;(* dtl non-recurring-engineeringcost, $M *) ;(* rfq non-recurring-engineering cost, $M *) ;(* inj non-recurring-engineering cost, $M *) ;(* inj materials cost, $M *) ;(* inj installation cost, $M *) ;(* rf power system non-recurring engineering cost. $M *) ;(* Low level rf nre, $M *) ;(*
(
1
gp'l prgm 1 doe = 0 labovrhd = 0.956 divovrhd = 0.13 gpovrhd = 0.24 prgovrhd = 0.039 doeovrhd = 0.032 1 ;
;(* sets lab overhead; 1-on, boff *) ;(* sets division overhead on or off *) ;(* sets group overhead on or off *) ;(* sets program office overhead on or off *) ;(* sets DOE "work for others" tax on or off *) ;(* lab overhead rate *) ;(* division overhead rate *) ;(* group overhead rate *) ;(* program office overhead rate *) ;(* DOE "work for others" tax rate *)
1II.A. -5-
eastwestcosts := ( (* kindly provided by M. Kihara, KEK *) jengrlabyen = 1.0000 ;(* J engineer at lab, YlOK/hr *) jengrlabg = 80 ;(* J engineer at lab, $/hr *) jengrindS = 50 ;(* J engineer, industrial, $/hr *) 1anlengrS = 100 ;(* lanl engineer, $/hr *) tech$ = 35 ;(* technician cost, $/hr *) yearfac = 1.5 ;(* productive year = 1500 hours; /1@6 = $M/y*) usmatls = 5. ;(* materials cost in US, $/lb *) jmatls = 3 usmatls ;(* materials in Japan est. 3 x US materials cost *) usgaselec = 1 ;(* unit cost of gas, electricity in US *) jgaselec = 3 ;(* gas, elec in Japan est. 3 x US *) uscomp = 1 ;(* unit cost of small components in US *) jcomp = 3 ;(* small components in Japan est. 3 x US *) usrent = 1 ;(* unit cost of real estate rent in US *) ;(* rent in Japan est 8 x US *) jrent = 8 discount = 0.35 ;(* discount to inst or univ same in US or Japan *) keage7 = 2 ;(* Keage 7 MeV linac complete ion source, rfq, dtl, rf, controls; Y250M $2M, at univ discount *) accsys2 = 0.8 ;(* Accsys 2 MeV rfq system complete $0.8M *) elinacpM = .018 ;(* e-linac structure production cost, $M/m, Mitsubishi *) elinacsdhi = .020 ;(* sales price, $M/m, discounted to univ; Mitsubishi *) elinacpV = .010 ;(* 'I production cost, $M/m, Varian *) elinacsv = .020 ;(* sales price, $M/m, Varian *)
-
-
-
'I
I'
1 ;
accLev2inputs := ( dtlphase = -30. dtleO = 4. dtlt = 0.8 cclphase = -30. qfactor = 0.80 kpbraveryfactor = 1.8 pksurftoaccgrad = 4.
;(* dtl synchronous phase angle *) ;(* dtl voltage gradient, MV/m *) ;(* dtl transit time factor *) ;(* ccl rf synch phase angle, degrees *) ;(* factor for actual Q below SUPERFISH Q *) ;(* Kilpatrick bravery factor *) ;(* ratio of peak surface field in structure accelerating cell to on-axis accelerating gradient Eo *)
1II.A. -6-
0
Default inout function defaults := ( 1evOinputs acclevlinputs acdcrflevlinputs cost Levlinpuks lanlovrhd eastwestcosts accLev2inputs
;(*
level 0 general description of accelerator *)
;(* level 1 inputs for structures *) ;(* level 1 ac,dc,rf power inputs *) ;(* level 1 cost factor inputs *) ;(* LANL overhead cost factors *) ;(* USe->Japan cost factors *) ;(* level 2 accelerator inputs *)
1 ;
defaults 0 Reset
;
functions
resetLevO
:=
(w
i =.; z =.; 1inacLevO f l ; 1
=.;
s
=.;
r
=.;
-.;
f
=.;
0
=.;
resetlev1 :- ( e 9.; crnt =. : fl einj 3.; erfq =.; rfqxmsn 3.; edtl =.; dtlgrad =.; dtlzt2 =.; cclrealestgrad =.; cclzt2 =.; bmldg =.; tranapratio =.; longapratio =.; du =.; pu =.; avail =.; frontenddctorf =.; ccldctorf a.; actodc =.; extrapower =.; klystronpower =. ; rfunitpower =. ; klystronlife 3.; 1
(* cost factors must be done locally or by editing the Inputs section.*)
1II.A. -7-
0
PrintinP routines -P
0
printcornpara := ( Print [StringPormt coatlavlraid"] 1 ; Print [StringForm["injector aoat '' ,in jmctoraoat ,aoatin jl 1 : Print [StringForm[ "rfq cost ' ' rfqcoat,coatrfql I : Print [StringTom["funnml C08t ,funnrlooat]] : Print [ StringS'orm [ " dtl C0.f . ,I ,dtlcoat, aostdtll 1 : Print [StringForm["frontand rf C08t
CO8tl.Vlgrll
'I
.. I .
..
It,
..
.
-.
..
''
,frontmdrfao8t,rFfrontmn~ao8tfao8tfrontmndr~p8]l:
.. "~l,frontmndaost,aubtotfl,coatflpartJ]: .. Print [ StringForm [ Ilea1 atruat aoat "ll,~claaca~at,calatruacoat,aoataalll: .. Print [StringForm[*laclrf aoat . . ,cclrfcoot,rfcclaoat~aoatoclrfps]]: .. Print [StringIPorm["ccl aoat .. .. Qrint [StringPorm["rf ays coat .. ,irontmndrf+oclrfaost,tioa.t,aostrfpo]]; Print [StringPonu["tot81 acaml '. . . , l i n a a c o a t , a a c m l c o a t , c o . t t o t a l ] l : .. Print [StringPorm[l*olma aoat 11
..
Print [StringForm[llfrontandcoat
.. ..
.. .. ..
It
I1
,OC~tOt008t,8Ubtotf2,C~8tf2p.rt]l~
I1
C0.t
..
11
~l,almccoat,mlmctriaitycoat]l;
]: Print [StringForan[" Print [StringTorm["aoatLmvO (aoatmdml I*]
* *
"~~,ao8tLmvOgpl,ao8tLmv~gru,co8t~av~rmid]]: Rrint [StringPoran[" *'I ] :
..
Print [SttingPorm["#inimm capital aoat mramplm"] 1 : Rrint [StringForm["a factor ,.-I, 8gtu, ataid]] ; Print [ StringForm [ I ' r factor * ,rgpl ,rgru ,rrmid] 1 ; Print [StringIPormE "fixad aorta * ,fgpl,fgru, frmidl I : Print [StrinqForm["ovmrhr8d f8ator ogpl,ogtu, ormid] 1 ; Print [StringForm[lloptlaagth
.-
..
.. ..
11
11
-
.. . I
..
\. . .. . , l m i n c o a t g p l , l m i n c o . t g r u , l m i n a o s t..r m i d ] ] : Print [Stringlform[lloptgradiurt "~~,gminaostgpl,gninaoatgru,gmincoatrmid]]~ .. Print [StringForm["opt bm ldg ,b~naoatg~l,bm~naoatgru,bminaoatraid] .. 1; Print [StringForm["mia coat 11
,I I
*
11
* *
I,
8
II
,cmincostgpl,cmincostgru,amincostrmid]1 :
p r i n t c o l o r := ( ); ( * can u s e c o l o r t o o ,
f o r headings,
1II.A. -8-
)
etc * I
.. .. .. ..
\
\
printmore
:=
(
1;
1II.A. -9-
Level 0 Model At Level 0, the "customer's level", the accelerator is just a black box, providing particles at the desired energy and current. We assume that the customer will want to minimize the life-cycle cost; Le. the sum of initial capital cost and operating cost. The accelerator is usually comprised of a low-energy "frontend" (to 20- 100 MeV depending on the application), and the high-energy part called the coupled-cavity linac, or "ccl" (e.g. to 800-1600 MeV for a waste transmutation or energy production facility). The cost of the ccl is usually the dominant factor, and the beam physics requirements are fottunately less stringent in the ccl than in the frontend, allowing tradeoffs to be made to achieve a cost minimization The only other accelerator technical parameter that is needed at Level 0 is the ccl shunt impedance, in order to get calculate power quirements from the beam voltage and current. To find the minimum cost, we trade off accelerator length vs. accelerating gradient, MeV/m. A higher gradient affords a shorter length, but at the cost of more rf power. If we have cost factors for the costs that are spent on a h~basis, and on a /watt basis, the optimum gradient and length giving the minimum total cost can be found. Fixed costs are then added, and the whole is multiplied by an overfiead factor. These factors are built up in detail in lower levels of the model. This model may have originated with Slater (Lapostolle & Septier, p.28, (Slater, J.C., 1946, Design of Linear Accelerators, Rev. Mod. Phys. 20,473.); see also Came, p. 597-599, and Citron & Schopper, pp. 1166 & 1177.) T.J. Boyd was one of the first to use these relationships at Los Alamos.
0
Minimum Cost model This section defines the function linacLevO[w,i,z,s,r,f,o]. Let the linac energy gain = W ,the beam c m n t = I, and the shunt impedance = Z. Then find the length L, realestate accelerating gradient G, and beam-loading factor B, when the cost C is minimized, using the cost factor S for the variable capital costs that are spent per meter (M$/m), and the cos factor R for the variable costs that are spent per watt of rf power (M$/MW). R will usually contains two terns for capital and operating costs, and each of these may be built up from peak and average costs/watt.
-
G=W/L Pcopper = W (GE) = WA2/LZ = Pbeam (1 - B)/B Pkam = WI B = PbeWPcopper + Pbem) = pbeam/B F = frontend cost + other fixed costs; (fixed with respect to /m and /Watt) 0 = overhead factor
C = (O)(SL + R( WWLZ dC/dL = 0 yields:
+ wr) + F)
Lmincost = w Sqrt[ mz1 Gmincost = WLmincost = Sqrt[SzJR] Bmincost = ( I Sqrt[RZ/S] ) / (1 + ( I Sqrt[RZ/S] ) Cmincost = (0)(2W Sqrt[RS/Z] + R Pbeam + F) The optimum length and gradient do not depend on the beam current, but only on the structure power losses, as would be expected.
II1.A. -10-
Note that at the minimum, SLmincost = R( WA2/LmincostZ)= W Sqrt[RS/Zl; i.e. the capital costs that are applied per unit length are equal to the capital plus operating cost of the rf copper power losses, Reducing R and S,and increasing 2,are seen to be the important points, with R dominating, especially for heavily beam-loaded linacs. The scaling of these variables with frequency and other variables is included in ttus code. S and Z have been extensivelyexplored, and the potential for significant changes is them is not m a t . Little development effort has been spent on reducing R in the past two decades, and the potential here may be significant if there were enough of a market to spur such development.
:= 1 i t i a c L e v O tw-, i-, 2-1 s-, ,r f-, 0-1 B l o c k [{temp}, cclwgain = w ;(* proton energy gain in the ccl in MeV *) cclrfpwr = cclwgain*i ;(* ccl rf power requirement, MW *) lmincost = w*Sqrt [r/(s*2)3 ;(* ccl length at minimum cost *) gmincost = S q r t [ (s*z)/r] ;(* ccl redestate gradient at min cost *) bmincost = (i*Sqrt [E*z/s]) / (1 + i*Sqrt [r*z/s]) ; (* ccl beam loading at min cost *) cmincost = 0*(2*w*Sqrt[r*s/z] + r*cclrfpwr + f) ; (* minimum accelerator cost *) Return[] ; 1
(* Example
*>
linaclevo[ 1600,0.1,23.8,.150,3.,500.,2.]
Print[ cclwgain,cclrfpwrJmincost,gmincost, bmi ncost,cmincost} ] 0- J
11600, 160., 1466.721 1.09087, 0.685707, 2 8 4 0 . 0 3 1 m
(* Plot the minimum cost as a function of beam current, with the cost/watt of rf power as the parameter, from $1-$5/w. At low beam currents, the cost is dominated by the copper losses, showing why a linac is naturally suited for high intensity beams. *)
r =.; i =.; Show[Plot[Release[Table[( linaclevo[ 1600.,i,23.8,. 100,r,500.,2.];cmincost), DisplayFunction -> Identity, (r,l,S}]I,( i,0,.25), PlotRange -> (0,6000),
AxesLabel-> {" beamcurrent",mincost}1, Graphics[Text["r = l",{ .165,1650},{ -1,O) I], DisplayFunction -> $DisplayFunction] ;
II1.A. -11-
mincost
6Ooo-
5000-
I
0.05
0.1
0.15
0.2
0.25
beamcurrent
(* The optimum beam loading is a strong function of the beam current, and a weak function of the cosb'watt of rfpower or the structure costhneter. *)
i =.; r =.; s =.; Show[Plot[Release [Table[( linacLevO[ 1600.J.23.8,. 100,r,500.,2.];bmincost), (r,l,5)]],(i,O,.25),DisplayFunction -> Identity, AxesLabel -> beamcurrent",mincostbmldg )I, Graphics[Text["r = 1",(.14,.65),( -LO)]], DisplayFunction -> $DisplayFunction]; ('I
mincostbmldg
beamcurrent
Show[Plot[Release[Table[( linaclevo[ 1600.,i,23.8,s,3,500. ,2.];bmincost), (s,.05,.20,.05)]],(i,0,.25), DisplayFunction -> Identity, AxesLabel -> beamcuITent",mincostbmldg)], Graphics[Text["s = .20',(.13,.68),(-1,0) 11, DisplayFunction-> $DisplayFunction]; ('I
Plot3D[( linacLevO[16OO.,. 1,23.8,s,r,500.,2.];bmincost), (s,0.05,0.20),(r,1,5}, Viewpoint->( 1,190, -2.000, -0.000), BoxRatios -> ( 1,1,0.8), AxesLabel -> (s,r,mincostbmldg)];
II1.A. -12-
0.8 0.7 mincostbmldg 0.6 0.
Plot3D[( linaclevo[ 1600.,. 1,23.8,s,r,500.,2.];gmincost), { s,0.05,0.20),( r,l,S), Viewpoint-> ( 1.190, -2.000, -0.000}, BoxRatios -> ( 1,1,0.8}, AxesLabel -> (s,r,mincostgradientj];
2 1.5
mincostgradient
1
0.5
0
III.A, -13-
=Level 1 Model This section defines the function linacLev 1[e,i,fl ,du,pu,cclrealestgrad,bmldg,tranapratio,longapratio]. At this level, the linac consists of an "accelerator" comprised of roughly modeled injector, rfq, funnel, dtl, ccl and rf power system, with cost information. The major inputs are the following six or seven quantities: the final energy "ener" in MeV, the peak current "curr" in amps, the rf frequency "fq" in MHz for the low-energy part of the accelerator, the duty fact( "df' as fraction of one, the rf pulse length "pl" in usec, and, either (the ccl real-estate accelerating gradient "cclregrad", in MeV/m, or the ccl beam-loading "bmload", as a fraction of one, for the main high-energy, coupled-cavity part of the linac), the desired transverse ratio of aperture to rms beam size "tranapratio" and tht longitudinal ratio of phase acceptance to beam phase size "longapratio". If the proton beam current is > 130 mA, the accelerator front end consists of two ion sources linked to two WQ's which are funneled into a single DTL followed by the CCL;if the current is e 130 mA, a single charm is used. The outputs are the accelerator lengths, ac/dc/rfpower requirements, overall efficiency, and costs, Three cost estimation models are developed; one per G.P.Lawrence/r.J. Boyd, "costLev1gpl"; another per Grumman cost report for the cost scalings, "costLevlgru"; and a third, "costLevlreid", from D. Reid's Linear Accelerator Cost Estimator LACE program. Additional details on how the cost scalings in the gpl and grumman models were obtained are on a spreadsheet available from R.J.LeClaire.
0
Accelerator T e c h'cal Model :=
accLevl
(
(* current and frequency rules *) I f [crnt = (yl/l)(sum over t = 1 to I of tA-b, where Identity, PlotRange -> {O,l}, AxesLabel -> {'I cclreale~tgrad","bmldg")l, Craphics[Text["beam current = 0.3 A",{3.5,.66},{-1,0}11, DisplayFunction -> $DisplayFunctian] ;
IILA. -25-
bmldg
"I
I
3
2
5
4
cclrealestgrad
(* Plot linaccost - gpl vs cclrealestgrad for currents of 0.1,0.2,and 0.3 A. *) cclrealestgrad =.; Show[Plot[Release[ Table[( linacLevl[1600.,i,700.,l,lOOOO,cclrealestgrad,-l,-l,-ll;linaccost), {i,.l,.3,.l)]],{cclrealestgrad,.l,5), DisplayFunction -> Identity, PlotRange -> {0,8000), AxesLabel -> {'* cclrealestgrad","linaccost gpl"}], Graphics[Text["beam current = 0.1 A",{2.5,2000),{-1,0)11, DisplayFunctioa -> $DisplayFunction] ;
-
3000 l
1
m
2
3
m
4
' cclrealestgrad 5
(* Plot accelcost -gru vs cclrealestgrad for cunents of 0.1,0.2, and 0.3 A. This cost model is seen to be different, and the area near the minimum is shown on an expanded scale on the next graph. *) Show[ Plot[Release[ Table[( IinacLevl[ 1600.,1,700.,1,10000,cclrealestgrad9= 1,-1,-11 ;accelcost),
{i,.1,.3,.1)]],{cclreaIestgrad,.l,5},
-
DisplayFunction -> Identity, PlotRange -> {0,8000}, AxesLabel -> {I' cclrealestgrad","accelcost gru"}], Graphics[Text["beam current = 0.3 A",{2.S,2200~,~-1,0)11, DisplayFunction -> $DisplayFunctionl ;
IU.A. -26-
80007000.
6OOo-
I
50004000-
30002000.1 1000-
beam current = 0.3 A
I
:
1
2
3
cclrealestgrad
5
4
Show[Plot[Release[
Table[( linacLev1[1600.,i,700.,l,lOOOO,ccIrealestgrad,-l,-l,-ll;accelcost), {i,.l,.3,.l)]~,{cclrealestgrad,l,5),DisplayFunction
-
AxesLabel -> {" cclrealestgrad","accelcost gru")], Graphics[Text["beam current = 0.3 A",{2.,184O),{-l,O)]], DisplayFunction -> $DisplayFnnction] ;
-> Identity,
-
accelcost gru
cclrealestgrad
-
(* Plot costtotal reid vs cclrealestgradat beam currents of 0.1,0.2, and 0.3 A. Because of some of the relations
in Re!id's model, a different method must be used to get a table for plotting. *) tab1 = Table[ ( curr = j;
IinacLev1[1600,,curr,7OO.,l,lOOOO,ccIrealestgrad,-l,-l,=lJ; {curr,cclrealestgrad,costtotal) ), ~,.1,.3,.l},{cclrealestgrad,.l,5.1,1} I
(* takes more than 5 minutes. *)
(((0,1,0.1,2672.), (0.1, 1.1, 1181.), (0,1,2.1, 1356.), (0.1,3.1, 1596.). (0.1,4.1, 1856.), (0.1,5.1,2121.))\ ((0.2,0.1, 3226.), (0.2, 1.1, 1729.), (0.2.2.1, 1900.), (0.:2, 3.1, 2137.), [0.2,4.1,2394.), (0.2, 51,2657.)). [ [0,3,0.1, 3765.), (0.3, 1.1,2266.), (0.3,2.1,2434.), (0.:3,3.1,2669.), (0.3,4.1,2924.), (0.3, 5.1,3186.)))
III.A. -27-
For[h=3, hc4, h++, (* a plot for each table column *) ForQ=l; pltlist = {}, j44, j++,(* plot each parameter *) For[k=l; blist = {}, ke7, k++, (* at each value of x-axis *) blist = Append[blist,~tabl[~,k,2ll,tabl~~,k,hll~ll ; pltQ] = Listplot[ blist, PlotJoined -> True, PlotRange -> {0,8000}, AxesLabel -> {" cclrealestgrad"," totalcost reid"}, DisplayFunction -> Identity 1; pltlist = Append[ pltlist, pltu] 1 1 ; Show[pltlist, Graphics[Text["beam current = 0.3 A", {2,3400},{-1,0)11, DisplayFunction -> $DisplayFunction] ]
-
5000 4000
beam current = 0.3A
1000 I
1
3
2
4
:
5
cclrealestgrad
(* Make a 3D plot of linaccost vs beam current and cclrealestgrad *) linaccost3D = Plot3D[( linacLev1[1600.,curr,7OO.,l,lOOOO,cclrealestgrad,-l,-l,-l]; linaccost), {curr,.005,.3}, (cclrealestgrad,.l,5), 1.200, 2.170}, ViewPoint->{-4.000, BoxRatios -> {1i1,0.8}i ; AxesLabel -> {"beam currentn,"cclrealestgradn,"linaccost")] (* took quite a long time to compute. *)
..
III.A. -28-
-5
cclrealestgrad
(* Make a 3D plot of bmldg vs beam current and cclrealestgrad. *) bmldg3D = PlotfD[( linacLev1[1600.,curr,7OO.,l,lOOOO,cclrealestgrad,-l,~l,-ll; bmldg), {curr,.005,3}, {cclrealestgrad,.l,5}, ViewPoint->{-4.000, 1.200, 2.170}, BoxRatios -a {l,l,O.S}, AxesLabel -> {"beam current","cclrealestgrad","bmldg"}] ; (* took quite a long time to compute.,. *)
ildg
bealm cur
"5
cclrealestgrad
II1.A. -29-
(* Make a 3D plot of linaccost vs beam current and beamloading. *) costvscurrbmldg3D = Plot3D[( linacLev1[1600.,curr,7OO.,l,lOOOO,-l,bmldg,-l,-l]; linaccost), {curr,.005,.3}, {bmldg,0.1,0.9), ViewPoint->{-4.000, 1.200, 2.170}, Lighting -> True, BoxRatios -> {1,1,0.8}, AxesLabel -* {"beam current"," bmldg","Iinaccost")] ; (* took quite a long time to compute *)
...
:ost
beam CUI
bmldg
Show[%, ViewPoint->{ 1.350,1.630,1.140),Lighting -> True] ;
I
linaccost
0.3
- without
o Arnini-v
costs:
UnacLevltoOgpl :( accLevl ; costLevlgp1 ; w = e edtl ; z = cclzt2 ; JgPl = CClCO8t ; If [scalerf 1, rgpl = rfunitcost/Sqrt[klystronpower/l.0] , rgpl = rfunitcost 3 ; fgpl = frontandrf*rfunitcost frontendcost i ogpl = (1. adandi management contingency) i C08tLeVogpl = ogpl*(sgpl*ccllength rgpl ( w A 2 / (ccllength*z) + w * i ) + fgpl) ; ( * here peak watts *) linacLevO [w, i, z, sgpl, rgpl, fgpl, ogpl] ; lmincostgpl = lmincost ; gmincostgpl = gmincost ; bmincostgpl = bmincoat ; cmincostgpl = cmincost ; Print[(sgpl,rgpl,fgpl,ogpl,costLevOgpl,lmincostgpl, gmincostgpl,bmincostgpl, cmincostgpl)I 1
-
-
+
+
+
IILA. -31-
+ +
IinacLevltoOgpl
(* Example *)
(0.15, 3.. 62.4644, 2., 1945.25, 1448.38, 1.09087, 0.685707, 1941.96) oa
..
v-w
i m oueratinp cos&
1inacLevltoOgru := ( accLevl ; costLevlgru ; w = e edtl ; z = cclzt2 : sgru = (0.79577 + 0.0474) ; ~ftscalerf == 1, rgrurf = 1.14259/Sqrt[rfunitpower/l.] rgrur2 = 1.14259 3 ; rgru = rgrurf + 0.64866*acccopperave/accrfave ; fgru = subtotfl + (1 + ianc)*(53.1 + 156.5 + 23.9 16) + 0.9*techdevel ; ogru = 0.9*(1. + 0 . 0 4 3 ) ; ( * too high by 0.043*techdevel * ) costLevOgru = ogru*(sgru*ccllength + rgru* ( w A 2 / (ccllength*z) w*i) fgru 1 ; linacLev0 [w, i,z ,sgru, rgru ,fgru, ogru] ; lmincostgru = lmincost ; gmincostgru = gmincost i bmincostgru = bmincost ; cmincostgru = cmincost ; Print[(sgru,rgru,fgru,ogru,costLevOgru,l~incostgru, gmincostgru,bmincostgru,cmincostgru}] 1
-
+
+
cclrealestgrad = 1.; i = 0.1; IinacLevltoOgru
+
(* example *)
(0.84317, 1.24434, 375.496, 0.9387, 1865.12, 393.442, 4.01584, 0.372117, 1159.84)
II1.A. -32-
,
linacLevlto0reid := ( accLevl : costLevlreid ; w = e edtl : 2 = cclzt2 : sreid = c:ostccllearnunit t (.924 + 1.749 t 1.6)*10A-3 : rreidpeak = costrfpavun*nrfpmod/cclrf : rreidave = l.O/ccldctorf ; rreid = rreidpeak t rraidave (costllrf llrfnre)/cclrf costcclmodbldg/(cclrf*l.6) ; ( * now o n l y c o r r e c t when ccl is c w aC d u t y f a c t o r = 1 . 0 *)
-
+
-
+
freid = costflpart t cclnre t (rfpnre t llrfnre)*(accrf frontendrf)/accrf t (.924 t 1.749 -t 1.6)*1OA-3*2O. ; oreid = 1.6 : costLevOreid = oreid*(sreid*ccllength t rreid* (wA2/(ccllength*z) t w*i) t freid) ; (* hem peak watts *) linaclevo [ w , i, z , areid, treid, frsid, oreid] ; lmincostreid = lmincost ; gmincostreid = gmincost ; bmincostreid = bmincost ; cmincost ; cmincostreid Print[(8re~d,rreid,~raid,oreid,oreid,costLevOreid,lminco8treid, gmincostreid,bmincostreid,cmincostreid~] 1
-
-
1inacLevltoOreid
(* Example *)
(0.0988142, 1.89488, 33.6408, 1,6, 983.924, 1418.24, 1.11406, 0.681157, 981.3061
Q
Com~areJ eve1 1-oc
for minimum @?ita1 -
cpst
1eve1 1-m
-- Expm~1e
Sa:cost model definitions; some m m g e m e n t s were made in the costing model summations to get similar groupings and burden application, etc, Since scaling with rf amplifier unit size is not done consistently in the three models, set scalerf = 0 for this comparison. linacLevl[e,i,fl,du,pu,cclrealestgrad,bmldg,tranapratio,~ongapratio] ; linacLevlto0gpl; linacLevlto0gru; linacLevlto0reid;
IILA. -33-
t0.15, 3 . 1 62.4644, 2 . r 1945.25, 1448.38, 1.09087, 0.685707, 1 9 4 1 . 9 6 ) (0.84317, 1.37014, 352.07, 0.9387, 1869.63, 412.85, 3.82705, 0.383435, 1187.23) 10.0988142, 1.95045, 29.4077, 1 . 6 , 997.102, 1438.89, 1.09807, 0.684287, 995.11 1
printcompare costlevlgpl
costlevlgru 7.56083 11.8174 0 41.1479 7.36583 77.6197 1043.11 430.731 1806.86 438.097 1768.96 102.739
c o s t l e v 1r e i d
costLevO (costmodel 1 9 4 5 . 2 5
1869.63
997.102
Minimum c a p i t a l c o s t example s factor 0.15 r factor 3. fixed costs 62.4644 overhead f a c t o r 2. opt length 1448.38 opt g r a d i e n t 1.09087 o p t bm ldg 0.685707 min c o s t 1941.96
0.84317 1.37014 352.07 0.9387 412.85 3.82705 0.383435 1187.23
0.0988142 1.95045 29.4077 1.6 1438.89 1.09807 0.684287 995.11
injector cost rfq c o s t funnel cost d t l cost f r o n t e n d rf c o s t frontend cost ccl s t r u c t cost c c l rf c o s t c c l cost r f sys c o s t t o t a l accel cost elec c o s t
12.4644 50. 237. 726.933 963.933 731.088 2052.79 102.739
(* Need basis for Grumman's formulae. +)
III.A. -34-
1.
1.62198 2.9043 7.95297 25.1059 151.625 463.8 1150.38 471.753 1175.49
Level 2 Model 0
m i a b l e Assirrnments to ObiectS
0
Linac Beam D
im
(See Section 1II.B. and C. Presently run separately.
0
&:elerator
Phvsics & Engineering. Constraintq
NOTE: Except f o r t h e beam dynamics s e c t i o n ( s e p a r a t e s e c t i o n o f t h i s report), Level 2 i s very i n c o m p l e t e . Some of the m a t e r i a l w i l l e v e n t u a l l y be d e l e t e d . I t is i n c l u d e d h e r e to g i v e the, r e a d e r an i d e a of what i t is i n t e n d e d t o become, and t o encourage the r e a d e r t o p r o v i d e r e l e v a n t m a t e r i a l f o r i n p u t . *) (*
11X.B.
(* R.eliability estimates. e.g.
Ifirfq -> adjustable vanes, rfqavail= 0.501; Ifirfq -> BEAR vanes, rfqavail = 0.951; *> (* Use fuzzy logic herein?? *)
@sa
ef frftobeamcrnl = 0 . 3 3 ; (* CRNL rf data for typical 100 MeV, 10 M W cw e-linac. 0.30 quoted later. For L-band 1249 MHz linac, with 16 1.2 MW cw sources feeding 5 m long on-axiscoupled structures with beam-loading 0.80. 100 kV gun source, chopped and bunched to keep loss $DisplayFunction ] ;
II1.A. 40-
I,
See Section VI of this Study Report, "Linac and Transport Studies Using the Envelope and Equipartitioning Equations", for the emerging treatment of this topic. The following paragraphs are other ideas on this subject by T.P. Wangler. (* From "ATP - Accelerator Production of Tritium", Presentation to the Energy Research Advisory Board, October 25, 1989, Los Alamos - Brookhaven National Laboratories (this section written by T.P. Wangler):
Our main objective in the linac design is to provide high transmission with low beam losses. To reduce
bean losses, it is important to control the growth of emittance (phase-spacevolume occupied by the beam) and the associated beam halo. Although the causes of beam halo fromation in phase-space are not
completely understood, much has been learned from our numerical simulation studies, in which it is observed that nonlinear space-chargeforces act to produce halo. Nonlinear focusing forces create filarnentation in phase-space and increase the rms normalized emittance, but are not observed in the simulation studies to produce halo. The halo appears to be the result of the nonlinear processes within the beam caused by the time dependent collective space-charge forces. Particles that populate the halo have acquired larger center-of-massenergies.
Transitions in the accelerator, where parameters change, appear to increase the amount of halo in phase-space. Transitions such as changes in the saength of the external focusing force, changes in the periodicity of the focusing lattice, introductionof deflecting elements, or changes in the rf frequency, cause a change in the external focusing, and as a result the beam must adapt. Given a sufficient number of beam plasma periods after such a transition is introduced, the beam has evolved to a quasi-stationarystate. During this evolution process, halo appears to be produced. The rms emittance will increase if the focusing strength decreases; then space-charge field energy is converted to thermal energy as the beam distribution evolves toward a more uniform profile in real space. An increase in focusing strength likewise results in an ms emittance decrease and a more Gaussian-like profile in real space. In both cases it appears that halo can be produced. The time scale for halo production is not yet well established but appears to be in the range of a few to a few tens of beam plasma periods. This time scale may have relevance in the design of emittance-filter systems. The evidence obtained from simulations suggests that strong focusing is an effective strategy for minimizing halo production. This is already known to be the most effective approach for minimizing rms emittance growth, even though it does increase the beam density. It does appear that acceleratortransitions should be minimized, and invoduced only when necessary; ion source extraction, bunching and (in some cases) funneling, are examples of some that are necessary. If these transitions are kept at the low energy end of the accelerator, the activation effects of the associated local beam losses are minimized, and collimator systems that act as emittance filters to remove the halo will be more effective and easier to implement. Good bearm matching across these transitions is very important to minimize the disruption to the beam.
With regard to rms emittance, we believe this is a quantity whose growth should be controlled. Not only is nns-emittance growth often conelated with beam halo production, but the rms emittance affects the overall spatial size of a given beam distribution; the larger the rms emittance,the larger the beam size and the greater the extension in real space of the halo that already exists. Therefore, an important figure of merit in the design of the high energy sections of the acceleratoris the ratio of effective aperture (bothradial and longitudinal) to the rms beam size.
II1.A. 41-
Using a uniform 3-D ellipsoidal model for the beam bunch in a linac, we have been able to derive analytical expressions for the ratio of aperture to rms beam size. In the transverse plane, the results are:
*>
(* need input for a= tranap ghi,phiS ,pi,beta,gamma,c,qlm,mc2- > m 2 ,etrms,elnns,lquadghiO=bngap *)
tranapratio = Sqrt [
(
(gamma*wt0*tranapA2)/ (ermsn*c)) (l/(ut + Sqrt[l + utA23)) 1 ;
*
(* where tranap is the aperture radius,a is the transverse nns beam radius, gamma is the relativistic mass factor, wt0 is the angular frequency of zero-current betatron oscillations, ermsn is the rms normalized emittance (assumed equal for transverse and longitudinal??), and c is the speed of light. The quantity ut is a transvene space-charge parameter given by: *) (1/(PO*Sqrt [51 *beta*gammaA2*b)) * ( c / (wtO*ermsn)) (q*zO*i/mc2) ;
ut =
*
(* where b is the nns phase half-length of the bunch, q and mc2 are the particle charge and rest energy, z0 is the free space impedance (377 ohms) and i is the average beam cumnt over an rf period. In the thin lens approximation for a focusingdefocusing (FD) quadrupole lattice, the betamn frequency can be expressedas: *)
wtO
= (q*bO*lquad)/ (2*gamma*m*ttanap)
i
(* where bo is the quadrupole pole-tip magnetic field and lquad is the quadrupole effective length. The aperture ratio
can be maximized by appropriate choice of the lattice parameters. A similar expression can be derived for the corresponding longitudinal ratio: *) longapratio =
( (beta*c*phiS)/ (2*pi*freq) ) Sqrt [ ( (gamma*wlO)/ (ermsn*c))
(l/(ul
longap
lonapratio*b
(* also want separatrix
+
Sqrt[l
+
*
*
UlA2]))1 ;
:
formula? *)
(* where phis is the synchronous phase, w10 is the zero-cmnt longitudinal oscillation frequency, and ul is a longitudinal space-charge parameter given by: *)
ul =
* ( (q*zO*i)/(gannnaA2*mc2)) * (cA2/(ennsn*w10*tranap)) * tranapratfo ;
(1/(4O*Sqrt[S]*pi))
(* The quantity w10 depends on the effective axial accelerating electric field EoT and is given by: *)
w10
= Sqrt [
(2*pi*q*freq*EoT*Sin (phis] ) / (gammaA3*m*beta*c) 1 ;
(* For control of unwanted beam spill, the designer must keep the transverse aperture ratio large. If it is also desirable to control space-sharge induced emittance growth, the ratio a/lambdaD should be kept small,where 1ambda.D is the beam Debye length. For a spherical bunch, this ratio can be expressed as: *)
aolambdaD
-
S q r t [ ( (3*q*i)/ (2O*Sqrt [ 5 ] *pi*ennsn*c*mc2) ( (tranap*c)/ (freq*ermsnA2) I ;
IILA. 42-
*
(* For a given current i and emittance ermsn, the ratio is minimized by minimizing the product of beam size times the rf wavelength, which implies strong focusing and high frequency. The physical explanation for the advantage of high frequency is that the total current, i, is distributed over more longitudinal buckets. The physical advantage of small beam size is less obvious. It results from the competition between the spacx-charge force which increases for small beam size (a disadvantage), and the spatial extent over which a given thermal energy input is distributed, which decreases for small beam size (an advantage).
The physics design of a high-brightness linac is based on the above ideas. The injector, rfq, dtl and hnriel constitute the front end of the accelerator. The primary objective of the front end design is to produce a high quality, low emittance beam that can be injected into the main coupled-cavity linac (ccl) at as low an energy as possible ( say 20 MeV for protons), and subsequently accelerated as a very compact beam to the final energy with minimal beam loss. The emphasis in the front end design is low emittance growth and low halo production as the beam experiences the major transitions of bunching, and funneling with frequency doubling. Minimizing beam loss in the front end is a secondary objective, as long as the activation consequences are acceptable, and heating consequences are addressed by providing sufficient cooling. The low emittance growth is achieved by providing a high frequency linac to reduce the particles per bunch, and by providing strong transverse focusing with rf-electric quadrupoles (the rfq), magnetic quadrupoles (dtl), and ramped accelerating fields for strong longitudinal focusing in the dtl. The primary objectives in the ccl are to (1) introduce no major transitions that can lead to further beam halo, (2) provide large apertures to minimize beam losses, which, even at relatively low levels, can lead to significant activation levels, and (3) provide sufficient focusing to maintain compact beam dimensions and minimize further emittance growth. An important figure of merit are the ratios of aperture over rms beam size, defined above. These are maximized by choosing a large product of pole-tip magnetic field times effective length for the quadrupoles, using a high density of quadrupole focusing lenses (large transverse phase advance per period), and providing the largest practical apertures. A high density of focusing elernents leads to short accelerator tanks (2-10 cells for AWATW, rather than 30-60 as in LAMPF). In a point design study, the APT/ATW ccl was divided into seven different sections so that larger apertures could be used as the particle velocity increases, and so that the ratio of aperture over rms beam size could be maximized for each velocity region, As the velocity increases, it becomes possible to increase the number of accelerating cell per tank,thereby reducing the number of components. *) 0
s t u c m r e heat dissipation limb
:= 0 . 5 (* MW/m *) (* Don't have enough info to make a model as fn( frequency (remember to do log fit), gradient, bmldg
linaheatdiasip [type] [freq_]
...*)
stxuconaxisdissdemoSband = { . 6 5 , .210, 3 . 5 , . 5 2 , . 2 8 6 ) ; (* CRNL data. *) (* highest demonstrated cw power dissipation at S-band, with -0.65 beam loading at structure gradient = 3.5 MeY/m (=> real estate gradient 100 MeV/35m = 2.86 MeV/m, factor 3.W2.86 = 1.224), structm length 0.52m if 50 structures are used, overall efficiency = lOW/35MW = 28.6%;(seeEqns, Table 2, & Summary of Interim Report) Ref. LaBrie, NTM A247.1986, p. 2,. *)
-
-
0
--
ZTA2scaling with T will vary like ( (sin(gap)/gap) (Io(lcr r)/lo(kr map)) )*2. See beam dynamics section. Assume the following are af nominal T where g (betalambdal2)/2, Le. haIf of a betalambdai2 cell length, and tranap -= betalambdaI9. (* i,n-axis
c w w
cw structuFe *)
II1.A. -43-
(* ztA2 = fn(Erequency) *)
struconaxiszt2freqdata = {(3000,80}, (2450,711, (2414,661, {1300,50), {805,36}} ; (* CRNL shunt impedance measurements with electron beams of on-axis coupled CRNL structures. *) (* ( freq MHz,ZTA2Mohms/m},2TA2= energygain~2/@owerloss/m)(cavitylength). ZTA2's -80% of SUPERFISH. Fit gave ZTA2= 1400.*freq(GHz)%.S;this fit was checked it is pessimistic at the high-frequency end, but will be used. Above 3000 MHz, aperture gets too big and web between cells too thick *)
-
10~(Apply[Plus,Table[N[Log[lO,struconaxiszt2freqdata[[j,2]]] 0.5*Log[lO,struconaxiszt2freqdata~[j,llll 1, Ci,5lll 15)
-
1.377071757900349945
Fit [Log[lO,struconaxiszt2freqdata],{l,x},x] -0.13039
+
0.58278"~
cclonaxiszt2[freqJ
:=
Block[{temp},
Plot[cclonaxiszt2[freq],{freq,500,3000)]
(* Side-coUOled
structure $1
(* ztA2 = fn(energy) *)
1.4*freqA0.5
I
;
-
st ruc sc zt 2energyda ta ( ( 2 0 , 1 0 1 , ( 5 0 , 1 6 1 , ( 1 0 0 ~ 2 5 ~ ~ { 2 0 0 ~ 3 3 } , { 3 0 0 ~(400,391r 36~5}~ (500,40.5},(600,41.3},(700,42},(800,42.5},(1300,43.4},~2000,44}} ; (* Lapostolle & Septier, "Particle Accelerators", p.612, with points at 20,50,1300,2000 MeV added: at 805 MHz. *)
Fit[strucsczt2energpdata,{xA-3,xA-2,xA-l,l,x),xl 46.01
-
961058/~"3 + 93125./~"2
Show[ListPlot[strucsczt2eaerggdatal,
-
-
-
2 9 7 4 / ~ 0.0002275*~
Pl0t[46.01 961058/xA3 + 93125hA2 (* log plots are also not linear *)
- 2974/~
II1.A. -44-
0.0002275*~,{~,20,2000)]1;
I1 I
500
1000
1500
zt2[ccl[sc]][energy_l := Block[{temp}, 46 - 9.61*10A5/energyA3+ 93125/energyA2 2974/energy + 2.275" 10A-4*encrgy]
2000
struc:APl"sczt2energydata=
{ {20,12.4),{40,13.4),(80,17.7),( 160,20.9},(320,24.3),(640,25.2),{ 1000,25.4},(1600,25.4)} ;
Show[ListPlot[strucsczt2energydata, PlotJoined -> True, DisplayFunction -> Identity],
ListPlot[strucAPTsczt2energydata, PlotJoined => True, DisplayFunction -> Identity],
ListPlot[jjkk, PlotJoined -> True, Plotstyle -> Dashing[{0.05,0.05}], DisplayFunction => Identity], DisplayFunction -> $DlsplayFunction] ;
-----35t7+ 30
II I
500
loo0
1500
ZOO0
(* Attempt to adjust the APT data by a TA2 factor depending on the Bessel fhnction effect for aperture size, ax on frequency using on-axisstructure rule. Doesn't work at all,but Murhematicu procedure is interesting. *>
(* APT data; aperturehtalambda: *)
1/(1.418.7,1.9/12.1,3.0/16.7,3.S122.3,3.512~.S,3.5134.4,3.5137.5,3.S139.~~
(6.214285714285714285, 6.368421052631578948, 5.566666666666666667, 6.371428571428571428, 8.142857142857142857, 9.828571428571428574, 10.71428571428571429, 11.37142857142857143)
II1.A. 45-
biO[x-] := N[BesselI[O,x]] ; jjj = (1/((l/(Map[bi0,2*pi*{ 1.4/8.7,1.9/12.1,3.0/16.7,3.~/22.3,3.~/28.5,3.5/34.4,3.5/37.5,3.5~39, S}]) "2)* (700/800) * 0.5)) * { 12.4,13.4,17.7,20.9,24.3,25.2,25,4,25.4}
{21.46090384137761144, 22.69089395699747077, 34.21914553803932866,
35.37646901197544379, 34.62385999708193413, 32.88292514653145999, 32.13367959658838398, 31.54288875865863969)
kkk = {20,40,80,160,320,640,1000,1600}
;
jjkk = ~ a b ~ e ~ ~ ~ ~ ~ ~ ~ j ~ l l , j j j ~ ~ j ~ l l ~ , ~ ~ , ~ , ~ ~ l [{20, 21.46090384137761144}, (40, 22.69089395699747077), {80, 34.21914553803932866),
(160, 35.37646901197544379),
(320, 34.62385999708193413}, (640, 32.88292514653145999),
{ l O O O , 32.13367959658838398), (1600, 31.54288875865863969)) beta[energ-] := Block[{ererg,gin}, gin = energ/938.3; Sqrt[gin*(2 + gin)]/(l + gin) I betadata = Table[{beta[strucsczt2energydata[[h,llll, strucsczt2energydata[[h,2I]},{ h,l,l2}]
{{0.2032363481979319209, lo), (0.3140450734029610145, 161,
(0.4281900206935794217, 25), {0.56615413919417673, 33), (0.6525654356698383004, 36.5), {0.7130498345699815708, 39), {0.7579028987406476996, 40.51, {0.792432938846557003, 41.31, {0.8197455919140865739, 42), (0.8418059675693611813, 42.51, (0.9078929573418701911, 43.41, (0.9476421260817666387, 44))
fitbeta = Fit[betadata,{l,x,xA2},xl -9.702611969730376322
+
101.4410393710560733*~
Show[ListPlot[betadata,DisplayFunction -> Identity], Plot[fitbeta,{x,.l,l,},DispiayFunction -> Identity], DisplayFunction -> $DisplayFunction I; (* log plots are also not linear *)
IILA. 46-
-
46.96008339558108416*~"2
..
o -verse
3
fn fireq, eo, quad strength, length (standard stability chart b and del - have eqns already), tune depression defines, so does sc limit.... Ramped gradient helps maintain longitudinal focusing, up to cost optimizationlimit.
(* 1.25 GHz, 8 m m
web, 20 m m aperture e-linac structures: ZTA2. Mhmhl 1 (both SUPERFISH values) THERAC 56 .8 1 Maim 56 .82
Profile LANL
Illinois
60 66
.a8 .86
*)
II1.A. 47-
struconaxisbmldgdemoSband = { .85, .022, 1.11, 1.62, . 4 0 } ; (* CRNL data. *) (* demo'd max beamloading, at real estate gradient of -lOOMeV/llOm = 0.91 MeV/m, => x 1.224 = structure gradient = 1.11 MeV/m, 1.62m structure length if 50 structures are used, overall efficiency = -10Mw/25MW = 40%, V S W R w/o beam,Prefl w/o beam in %. Ref: McMichael, 1979 Linac Conf., p.180. *) I
struconarislbanddata
struconarisSbanddata
=
(i.60, .222, { . 6 5 , ,145, {.70, .092, f.75, .056, {.80, .031, {.85, .016,
.OOO, .OOO, .OOO, .OOO, .OOO, .OOO,
1.2, 1.5, 1.9, 2.4, 3.2, 4.5,
.28, .30, .33, .35, .37, .40,
2.50, 2.86, 3.33, 4.00, 5.00, 6.67,
181, 23), 291, 361, 441,
5511 ;
=
.53, .30, 2.86, 231, .203, .OOO, .67, .32, 3.33, 291, ,129, .OOO, .078, .OOO, .86, .34, 4.00, 361, .044, . O O O , 1.14, .37, 5.00, 44), 1 . 8 5 , .022, . O O O , 1.62, .39, 6.67, 5 5 } } ; (* CRNL data for cw on-axis coupled structure; beamloading, power dissipation MW/m, structure gradient, structure length of each of 25 structures used at L-band, or of 50 used at S-bandto achieve 100 MeV, overall efficiency for a 10 M W beam system, VSWR and Prefl(%)w/o beam. Fit to length gave: Length (m) for 100 MeV, 10 M W cw e-linac = 7.14*105*(B/(l-B))*(freq(Hz))'Y).S Should be able to duplicate this using the 65, I.70, (-75, {.80,
{ {.
Level0 model. *) (* At higher power dissipation, get less beam loading, less efficiency,more comples cooling, higher risk, more outgassing -> arcs, multipactoring. At higher beamloading, get lower power dissipation, longer structure, higher VSWR w/o beam -> arcs, more severe transients,and more difficult conditioning. Number of components is less at lower frequency with larger rf amplifier size -> better reliability. *) strucH2Oialettemp = 35. ;(* degC. If inlet water has to be chilled, increases electrical power demand and costs signnificantly.*)
StrucVSWRnobeam
-
(need formula)
;
-
(* Cooling/StressThermal Analysis AECL, uses MARC,a 3-Dcode. *)
-
(* Use no mechanical tuners in cavities esthute uvuflabflffyfucfor tJ used. Use H20 control. Femte tuners? *)
@A (* better to have no beam transport between dtl and ccl. Estimute availability factor is there is one. *) (* Use no mechanical tuners in cavities estimate availabiliry factor if used. Use H20 control. Femtetuners?? *) (* Ramped gradient may help with longitudinalfocusing or input matching; allows getting up to cost-optimized gradient *)
-
II1.A. 48-
0
zt'\2&
Assume the following are at nominal T where g -= (betalambda12)12, Le. harf of a betalambda12 cell length, and tranap -= betalambdal9. (* ztA2 2: fn(energy) *) (* Lapostolle & Septier, p.
731-732*)
(* scaled by 38/41 to match hi data *)
strucdtlzt2energydataJ.o = (38/41)
*
((1t21.21, {2,281, (3,32*5),14,361, (6,391, {8,401, (10,41)1 ;
st xucdt lzt Penergydat ahi =
( (10,381, (20,39},{30,37.3),
(40,34.8 1, ( S O , 32.2), {60,30.5),(70,28),(80,25.8~,{90,24},(100,22.2~, Cl20, 2 0 ) , { 140,17.5) ,. (160,15.3), { 180,13.3), (200,121 }
Fit[strucdtlzt2energydatalo,{l,x,x "2,xA3},x1
11.54993242934498'748 t 9.969746353344637133"~ 1..336186643808260299*xA2
+
;
-
0.06134730170183528899*xA3
Fi tlstrucd tlzt2energydatahi,{l/x,l,x,x A 2) ,XI
-
-
48.02364625424929306 66.90226997463056178/~ 0.3184426194472201709*~ t 0 . 0 0 0 7 1 O 8 3 8 8 6 8 1 2 7 1 9 3 5 6 7 2 * x A 2
Show[ListPlot[strucdtlzt2energydatalo, DisplayFunction => Identity], ListPlot[strucdtlzt2energydatahi,DisplayFunction -> Identity], Plot[ 11.54993242934498748
-
+
9.969746353344637133*~
-
-
1.33618664380826Q299*xA2 + 0.Q6134730170183528899*xA3,{x,l,10}, DisplayFunction -> Identity I,
Plot[48.02364625424929306 66.90226997463056178I~ 0.3184426194472201709*~+ 0.0007108388681271935672*xA2,{x,10,200}, DisplayFunction -> Identity 1, PlotRange -> {{0,200},{0,45}}, DisplayFunction -> $DisplayFunctIon 1;
1
25
dtlzt2 [energy-] Iffenergy
1
3:
50
$1.25/wattwithout circulator; considerably higher than above. *) (*
o
klvstron Pout, Eff, Gain, BW, BmV, BmI, Cool InletTemp EMPwr, % dB -1 dB KV A Ymin IRC) KW 353 1.0 65 40 3 81.5 17.5 80 22.5 950 40 6.5 1300 1.0 55 43 4 433 1.0 (4 MW peak) 2 prototypes de1;ivered 7/89 509 1.2 61.4 56 1.2 93 21 50 98 4.5 1250 1.2 65 50 0.5 85 22 50 98 4.0 1.2 60 1.0 58 .8 56 New 2450 .25 65 50 1 50 7.7 380 60 E3720 Fusion 5000 1. 54.7 - 62 29.5 Valvo YK1350 LEP 352 1.1 68 40 1 90 16.3 1200 75 3 900 2 76 17 50 1.3 500 .8 61 43 YK1301 Hera/Peaa 41 1 90 100 90 6.3 YK1303 Tristan 18.2 503 1.1 61 50 4 450 11 4 57 YK1250 Petra lo00 .4 60 43 20 62 16 900 76 VarianVKS8269 Princeton 2450 .48 52 57 NIST 2856 . 6 *)
(*
T e User ThomTH2089 CERN New Boeing Tosh E3786 Tristan E3718 Dev.-PNC (Modanode ->
Frea MW
(* Thomsen unit price $500K for 1 MW, 1st tube 15 months ARO, production l/month *)
(* Pulsed tubes:
Phillips YK1240,1300 MHz, 330 KW peak, 1.5 s pulse length. Toshiba E3775, 1300 MHz, 5 MW peak, ? pulse length Varian VA862C, 930 MHz,250 kW ave, 2 M W peak, 10 ms pulse length. SLAC:
freaPkPwrAvePwrPulseLennthVoltane_Effw 1.3GHz 6MW 50KW 37 20 3.0 3.0 (180pps) 150
30011s 5
1
130 KV 275 450
IILA. -54-
48 55
53dB
SF6 Ip = 600 A *)
(* Limiting factors: (Information from Phillips and other sources) limklyvoltagehard 1 at k e 2.
efFklyelec = 0.8418 upew = 2. *)
-
0.1717*uperv ; (*from 70%at uperv = 0.75 to 50% at
-
1/(1 + 1/((1.22 O.l*uperv) * (3*10A-2) * (uperv)* ( (lambda*vO)A O . 5) ) ) (* klystron circuit efficiency, where v0 is the dc operating voltage. uperv should have a small &itivistic correction between 100 -> 500 kV. effklyckt
effklycntrl pwxkly
= 0 . 90
;
-
; (* reduction from saturation to afford closed-loop control. *)
= uperv*10*6*v0A(5/2)*.ffklyelec*effklyckt*effklycntrl
;
...
Plot overall efficiency and power out - maybe change to simpler form vs frequency
oklvstrode
SDI - 450 MHz, 500 kW peak, 11 ms pulse, 50 kW ave, eff = 70%,21 dB gain, BW = 5 MHz, 85 KV C R I C 267 MHz, 250 kW cw, eff = 70%,23 dB gain. Test started 4/91. SDI Contract 850 MHz, 500 kW cw, n = 70%, 20 dB gain. In design. To use improved bunching through velocity modulation and multi-segment depressed collector.
-
-
Varian/Eimac could develop 8 0 MHz, 250 KW cw klystrode, nre > $1M. *) Klystrode collector does not have to handle full beam power like klystron does. Klystrode operating perveance is determined by rf drive level, unlike klystron. Class B operation means efficiency stays high with drive modulation of amplitude. SDI tube demonstrated input/output phase shift of -1.23deg per 1% change in anode voltage at 85 kV. Phase shift vs drive small (CHECK) over last 50% of rf drive change. Efficiency stays at -70% over operating control range. 0
o
t
l
m
(* solid-state *)
II1.A. -57-
1986 data: 425 Mhz, loo0 k W ,0.3g/w, 40 v source. Package weighed 660 lbs, 38 cuft (3 x 3 x 4.5 ft), efficiency = 60%, $8.00/watt. (* gridded tubes *)
Hoffert paralleled planar triode amplifier. At 425 MHz, eff = 60%, gain = 13 dB, 150 KW, 60 us pulse. $2.00 per watt including power supply and driver.
Tetrode amplifiers - data from M. Loring, Eimac:
-
Eimac X2274 at JAERI JT-60ICRH 131 MHz; tested (system limited) to 1.7 MW, 5.4 s pulse length. Max anode dissipation rating 2.5 MW. Tube reaches steady-state temperature in a pulse this long, hence tube is ok for 1.7 MW cw.
Efficiencyvs.outputpower,MW: { { 1 . 7 , . 6 0 ) , i1.5, . 5 5 ) , {l.O, . 5 1 1 ) OK for VSWR 7 1.5:1, any phase. Anode dissipation at VAWR = 1S:l about 1.4 times that at VSWR 1:l. Applications: Siemens RS2074SK, 108 MHz, 1.8 M W peak, 25% duty factor Eimac 8973,201 MHz, 2 MW rating, at DESY,daily ops 1-1.5 MW, 250 us at 1 pps, eff = 60%. Tests run to 400 us. But would use new tube like X2274 now, with lower power 1.4 MW anode design. (Saves $5K.) BTA spec - 200 MHJz, 1 MW, 1.2 ms,12% duty factor. At 2 M w ,x2274 would require 25 KV, Ib = 140 A, Eg2 = 1900 V,Ig2 = 3.5 A, gives 12.5 dB gain. TAC 473 MHz, 100 kW peak, 50 us, 0.5% duty factor, eff = 56%. 23 dB gain using Eimac 2KDW6OLA.
-
(* crossed-field-amplifiers *)
Cathode-driven Raytheon CFA: 30 dB isolation port-to-port. S-band(-3 GHz), 1.25 M W , eff = 60%, gain = 24 dB, 70 lbs. (* two-beam systems *)
Use of microwave FEL's to drive??
IEA. -58-
(* see also instrumentation and control *)
(* Commercial VQ demodulators are available: i l degree,k0.5 dB balance, or better with tunable Merrimac demodulators. Get full 360 degree phase shift range. CRM, doing their own I/Q work. *) (* lo0 second ramp from @loo%power level ok, *)
-
(* Klystron ripple f 5 degree phase modulation at up to 360 Hz,or f2.5 degree up to 720 Hz requires loop gain >10 at 720 Hz and higher at lower frequency. Control loop has single-pole,high-gain, lo-pass filter with gain = lO00, comer frecluency = 100 Hz,wideband proportional gain = 10,lO MHz electronics,65 kHz structure bandwidth, loop transit time of 150 ns. No attempt to overcome structure time constant; this avoids controller induced rf mismatches when attempting to rapidly alter structure fields.
..
(* fuzzy control. *)
oa-
(* 9QkV-25Asupply cost: 2 for $.45Meach, 25 for $0.4M each. Cost/kW lower for WkV-25A supply, compared to 7OkV-20As~pply. *) (* CWDD supply: 66kV to 1kV 5MW matching transformer to phase-controlled SCRs to step-up HV transformer-rectifier. Includes fdter bank,crowbar, klysmn heater and anode control. AC/DC conversion efficiency = 0.93. *)
OcilmktQK
data. Circulators give protection from reflectionsdue to c m n c changes of rfconditioning; however, they are expensive. CRNL recommends using a circulator for conditioning, but operating without a circulator, using careful matching (of line length) between amplifier and accelerator load. For conditioning, use circulator or variable iris or variably-displaceddielectric or 1:l VSWR coupler section; removed for operation, Bandwidth f 1.5%. Isolation > 20 db (>WdB quoted) Insertion Loss 4 . 2 dB (c0.15 dB quoted) Input VSWR < 1.15 Power Level: 1300 MHz 200 KW cw, 1 MW for 10 usec 2400 MHz: 100 KW cw, ).5 M W for 10 usec !SF6 pressurized Water cooled Price: 1300 MHZ: 161 IC$ each in lot of 25 2400 MHz 183 K$ each in lot of 50 Weight = 100 kg at 1300MHz or 2400 M H z (* C'RNL
-
Experiments at DESY using waveguide transformers to match at different beam-loading conditions B. Dwersteg, DESY Rpt. M-89-13, August 1989.
-
m.A. -59-
e cooliny svstem
-
(* delta temp 35 degC. Tower cooling nominal 40 Wmin H20 from 52->32 degC at entering wet-bulb temp of 26 degC. -150 kW of fans, 1.12 MW of pump power. *)
e electncal svsteq (* 33.7 M W total for 10 M W e-beam system;31 M W for klystrons. 30%excess installed over demand -> 45 MW
installed.
General services: Cooling tower fans Pumps Primary H20 pumps Resonance control H20 pumps Beamline optical elements Electron gun Control & low-level rf
Lighting
Heat, N C , ventilation
148 kW (37 kW x 4 ea) 1120 592 (37 kW x 16 ea) 240 (15 kW x 16 ea)
5
100
(lAx100kV)
5 64
AQQ
2.37 M W
Klystron: Supply (usable) 1870 kW (85 kV x 22 A) Losses - Matching transformer 24 18 SCR controller HV xfmr/rect 49 1.957MW x 16
III.A. -60-
111. Framework for Codification
B. Linac Beam Dynamics, LINACS Level 2 Model
0 U a c B e a . m DvnamicS
- Introductioq o Historv ~
"he equations for the linac acceptance quantities here are basically those in "Space-Charge Limits in Linear Accelerators", by T. P. Wangler, LA-8388, Los Alamos National Laboratory, 1980. Relations for the beam itself have been added. The approach is similar to other treatments, with some differences in notation and approximations; e.g. R.L. Gluckstern, "Nonlinear Effects" and "Space Charge Effects", Chapters C. 1.2d and C, 1.3c, Linear Accelerators, ed. Lapostolle 81: Septier, North-Holland, 1970; K. Mittag, "On Parameter Optimization for a Linear Accelerator", Kemforschungszenhum Karlsruhe, KfK 2555, January 1978, and "Parameter Optimization for a High-Current Deuteron Linear Accelerator", KfK, June 1978; and R.A. Jameson, "LA Notebook R-3455",1979, and "Equipartitioning in Linear Accelerators", 1981 Linac Conference, Santa Fe, NM, Los Alamos Conference Proc. LA-9234-C. All of the equations are based on the rms properties of a beam with uniform beam density.. They are based on a smooth approximation of the transverse and longitudinal periodic focusing. They are applicable locally, i.e. at any energy or cell along the system. The acceptance and current limit equations were programmed in a FORTRAN code, named CURLI, in about 1980, and used for the next ten years for scaling calculations and as a design guide. The CURL1 code had two solution options for RFQ or DTLs: mode = 1 : fixed apemue, variable m for FWQ; vgap for "conventional"; calculate cunent limits il and i t mode = 2 : vary aperture, search on m for rfq or vgap for conventional; find point where il = it and print value of optimum cunent. i t y p e = : RFQ pi-pi Wideroe pi-3pi Wideroe Alvarez
----- drift-tubelinacs (dtl) --
For the dtl's, the focusing order must be specified. This is done thmugh the parameter mult: mult= 1 (fodo) 2 (fofododo) 3 (fofofodododo) etc
........
This Muthemticam version is more complete and versatile. Two-beta-lambda Alvmz and pn-mode coupled-cavity linace have been added. Not only m the quantities related to the structure calculated (acceptances), but also the quantities related to the beam (emittances) are found, and the interrelationships between the structure and the beam can be determined using the matching equations, the equipartitioning relationship, and other conditions. As in the other code sections, the user can set the variables to numbers or use them in symbolic form. IILB.
- 1-
The smoothed approximation used leads to limited accuracy when the phase advances are not 0. ;
-
-
(* Bessel function *)
biO [x,]
:= N[Besself [0,x] ]
;
cont = 8.*pi*cayt/(3.*~0) ; contl = Sqrt[ 1. cayt 1 ; con1 = 8. *piA2*cayl/ (3.*zO) ; gin = energy/(him*erest) ; beta = S q r t [gin*(2. + gin) I / (1. gamma = l./Sqrt[l. betaA2] ; qom = q/(him*erest) ; wave1 = clight/freq ; betalam = beta*wavel ; cay = 2*pi / (gamma*betalam) ;
-
-
+
gin)
;
-
1II.B. 8 -
-
(* Function needed for computation of phase acceptance *)
pac[phis-]
:= Block[
phir = NE2 .*phis*Degreel, phisr = N[phis*Degree], dphir = 0. 1, If [NumberQ [phir], (* needed for reset *) ( D o [ phir = Round[ (phir t dphir)/Degree ]*Degree ; dphir = N[ ( Sin [Abs [phisrl I Abs [phisr]*Cos [phisrl (Sin[phir] phir*Cos [phisrl 1 1 / (Cos[phir] Cos [phisrl) 41 {
-
-
-
I i5) 1 ; Abs [ (phir phisr)/Degree 1 Return [ 3
+
1
-
1,
I;
(* For an RFQ, the specifications result in a phase acceptance, degrees, and the maximum ratio of the energy at the exit of the gentle buncher to the injection energy, wovwimx: *)
1II.B.
-9-
phaseacceptance [rfq] = N [ pac [phis[rfq]1, 01
;
wg = N[ (99.5/phis [rfq]) "2*injenergy] ; (* estimate the energy at the end of the gentle buncher, where the current limit bottleneck is: *) wovwimxErfq3 = N[ (360./phaseacceptance [rfq]) *2 (* max ratio of gentle buncher exit energy to injection energy *) betain = Sqrt [2*injenergy/(him*erest)3 cayin = P*pi/(betain*wavel)
nblt = n[rfq]
;
;
;
;
enhancatrfql = 0.2225 t[rfq] = pi/4.
: enhancb[rfq] = 0.0792
bica = biO[cayal
;(* 2pi a/gamma*betalambda *)
;(* Bessel function correction for aperture *)
-
aalrfq] = N[ ( em[rfql"2 l.)/( em[rfq]*2*bica biO [em[ rfq] *caya] ) 3 ; s[rfql = N[ 1.
:
;(* transit time factor *)
caya = cay* (O.Ol*a [rfql)
-
aa[rfq]*bica]
+
;
r0trfql = N[ (O.Ol*a[rfq])/Sqrt[ xx[rfq] 3 1
;
ckappa[rfql = N[ E x p [ enhancarrfq] + (enhancb[rfq]*cayin*rO [rfq]) ] ] v trfql
41
,
= N[field*rO [rfq]/ckappa [rfq] 3
e0 [rfq] = N[ 2. *aa [rfql *v[rfq]/betalam 1
;
; ;
b[rfq] = N[ qom*v[rfq]*( wavel/rO[rfq] )A2 ] (* thetaA2*)
;
del [rfq] = N[ pi*qom*eO [rfq]*t [rfq]* Sin [Abs [phis[rfq]*Degree] 1 *wavel/beta 1
1II.B.
- 10 -
I
;
o
DTL and CCf, A t t r i w accum[mult-1
:= Block[ {acon = pi/(2.*mult), j = loo.,
accum = 0 . 1, For[ j = 100.; jj = O., j != l., jj++, j = 2.*(mult jj) 1. ; accum = accum Return[accuml I ;
-
-
+
Sin1-j sconl
3
;
dtlcclforms := ( Whichttype == dtl, typetype = dtltype, type = ccl, typetype = ccltype 3 ; (* n is the number of betalambdas per transverse focusing period, ng is the number of gaps per betalambda. *)
n [dtl[pipiwid]I = mult [dtll
ng[dtl [pipiwid]3 = 2 ;
;
n [dtl[pi3piwid]I = 4*rnult [dtl] ; ng [dtl[pi3piwid]3 = 1 ; n[dtl[alvarez]l = 2*mult[dtl] ;
ng[dtl[alvarez]] = 1 ;
n[dtl[2blalvl I = 4*mult [dtl]
ng[dtl[2blalv] ] = 1/2
;
;
n [ccl[typetype]] = (2*(cellspercav*(1/2) + lqibetalam) ) *mult [ccl] ; ng[ccl [typetype]3 = 2 ; nhlt = n[type [typetype]]
;
(* The longitudinal force is effective through eO[type] on a per meter basis, (Le. is real-estate gradient), so is computed over the transverse focusing period. *) (* electric quads: calculate focusing voltage; else, for magnetic quads: calculate equivalent focusing voltage --"field' is now B in Tesla. *)
If![ ifocus[type] v[typel
elec, = field*(O.Ol*a[typel) r=
-
,
0 ]
;
If![ ifocus[typel mag, v[type] = clight*field*(O.Ol*a[type])*beta
-[type3
= vgap [type]/v[type]
,
0 ]
;
t [type] = N [ Sin [pi*gapobl [type]1 / (pi*gapobl[type]1 1 ;
(*transit-timefactor *)
gap = gapobl [typeJ *betalam
;
1II.B.
- 11 -
;
caya = cay* (O.Ol*a [type] ) b i c a = biO[ caya I
;
(* 2 pi a/gamma*betalambda *)
;
aa[type] = N[ l . / b i c a 1
;
x x [ t y p e ] = N [ 4 . * s i n [ ( p i * f i l f a c [type] ) / ( 2 . * m u l t [type] ) 1 * accum[ m u l t t t y p e l I / p i I ; t r a n s f [type] = N[ t[typel*aa[typel 1 (* transit time factor, corrected for aperture size *)
;
Which[voltage = gap, e 0 [type] = N [ n g [ t y p e [ t y p e t y p e ] 1 *aa [type] * vgap [type] /betalam], v o l t a g e = grad, vgap [type] = N [ ( e 0 [type] *betalam) / ng [type [ t y p e t y p e ] 1 *aa [type] 1 I voltage = ezerot, e 0 [ t y p e ] = N [ e O t [ t y p e ] /t [type] I 1 ; b [ t y p e ] = N [ qom*v [type] *xx [type] * ( wavel*nblt/(0.01*attypel) l"2 / (* thetaA2*)
del [type] = N [pi*qom*eO [type] *t [type] * S i n [Abs[ p h i s [type] *Degree] 1 *wavel* nb1tA2 / (beta*ganrmaA3) 3 ;
1II.B.
- 12-
1
;
o
0
..
Phase Advance. Current Limit. Accentance Em ittance Ouamties mi-
-
It is not so easy to find the definitions of longitudinal emittance in various units. We start from p(i) = momentum(i) = mv(i) = m p(i) c = ymO Q(i) c, where mO is the rest mass. In the paraxial approximation, p = Sqrt[ pxA2+ pyA2+ pzA2]-= pz, and px = p dx/dt,
py = P dy/dt, Pz =
P.
p(x) = mO c py dx/dt, and Ap(x) = mO c py A(dx/dt); same for y. Normalized emittance is defined as en = (Ax Ap(x))/(mO c) or (Ay Ap(y))/(mO c) or (AzAp(z))/(mO c). So, generally, for transverse, m(x) = Ax A(dx/dt) py = &real(x)py, and same for cy; Ax and A(dx/dt) are the quantities usually measured in the lab.
For longitudinal, p(z) = m0 c by, and Ap(z) = mO c( p Ay + y Ap). Also, Ay = ATNO, where WO is the rest energy, and p = Sqrt[ 1 - 1/r\2]. Differentiating p with respect to yields A@in terms of AT, and we get Ap(z) = AT&.. The same result is obtained non-relativistically from kinetic energy = T = 0.5 m vA2.and p = m v. Az = pc At, so Az Ape) = AT At. Normalized &ln = AT At/mO c.
To relate to z as the independent variable, dt/dz = l/v = l/pC, and we have to invoke the definition of
a synchronous phase (see L. Smith, Handbuch der Physik, Vol. 44. p. 344), obtaining d/dz(+ - $s) = w(dt/dz dts/dz) = (-2 pi/h)(Ay/(ysA3 psA3),or d(Az)/dz = AT/(WO pA3 PsA2,) Using A+ = Az 360/ph, we get A+ AT = (d(Az)/dz Az)(WO p 3 p 360h ) in MeV-deg., and &ln = AT At/ mOc = (d(Az)/dz Az) flp 3 ,
where (d(Az)/dz Az) is the real total longitudinal emittance in the matching equations. The same result can be derived using Mittag's formulas, and is given as his Eq. (120).
calaforms
:=
(
erbsphis = Abs[ phisttype]
3
;
phir = N[ phis[type]*Degree I bsmd = N[ b[typelA2 /(8.*pi*2)
;
-
dalttype] 1
-
(* square of smoothed phase advance per focusing period Eq.18 *)
;
sigOtr = N [ Sqrt [bsmd] I ;(* transverse phase advance without current *) zrigOt = N[ sigOtr/Degree 1 ; sigOlr = Sqrt I 2.*del [type] 3 ;(* longitudinal phase advance without current *) sigOl = N[ sigOlr/Degree 1 ;
1II.B.
- 13 -
gammam = N[
(1.
-
b 0 t p s q ) ~ 2 /sigOtr ]
;
gammap = N[
(1.
+
b0tpsq)~2 /sigOtr ]
;
psi
= N[Sqrt tgammap/gammaml I
;
(* flutter factor; does not depend on beam current in this approximation (which is not very accurate unless phase advances are cc 1 (radian). *)
I
ez = N [ e0 [type]*q*t [type]*Cos [Abs[phirlI
;(* dwdz *)
(* Now calculate quantities for the beam itself: *)
p = N[ gannua*bmlen/bmrad ] ;(* get ellipsoid form factor ff *) (* This gamma produces the beam length in the beam reference frame. See K. Mittag, Eq.(44) and S. Humphries, Jr. "Charged Particle Beams",Eq. (6.106). It makes p very large at high energy, so it is necessary to use
the full form for the form factor -- see function felipse under General Quantities above. For some problems, p c 1 and the full form for that needs to be used. For now, the various forms are all given here and the proper one can be selected, with the others commented out with the (* *) brackets, after which the formula block must be re-executed. This needs to be f i e d so the choice can be used --problem now with Newton or secant FindRoot method. *) ff = 1/(3.*p) (*
(*
ff =
(*
-
N[ felip[pl 1
;
-
N[l./Abs[l. pA2J p*ArcCos[pl/Abs[l. pA21Al.51 ; *) ( * f o r p c 1 *)
ff = N[p*ArcCosh[pl/Abs[l. I./A~s[I. pA2]] *)
-
delsc
*)
;
pA'21A1.5
-
(*forp>l*)
0.375*10A-6*z0*qom*curamp*(100.*wavel)A3* (1. ff) *nbltA2 / ( p i * b m r a d A 2 * b m l e n * g a A 3 ) ]
= N[
bsmdi = bsmd
-
-
-
-
delsc
;
sigtr = Sqrttbsmdi] ; sigt = N[ sigtr/Degree 1 ; sigtosigot = sigt/sigot ; et = bmtadA2*sigtr / (nblt* (100*betalam)) ;(* real transverse total beam emittance, cm-rad, for matched beam transversely. This is the transverse matching equation; we assume it must always be satisfied. *) etn = et*beta*gamma ;(* normalized et, cm-rad. *) etrms = et/5. ; (* uniform beam particle distribution *) etnrms = etn/S. ; mu1 =
(
P*delsc*ff
siglr = Sqrt[ 1.
-
)/(
sig0lrA2*(l.
mu1 ]*sigOlr
;
1II.B.
- 14 -
-
ff) )
;
;
sigl = N[ siglr/Degree ] ; Biglosigol = sigl/sigOl ; el = bmlenA2*siglr / (nblt* (100*betalam)) ; (* real longitudinal total beam emittance, cm-rad, for matched longitudinal beam longitudinal matching equation; assumed always satisfied. *) e:ln = beta*ganrmaA3*el ;(* normalized longitudinal emittance, cm-rad *) olnmd = eln*erest*him*360 ./ (wavel*100.) ;(* eln, MeV-deg *) elnms = eln*erest*him/(lOO.*clight) ; (* eln, MeV-sec *)
--
elrms = e1/5. ; e:Lnrms = eln/5. ; (* uniform beam particle distribution *) e:lnmdrms = elnmd/5. ; elnmsrms = elnms/5. ; (* Calculations for acceptance and current limits *)
renbar = N [a [type] /Sqrt [psi]3
;(*
average envelope radius, cm; bore filled *)
bzO = (100.*betalam)*absphis/360. ;(* bucket width at zero current. *)
bz
=
(100 .*betalam) * (3/2)* (absphis/360)* (sigl/sigOl)"2
;
(* bunch length at current limit -- Mittag Eq. (79),(80) *) (* bz = lOO.*betalam*absphis/360.is assumed in CURL1 *)
:phimax =
(3/2)*absphis* (sigl/sigOl)"2
;
pa0 = N [gamma*bzO/renbar] ;(*for calculating acceptance based on phis bucket width. *) pa = N [gamma*bz/renbarl f!faO = 1/(3*pa0)
(*
get ellipsoid form factor ffa *)
;
ffa = 1/(3*pa) (*
;(*
(*
-
-
Ntfeliptpall * )
ffa = N[l./Abs[l. paA2] pa*ArcCostpal/Abstl. paA2]"1.5] ; *) (* for pa < 1 *)
-
ffa = N[pa*ArcCosh[pa]/Abs[l. pa"21"l.S l./Abs[l. paA2]];*) (* forpa> 1*)
-
I
-
-
(* ct0 and c10 are current limits based on phis bucket width. ct and cl are transverse & longitudinal current limits,
A, based on reduced bucket width = (phis)(l - r-l.1). Another set of limits is suggested by Mittag, using the total reduced bucket width = (3//2)(phis)(l - pl); this only differs by a constant so does not affect scaling studies. *) ctO
= N[
c10
= N[
c o n t * (renbar*sigOtr /nblt) "2*bz0*gammaA3/ (qom*(lOO*wavel) "3*(1. ffa0) * 1 0 A - 6 ) 1 ;
-
conl* (ranbar/ (100*wavel)) "2* (O.Ol*bzO) *
e0 [type]*t [type]*Sin t Abs [phirl 1 /
( ffa0 *beta*lO
"- 6) I
;
1II.B.
- 15 -
ct
=
cl
= N[
N[
cont* (renbar*sigOtr /nblt) A2*bz*gammaA3/ (qom*(lOO*wavel) A 3 * (1. ffa)*1OA-6I 1 ;
-
conl*(renbar/(100*wavel))A2*(0.01*bz)* e0 [type]*t [type]*Sin [ Abs [phirl I / (ffa*beta*l0”-6) ] ;
(* Get transverse quantities for beam, at current limit. *)
delscta
= N[
bsmdita = bsmd
0.375*10A-6*z0*qom*ct*(100*wavel)A3* (1. ffa) *nbltA2 / (pi*renbarA2*bz*gamA3)
-
-
delscta
I
;
;
(* Logical checks are to be avoided - see discussion under general quantities above. *) fnbs[bsmdi-] := 0. /; bsmdi 0.
;
(* xmui is phase advance with current for calculation of acceptance with current; sigma-i/sigma-0 is tune depression *)
xmuir = Sqrt[bsmdita] xmui = N[ xmuir/ Degree 3 sios0 = xmui/sigOt ; aOt
=
( * fnbs[bsmdita]
;
renbarA2*sig0tr/ (nblt* (100*betalam))
*)
;
;
(* zero current normalizedacceptance cm-rad *) aOtn = 1000. *aOt*beta*gamma ;(* normalized transverse acceptance, cm-mrad *) at = aOt*siosO ;(* real acceptance with current, cm-rad *) atn = aOtn*siosO ;(* normalized acceptance with current, cm-mrad *)
(* Longitudinal quantities. Note that the phase advances also have nbltA2in them, so the phase advance is over same focusing length as transverse focusing period. *)
delscla = delscta*cl / ct bsmdila = bsmd mula =
(
-
delscla
P*delscla*ffa
; ;
-
siglra = Sqrt[l. mula]*sigOlr sigla = N[ siglra/Degree ] ; siglosigola = sigla/sigOl ; a01
-
sig01rA2*(l.
)/(
ffa) )
;
;
= bzOA2*sig01r / (nblt*(100*betalam))
;
(* zero current real longitudinal acceptance, cm-rad *)
aOln = 1000.*beta*ganrmaA3 a h = aOln*siglosigOla ;
*
a01
;
(* normalized longitudinal acceptance with current, cm-mad *)
alnmd = aln*erest*him*360. / (wavel*100.) alnms = aln*erest*him/ (100.*clight) ;
1II.B.
- 16 -
a h , MeV-deg *) (* a h , MeV-sec *)
;(*
1
o
Us;: rfa or dtl or ccl formulifs
If a function is built later, have to use only the “head”in the argument list, e.g. “at‘,not “a[dtl]”-the function won’texecute with the latter... e.g. fn[energy-,a-,em-] runrfq := ( gq ; rfqforms ; calcforms ; 1 ; rundtl := ( gq ; dtlcclforms ; calcforms
; )
;
runccl :=
; )
;
(
gq ; dtlcclforms
;
calcforms
1II.B.
- 17 -
111. Framework for Codification
C. Linac Beam Dynamics Examples
and Comparison With Simulation Results
e Solve. Be sure to Initialize, then execute a Specify list and the Formulas first. The examples in this section illustrate many points and may be used to set up new work.,)
0
A 3 m I Mode 1 - fixemerture. varv m and -late
current limits ct and cL
rfqaemvar = (resetrfq; type = rfq; injenergy = .05; energy = wg; curamp = .05; freq = 425. ; him = 1.0073 ; q = 1 ; cayt = .84 ; cay1 = .84 ; field = 35.8; phis[rfq] = -35.; a[rfq] =.; em[rfq] =.; bmrad = .8*renbar;bmlen = .8*bz0; runrfq; ) Unset::norep: Assignment on a for a[rfql not found. Unset::norep: Assignment on em for em[rfql not found.
Select independent variable (aperture), starting value and increment for dependent variable (m), and set up table: (* Select independent variable and number of steps: *)
indepvar = {a[rfql-> 0.1, em[rfql -> 1.5 + .5 i} ; steps = 5 ; (* This is a direct calculation (no unknowns) - request a table of desired quantities at each step: *)
ctab =: Table[ {em[rfql,ctO,clO} /. indepvar, {i,steps} ] ; table := (Print[ StringForm[" m N[ TableForm[ctab],3 1) ;
ctO
c10
a = *"',
a[rfql /. a[rfql-> 0.1 1 1 ;
Routine for plotting both current limits vs m: cttab = Table[ (ctab[[i,lJJ,ctab[[i,2J]}, {i,steps}l ; gct = ListPlot[cttab, PlotJoined -> True, AxesLabel -> {"m","current limits ctO & cIO"}, PlotStyle -> {RG~Color[l,O,Ol), DisplayFunction -> Identity ] ; cltab = Table[ {ctab[[i,lIl,ctab[[i,311}, {i,steps)l ; gcl = ListPlot[cltab, PlotJoined -> True, AxesLabel -> {"m","current limits ctO & clO"}, PlotStyle -> {RGBColor[O,l,O]), DisplayFunction -> Identity ] ; graf := Show[gct,gcl, DisplayFunction ->$DisplayFunction] ;
IILC. -1-
table m
ct
cl
2.
0.0652
0.0395
2.5
0.0434
0.0578
3.
0.0279
0.0744
3.5
0.0165
0.0893
4.
0.00793
0.103
a = 0.1
graP;
c u r r e n t limit 0.0
0.0 0.0
0.0
o
CURL1 Mode 2 - varv aDerture. search on m for (ct - c1== 0.). rfqaemvar = (resetrfq; type = rfq; injenergy = .OS; energy = wg; curamp = ,OS; freq = 425. ; him = 1,0073 ;q = 1 ;cayt = J 4 ;cay1 = 8 4 ;field = 35.8; phis[rfq] = -35.; a[rfq] =.; em[rfq] =.; bmrad = .S*renbar; bmlen = .S*bzO;tfac =.; lfac =.; runrfq; ) Unset::norep: Assignment on a f o r a[rfql not found.
Unset::norep:
Assignment on ern for em[rfql not found.
Select initial value for aperture, step size and number of steps; solve ct - cl = 0 for m, make table and graphs:
OfflFindRoot::precwarn] (* Select independent variable and number of steps: *)
indepvar = {a[rfq] -r 0.05 + .05 i} ; steps = 5 ; indepvarrules = Flatten[ Table[ indepvar, {i,steps}] ] ;
1II.C. -2-
(* Specify or solve for dependent variables: result in form of substitutionrules: *)
depvarrules = Flatten[ Table[ FindRoot[ ctO c10 == 0. /. indepvar,{em[rfq],{2.4,2.5)) {i,steps)l 1
-
{em[rEql -> 2.306, em[rfql -> 1.850,
tabrules = Thread[{indepvarrules,depvarrules)] ;
1,
em[rfql -> 1.608, em[rfq] -> 1.461,
tab = Table[{a[rfq], em[rfq], ctO} /. tabrules] ; table := (Print["Aper m CurLim ctO=c10"] ; N[TableForm[tabl,3] ) ; mplol;= Table[ {tab[[i,l]l,tab[[i,211), {i,steps}l ; mgra!! := ListPlot[mplot, PlotJoined -> True, AxesLabel -> {"aperture","m"}, PlotStyle -> {RGBColor[l,O,Ol)l ; cplot = Table[ {tab[[i,lIl,tab[[i,311), {i,steps}l ; cgraf := ListPlot[cplot, PlotJoined -> True, AxesLabel -> {"aperture","current limit ctO=cIO"}, PlotStyle -> {RGBColor[l,O,Ol)l ; table Ape r
m
C u r L i r n ctO=c10
0.1
2.31
0.051
0.15
1.85
0.075
0.2
1.61
0.0922
0.25
1.46
0. 103
0.3
1.37
0.3.09
1II.C. -3-
em[r
mgraf;
m
cgraf;
currenb
1II.C. -4-
o
Exmple: JAERIBHI DTL (* Reset, execute this Specify list, and the dtl formulas: *)
dtlSHIJAER1 = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 2. ; curamp = 0,100 ; freq = 270.; him := 1,0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgapldtl] =.; eO[dtl] = 3.; gapobl[dtl] = 0.2; phis[dtl] = -30.; ifocus[dtl] = mag; filfac[dtl] = .5; mult[dtll = 1; field = .5735; a[dtll = 1.0 ; bmrad = rmsr*N[Sqrt[S.ll ; bmleln = rmsl*N[Sqrt[5.31 ; (* bmrad is total transverse beam radius; bmlen is total longitudinal beam radius. rmsr and rmsl are the rms radii, for a uniform beam particle distribution. *) rmsr = a[type]/tfac ;(* transverse rms beam ellipsoid radius (rmsr); defined here as ratio of aperture to transverse "stay-clear'' or "aperture ratio" factor. *) rmsl = bzO/lfacO ;(* rms longitudinal beam ellipsoid radius; defined here as zero current longitudinal phase acceptance to longitudinal aperture ratio. *) tfac =.; lfac0 =.; lfac = bdrmsl ; rundtl; )
Unset::norep: Assignment on vgap for vgap[dtll not found.
{type,energy,curamp,freq,him,q,phis[dtll,cayt,cayl,field,rmsr,rmsl,dtltype,a[dtll, voltage,vgap[dtl],eO[dtll,ifocus[dtll,gapobl[dtl],filfac[dtll,mult[dtl]} { d t l , 2., 0.1, 270., 1.0073, 1, -30., 0.84, 0.84, 0.5735,
0.603172
-------lfacO
I
1.
----, tfac
alvarez, l., grad, 0.161337, 3., mag, 0.2, 0.5, 11
(* Lists of the basic DTL quantities: *)
{v[dtl],em[dtll,t[dtll,aa[dtll,xx[dtll,transf[dtl],eO[dtl], b [dtl],del[d tll,egap[dt I]} {0.112078, 1.61914, 0.935489, 0.835721, 0.900316, 0.781808, 3 . , 5.29202, 0.318064, 12.5358) { b sm d, b ot p s q ,ga m mam ,g a mm a p ,psi}
{0.0366292, 0.134048, 3.91808, 6.7197, 1.30961
1II.C. -5-
(* Quantities at the current limits. In a DTL,the quad field B and the accelerating gradient e0 are independent, so ct does not have to equal cl. *)
{renbar,bzO,paO, ffaO, sigOt,xmui,siosO,sigOl,sigla, siglosig01a,ctO,c10,ez,a0tn,atn,aln}
I0.873838, 0.603172, 0.691727, 0.481886, 10.9657, 4.38628, 0.4, 45.6978, 18.2791, 0.4, 0.104821, 0.978625, 2.43047, 0.659498, 0.263799, 0.52602)
(* Note that the current limit ct = only 100 mA, indicating that the quad strengths are too low. The zero current phase advance should be up around 60 degrees at least. The cl = 977 mA comes from the e0 = .03 MeV/cm, giving sigOl = 46 deg, which looks all right. So, leave the field as a variable, and solve for what it should be to give sigOt = 60. *)
field =. ; rundtl ; FindRoot[ sigOt == 60., {field, l.O)] {field -> 1.145351
(* Plug it in and run again: *) field = 1.14535 ; rundtl ;
(v[ d tl1,em [dtl], t[d tl] ,aa[d tl] ,xx[dtl], transf[ d tll,eO[dtl], b [dtll,del[dtll,egap[dtll} (0.223833, 0.810738, 0.935489, 0.835721, 0.900316, 0.781808, 3., 10.5688, 0.318064, 12.53581
{bsmd,botpsq,gammam,gammap,psi}
{1.09663, 0,267711, 0.512076, 1.53465, 1.73116}
{renbar,bzO,paO, ffa0, sigOt,xmui,siosO,sigOl,sigla, siglosig01a,ctO,c10,ez,a0tn,atn,aln}
(0.760031, 0.603172, 0.795307, 0.419125, 60.0002, 24.0001, 0.4, 45.6978, 18.2791, 0.4, 2.1175, 0.85117, 2.43047, 2.72979, 1.09192, 0.52602}
(* Quantities for the beam. To find out how much the beam size can be reduced for tune depressions of 0.4, tfac and lfac0 were introduced into the equations for rmsr and rmsl, and solved for in the following. The lfac with the reduced longitudinal acceptance width is found later -- if it is used directly in FindRootn, an infinite recursion occurs. (At first, logical tests were involved and the secant method had to be used. It took some fiddling by plugging in numerical values for tfac and lfac to get starting values close enough for convergence. This was easily done using the list below: (rmsr, rmsl,....) /. (tfac -> (value), lfac -> (value). Later, this was changed so the more robust Newton’s Method could be used. ) *)
IILC. -6-
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, sigliosigOl,et,el,etn,eln,sigt/sigl,rrnsl/rmsr} /. {tfac -> 9.2,lfacO -> 3.4) (0.108696, 0.177404, 1.63559, 0.2038, 60.0002, 26.2594, 0.437655, 45.6978, 24.4607, 0.535271, 0.00187027, 0.00464075, 0.000122178, 0.000304458, 1.07353, 1.63211)
facs = FindRoot[{sigtosigOt == 0.4, siglosig01 == 0.4}, {tfac, {9,2,9.4} 1 , {IfacO, {3.3,3.4 1 1 I { t f a c -> 9.09887, lfacO -> 3.70961
(* The factors tfac ~ - 9 . and 1 lfac0 -> 3.7 are the "stay-clear" factors = (aperturehms beam radius) and (longitudinal zero-current acceptanceradius/ beam rms bunch length. *)
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,eln,sigt/sigl,rmsl/rmsr} /. facs {0.109904, 0.162598, 1.48261, 0.224829, 60.0002, 24.0001, 0.4, 45.6978, 18.2791, 0.4, 0.00174756, 0.00291326, 0.000114162, 0.000191126, 1.31298, 1.47946) (* What is the equipartitioned case when transverse tune depression sigt = 0.4? *)
{rmsr,rmsl,p, ff, sig0t,sigt,sigtosig0t,sig0l,sigl,siglosigOl, et,el,etn,eln,sigt/sigl,rmsl/rmsr} /. {tfac ->9.2, lfac0 -> 3.4) I0.1.08696, 0.177404, 1.63559, 0.2038, 60.0002, 26.2594, 0.437655, 45.6978, 24.4607, 0.535271, 0.00187027, 0.00464075, 0.000122178, 0.000304458, 1.07353, 1.63211)
faczr = FindRoot[{sigtosigOt == 0.4, sigt/sigl == rmslhmsr }, {tfac, {9.2,9.31 1 , {lfaco, {3.3,3.41 { t f a c -> 9.04572, lfacO -> 3.780981
1 1
sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,eln,sigt/sigl,rmsl/rmsr} /. facs
{rmsr,rmsl,p, ff,
IO.I.10549, 0.159528, 1.44612, 0.230502, 60.0002, 24.0001, 0.4, 45.6978, 16.6316, 0.363947, 0.00176816, 0.00255153, 0.000115508, 0.000167394, 1.44305, 1.44305)
1II.C. -7-
(* bunch length radius in degrees of rf phase: *) phrad =bmlen 360. / (100.*betalam) /. facs
17.742
The synchronousphase angle is -30 degrees; lfac indicates that the phase half-width of the input bunch should be 17.9 degrees -- this shows why it is hard to achieve equipartitioning across a frequencyjump, because for efficiency reasons, we usually want to make the jump at as low an energy as possible, resulting in a nearly full phase bucket at (*
the transition. One way to get around this problem, in terms of avoiding emittance growth, is to use as much focusing as possible and try to get the zero current phase advances up. If the tune depressions are above 0.4, there won't be much emittance growth due to equipartitioninganyway. *)
0
Examde - FMIT 80 MHz case, dtlFMIT = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 2. ;curamp = 0.100 ;freq = 80.; him = 2.0073 ;g = 1 ; cayt = 0.84 ;cay1 = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] = 2.; gapobl[dtl] = 0.2; phis[dtll= -35.; ifocus[dtl] = mag; filfac[dtl] = .5; mult[dtl] = 1; field = .767963 (*Tesla*); a[dtl] = 2.5 ; bmrad = rmsr*N[Sqrt[S.]] ; bmlen = rmsl*N[Sqrt[5.11 ; rmsr = a[type]/tfac ; rmsl = bzOhfac0 ; tfac =.; lfac0 =.; lfac = bdrmsl ; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtll not found.
{v[dtl],em[dtl],t[dtl]~a[dtl],xx[dtl],transf[dtl],eO[dtl], b[dtl],del[dtll,egap[dtl]}
(0.266002, 1.07085, 0.935489, 0.822373, 0.900316, 0.769321, 2., 11.499, 0.582946, 8.22373)
{renbar,bzO,paO, ffa0, sigOt,xmui,siosO,sigOl,sigla, siglosigOla,ctO,c10,ez,aOtn,atn,aln}
(1.85212, 1.68376, 0.910069, 0.366272, 59.8663, 23.9465, 0.4, 61.866, 24.7464, 0.4, 1.65512, 1.5291, 1.53262, 4.78744, 1.91497, 1.63901)
'
Evaluate performancefor normalized transverse emittance em = 1.0 cm.mracV1000 = cm.rad, and requiring equipartitioning: *)
1II.C. -8-
facs
:
FindRoot[ { etn == 1.0/1000 , eln/etn == gamma*rmsl/rmsr {tfac,5),{lfac0,4,} ]
},
{tfac: -> 5.88963, lfacO -> 4.116743
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,eln,el/et, rmsl/rmsr} 1. facs
I0.424475, 0.409004, 0.964583, 0.345573, 59.8663, 47.6152, 0.795359, 6L866, 49.3635, 0.797911, 0,0216148, 0.0208048, 0,001, 0.000964583, 0.962523, 0.963552 I
0
ExmtAe - 425 MHz case
dt1425 = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 2. ;curamp = 0.100 ;freq = 425.; him = 1.0073 ;q = 1 ; cayt = 0.84 ;cay1 = 0.84 ; voltage = grad; vgap[dtll =.; eO[dtl] = 5.; gapobl[dtll = 0.2; phis[dtl] = -40.; ifocus[dtll = mag; filfac[dtl] = S;mult[dtl] = 1; field =: 1.8 (*Tesla*); a[dtll = 0.5 ; bmratl = rmsr*N[Sqrt[S.l] ; bmlen = rmsl*N[Sqrt[5.]] ; rmsr ::a[typel/tfac ; rmsl =: bzO/lfacO ; tfac =.; lfac0 =.; lfac = bdrmsl ; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtll not found.
{renbar,bzO,paO, ffa0, sig0t,xmui,sios0,sig0l,sigla, siglosigO1a,ctO,c10,ez,aOtn,atn,aln} { O .3!j106, 0.510922, 1.45847, 0.22855, 77.7973, 31.1189, 0,4, 53.3158, 21.3263, 0.4, 1.88934, 1.49758, 3.58313, 1.18869, 0.475474, 0.693131
II1.C. -9-
(* Can handle transverse normalized rms emittance = 0.015 if equipartitioned at 100 mA and longitudinal tune depression is 0.4: *) { siglosigol == .4 , eln/etn == gamma*rmsYrmsr }, {tfac,7) ,{lfacO,5) 1
facs = FindRoot[
(tfac -> 8.58944, lfacO -> 5.26908)
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,etnrms,eln,curamp, eln/etn, gamma*rmsYrmsr}
/. facs
(0.058211, 0.0969662, 1.66932, 0.199682, 77.7973, 35.6005, 0.457605, 53.3158, 21.3263, 0.4, 0.00114468, 0.00190273, 0.0000747763, 0.0000149557, 0.000124829, 0.1, 1.66932, 1.66932)
(* What is current if equipartitioned,and rms beam radius is 1/5th of bore, and longitudinal tune depression = 0.4 ? Answer is 507 mA, with etnrms = 0.044 cmmad. *)
dt1425 = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 2. ;curamp =. ;freq = 425.; him = 1.0073 ;q = 1 ; cayt = 0.84 ;cay1= 0.84 ; voltage = grad; vgaprdtll =.; eO[dtlI = 5.; gapobl[dtll = 0.2; phis[dtl] = -40.; ifocus[dtll = mag; filfac[dtl] = .5; mult[dtl] = 1; field = 1.8 (*Tesla*); a[dtl] = 0.5 ; bmrad = rmsr*N[Sqrt[S.l] ; bmlen = rmsl*N[Sqrt[S.]] ; rmsr = a[type]/tfac ; rmsl = bzOhfac0 ; tfac = 5.; lfac0 =.; lfac = bdrmsl ; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtl] not found.
facs = FindRoot[ { elnletn ==gamma*rmsVrmsr , siglosigol == .4 }, (curamp, .400}, (* Newton's method*) {lfacO,3} ]
(curamp -> 0.506973, lfacO -> 3.067181
1II.C. -10-
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,etnrms,eln,curamp, eldetn, gamma*rmsl/rmsr}
/. facs
(0.1, 0.166577, 1.66932, 0.199682, 77.7973, 35.6005, 0.457605,
53.3158, 21.3263, 0.4, 0.00337813, 0.00561521, 0.000220681, 0.0000441363, 0.000368388, 0.506973, 1.66932, 1.669321
(* How small can etnrms be, at current = 100 mA, when the transverse tune depression is 0.4 and we let the whole longitudinal acceptance width phis be filled -- maybe "typical" for a frequency jump... Answer is etn = ,006;tfac is 12.5 -- large. Emittance would probably grow from equipartitioning, unless acceleration rate is fast enough. *)
curamp = ,100 ; tfac =.; rundtl[] ; facs = FindRoot[
== 0.4 , bmlen == bzO }, {tfac,ll},{lfac0,2} I
{ sigtosigot
{tfac -> 12.528, lfacO -> 2.236071
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglooigOl,et,el,etn,etnrms,eln,curamp, eldetn, gamma*rmsl/rmsr}
/. facs
(0.0399107, 0.228491, 5.73727, 0.0580997, 77.7973, 31.1189, 0.4, 53.3158, 47.0677, 0.88281, 0.000470353, 0.0233175, 0.0000307265, 0.00000614531, 0.00152976, 0.1, 49.7862, 5.73727)
(* Find current for transverse tune depression of 0.4,and etnrms = .02 *)
curamp =. ;bmlen = bzO ;rundtl ; { sigtosigOt == 0.4 , etnrms == .02/1000 }, {tfac,6}, {curamp, .3} I
facs = FindRoot[
(tfac -> 6.94444, curamp -> 0.342435)
lfac0 = bzO/bmlen; {rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,etnrms,eln,curamp, eln/etn, gamma*rmsl/rmsr}
/. facs
I0.072, 0.510922, 3.18025, 0.104813, 77.7973, 31.1189, 0.4, 53.3158, 40.6453, 0.76235, 0.00153077, 0.0201358, 0.0001, 0.00002, 0.00132102, 0.342435, 13.2102, 7.11126} 1II.C. -11-
At 20 MeV, current of 0.1 A, eO[dtl] = 2 MeV/m, phis = -30, set a[dtl] = betalambdd9, and the transverse aperture ration tfac = 9. (tfac and lfac pertain here to the ratio of apertures to total beam radius.) Using equations, require the normalized rms beam emittance to be 0.1 cm.mrad, and the longitudinaltune depression to be 0.4 (i.e. no less than 0.4 is desired.). Solve for the required magnet field and the longitudinal aperture ratio, 1facO.
dtlSHIJAER1 = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 20. ; curamp = 0.100 ; freq = 400.; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgapidtll =.; eO[dtl] = 2.; gapobl[dtll = 0.2; phis[dtl] = -30.; ifocus[dtll = mag; filfac[dtll = .5; mult[dtl] = 1; field =.; a[dtl] = 100*betalam/9 ; bmrad = a[type]/tfac ; bmlen = bzO/lfacO ; tfac = 9.; lfac0 =.; lfac = bzhmsl ; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtl] not found.
Test of ellipsoidal form factor approximation. This was done with tfac and lfac pertaining to the ratio of apertures to total beam radius, and before the relativistic gamma factors were added. and before some other changes were made, so the numbers will not reproduce exactly. With the full functional form for the ellipsoidal form factor:
frequency 400 300 200
field .846 .623 .43
sigOt 40.5 39.1 39.5
With bmrad/(3*bmlen) form factor: 400 300 200
.841 .622 .433
40.3 39.1 39.7
sigtosigOt .58
lfac 2.16 .45 2.46 .30* 2.96 * below 0.4, thus not desirable. .58 .45 .296*
2.12 2.45 3.00
FindRoot[ sigOt == 90., {field, l.O}] {field -> 1 . 8 5 2 7 7 )
I1I.C. -12-
(* This statement was useful in getting the two starling values needed for the FindRoot secant method when the full ellipsoid form factor function was being used. However, had to be fairly close to the solutions before the FindRoot would work *) {bmrad,bmlen,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,eln} 1. {field -> .84, lfac -> 2.5)
FindRoot[[ em == 0.1 , siglosigol == 0.4 } , [ field, (.85,.84)), [ IfacO,(2,2.1)] 3 (* Wirh the rmsr/(3*rmsl) form factor, the Newton's method is now more robust: *) facz = Chop[FindRoot[{etn == 0.1/1000, siglosigOl == 0.4 }, { field, .5 ),{ lfac0, 11 I ,10A-4]
I':eld
-> 0.85598, lfacO -> 2.11213)
(bmrad,bmlen,p,ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,etn,eln) /. facz
(0.188051, 0.60098, 3.26394, 0,102126, 40.2109, 23.7794, 0.591367, 16.8745, 6.7498, 0.4, 0.000481769, 0.00139668, 0.0001, 0.000302396}
{renbar,bz,pa, ffa, sigOt,xmui,siosO,sigOl,sigla, siglosiigOla,ct,cl,ez,aOtn,atn,aln}/. facz I1.43318, 0.304643, 0.217095, 1.53543, 40.2109, 16.0843, 0.4, 16.8745 6.7498, 0.4, -6.37783, 0.195834, 1.62031, 9.82185, 3.92874, 1.34902
o
Makeatable with indetxndent variable and parameter. and plot praphs dtlGEN = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 20. ;curamp = 0.100 ;freq =.; him = 1.0073 : q = 1 : cayt = 0.84 ;cay1 = 0.84; voltage = grad; vgapidtl] =.; eO[dtlI I.; gapobl[dtll = 0.2; phis[dtll = -30.; ifocus[dtll= mag; filfac[dtl] = .5; mult[dtl] = 1; field =.; a[dtl] = 100*betalam/9 ; bmracl = a[dtll/tfac ;bmlen = bzO/lfacO ;tfac = 9; lfac0 =.; lfac = bz/rmsl; rundtl; )
Unset::norep: Assignment on vgap for vgap[dtl] not found. Unset::norep: Assignment on e0 for eO[dtlI not found. (* Finding roots takes some time, but once they are found, filling in the table is fast, so it is efficient to make a table of as many things as you might want to study. *)
1II.C. -13-
tab1 = Table[ ( eO[dtl] = j; rundtl; N[ ( eO[dtl],freq,field,sigOt,sigtosigOt,sigl,lfacO)] /. Chop[FindRoot[ ( etn == 0.1/1000 , siglosigOl == 0.4 ) , ( field, .5 ), ( lfac0, 1 ) 3 , 10"-4 1 ) (j,2,4,1),(freq,100,800,100)1 I
FindRoot::convNewt: Newton's method failed to converge to the prescribed accuracy after 1 5 iterations. { { {2.,
loo.,
0.24549
+
0 . 0 0 5 1 9 2 5 6 I, 41.7862
0 . 1 0 8 0 4 4 t 0 . 2 7 6 6 3 6 I, 1 3 . 4 9 9 6 ,
+
1 . 1 7 1 9 6 I,
4.224261,
{2.,
ZOO.,
0.438059,
39.4752,
0.301194,
9.54566,
{2.,
300.,
0.631197,
38.8693,
0.458833,
7.794,
2.43888},
(2.,
400.,
0.85598,
40.2109,
0.591367,
6.7498,
2.112131,
{2.,
500.,
1.12624,
42.8401,
0.693841,
6.03721,
1.88915},
{2.,
600., 1 . 4 4 9 9 8 ,
46.3542,
0.769489,
5.51119,
1.724551,
{2.,
700.,
{2.,
EOO., 2.27298,
55.0463,
loo.,
+
{(3.,
0.137446
1.8315,
50.4837,
0.264593
+
0.824303,
5.10237,
0.863977,
0.00907094
0 . 4 2 5 5 3 5 I, 16.5336,
1.59662},
4.77283,
1.4935}},
I, 42.858 t 2 . 1 5 1 4 3 I, 5.17364},
t3.1
ZOO., 0.482722,
42.5546,
0.279398,
11.691,
(3.,
300.,
0.687867,
41.6533,
0.428166,
9.54566,
(3.1
400.,
0.920357,
42.665,
{3.,
500.,
1.19479,
44.9759,
0.660891,
7.39404,
I3.r
600.r
1.52017,
48.2051,
0.739943,
6.7498,
{3.,
700.,
1.9017,
{3.,
EOO.,
2.34221,
52.0902,
{{4., loo., 0 . 2 8 1 0 4 9 0.125773
+
0.497718
56.4473,
+
0.55735,
0.798881, 0.842533,
0.00890678
I, 19.0913,
2.987},
8.26678,
6.2491, 5.84549,
3.65832}, 2.9871,
2.586821, 2.313721, 2.11213},
1.955451, 1.82916}},
I, 4 3 . 5 5 9 t 2 . 2 0 7 7 8 I, 5.974011,
1II.C. -14-
{4., 200.,
0.517748,
44.7782,
0.265524,
13.4996,
4.22426},
{4.,
300.,
0.732625,
43.7203,
0.407923,
11.0224,
3.4491},
{4.,
400., 0.971703,
{4.,
500.,
1.25004,
46.6203,
0.637581,
8.5379,
{4.,
600.,
1.57728,
49.6491,
0.718423,
7.794,
{4., 700.,
1.95926,
53.3567,
0.779918,
7.21585,
{4.,
2.39933,
57.5611,
0.826229,
6.7498,
800.,
44.524,
0.53408,
9.54566,
2.9871, 2.671661, 2.438881, 2.25796}, 2.112131}1
(* This graphics command is quite powerful, affording many options and deep nests -- see other examples in following sections. There are imaginary solutions at frequency = 100, so plot is from 200. *)
For[h=3, hc8, h++, (* a plot for each table column *) Forlid; pltlist = {}, jc4, j++, (* plot each parameter *) For[k=2; blist = {>,kc9, k++, (* at each value of x-axis *) blist = Append[ blist,{tabl[~,k,211,tabl[~,k,hll~11 ; pltu] = Listplot[ blist, PlotJoined -> True, DisplayFunction -> Identity I; pltlist = Append[ pltlist, pltul I 1 ; Show[pltlist,DisplayFunction -> $DisplayFunction] I
(* field; when em == 0.1 and siglosigol == 0.4 *) (* parameter is eO[dtl] = 2 , 3 , 4 MeV/m *)
1.
0.
IILC. -15-
(* sig0t; when em == 0.1 and siglosigOl == 0.4 *)
57 .5-
5 5.5 2 . 5-
5 04 7 .5--
7
v
w 4 0 0
500
600
(* sigtosigot; when em == 0.1 and siglosig01 = 0.4 *)
0. 0.
0. 0.
0.
(* sigl; when em == 0.1 and siglosig01 == 0.4 *)
1II.C. -16-
700
800
(* lfac:; when etn == 0.1 and siglosigOl == 0.4 *)
3.
2.
1.5t
o
M:inimum ellipse beta vs transverse
advance?
Is there an optimum transverse phase advance giving a minimum ellipse beta, and by implication a maximum tfac? Mittag's more accurate formulas suggest there is -- see RAJ BigLog pp.12-13. Wangler's approximations say there won't be - see Eq.( ). Result here does not show a minimum. dtlGIZN = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 20. ;curamp = 0.100 ;freq = 200.; him =: 1.0073 ;q = 1 ; cayt := 0.84 ;cay1 = 0.84 ; voltage = grad; vgap[dtll =.; eO[dtl] =.; gapobl[dtll = 0.2; phis[dtl] = -30.; ifocus[dtl] = mag; filfac[dtll = .5; mult[dtl] = 1; field =.; a[dtl] = 100*betalam/9 ; bmrad = rmsr*N[Sqrt[S.]] ; bmlen = rmsl*N[Sqrt[5.]] ; rmsr = a[type]/tfac ; rmsl = b d 2 . 5 ; tfac =:.; lfac0 =.; lfac = bdrmsl; rundtl; )
Unset::norep: Assignment on vgap for vgap[dtll not found. Unset::norep: Assignment on e0 for eO[dtll not found.
j =.; k =.;
II1.C. -17-
tab1 = Table[ ( eO[dtl] = j; rundti; N[{sigOt,tfac,gammap}] /. Chop[FindRoot[{ etnrms == 0.1/1000 , sigOt == 20 + (k-1)*10 } , { field, .5 1, { tfac, 1 1 I
, 10*-4 1 ,
GA4J},{k,1,81 1 { {
{ZO., 10.3966, 3.484041, {30., 13.1891, 2.461261, (40., 15.4977, 1.962631, (50., 17.5758, 1.670261, {60., 19.4049, 1.47981, { 7 0 . ,
21.0785, 1.347051,
{EO., 22.6303, 1.250141, (go., 24.0836, 1.177)1, {
{20., 10.3969, 3.548681, (30., 13.1905, 2.495611, (40., 15.501, 1.98391, (SO., 17.576, 1.684781, (60., 19.4051, 1.49039), (70., 21.0789, 1.355171, { 80.,
22.631, 1.256591 , {go., 24.0844, 1.182271 1 ,
((20., 10.3971, 3.608471, {30., 13.1919, 2.528381, {40., 15.5044, 2.004541, {SO., 17.5299, 1.699), {60., 19.4054, 1.50083), (70., 21.0793, 1.36321, {
80., 22.6315, 1.26299), (90., 24.085, 1.18751)} }
1II.C. -18-
c
0
h
e
e
p
Use ccldsn AT1 AFT32 20.6MEV- DESIGN OUTPUT,and ccldyn AT1 APT32 DYN. OUT.-MATCHED runs by R. Garnett, 14 Sept 1989, for an APT linac from 20.6-1600 MeV, 700 M'Hz, 250 mA linac, in which the transverse zero-current phase advance is held constant at -71 degrees. We test this, letting the filfac[dtl] = 0.5 because we are just going to solve for any field number that gives a sigOt = 71 degrees. ccldyn's calculation of zerocurrent longitudinalphase advance is over one tank,instead of over the transverse focusing period, so column is multiplied by two here. Definition of tfac here does not include flutter factor.
CCLDYN RESULTS:
Sect J k L
1 3 6 7
Tank Energy eOt zt*2 4s hp ql decl oOt J O . MeV 0 20.6 2.5 12.9 -60 7.30 5.8 1.5 70.9 439 160 1.5 27.5 -40 4.40 8.2 1.0 70.5 796 500 1.25 38.6 -40 2.56 8.6 1.0 70.3 '1122 1000 1.2 44.1 -40 2.36 8.6 1.0 70.2 1291 1300 1.2 45.6 -40 1.86 11.1 1.0 70.2 1456 1600 1.2 46.6 -40 1.86 11.1 1.0 70.2
-
Energy MeV 20.6 160 500 1000 1300 1600
a01 rmsx rmsy rmsr &t,rms,net100%,n cm cm-mrad 30.4 .1197 .0626 .0866 .0257 .139 16.2 .0663 ,1061 .0839 .0265 ,316 15.0 .1368 .0719 .0992 .0277 .370 10.6 .1250 .0664 .0911 .0291 .393 8.4 .lo98 .0571 .0792 .0296 .434 6.8 .lo36 ,0554 .0758 .0302 .451
rmsl &l,rms,n el,100% a0 tfac lfac0 dee- cm MeV-dep bS/rmSl 9.85 .7&2 .384 2.045 1.4 16.2 6.1 8.685 6.33 .391 .655 3.5 33 6.3 4.21 379 1.021 44.7 3.5 35.3 9.5 3.47 361 1.268 37.9 3.5 52.7 11.5 3.5 44.2 13.1 3.06 330 1.340 47.2 2.82 311 1.351 3.5 46.2 14.2 18.8
Et.100VC ~1.100%
et.rms 5.4 11.9
e1,rmg 5.32 13.3
13.5
29.9
14.9
13.9
LINACS RESULTS from runs below; asking for a field giving the Same oOt, and solving for the ccldyn values of etrms,n and d,rms,n from the above table, to see how well various other quantities agree: Energy aOt at
20.6 160 1000 1600
70.9 70.5 70.2 70.2
42.7 46.3 56.9 61.3
a
sot .60 .66 .81 .87
a01 01 d 29.4 9.0 20.8 7.0 10,3 4.2 6.7 2.5
l .31
.34 .41 .38
rmsr rmsl u]1sI yrmsl sr .085 ,249 2.93 3.0 ,098 .380 3.88 4.5 ,085 ,357 4.18 8.6 .072 .317 4.32 11.6
tfac lfac0 lfac rmsl2 16.5 35.7 41.0 47.8
5.9 0.84 6.5 1.1 11.7 2.9 .3 14.0 3.1 .26
pt
a1 4.7 6.6 13.5 24.0
& etq 1.82 2.28 10 14.3
The: agreement is very good. The ellipsoid shape ratio yrmsllrmsr in the rest frame is large; the exact form for the form-factor when p > 1 was used here. Using the matched beam equations at each energy is seen to take care of the damping from the acceleration, as would be expected. This also indicates that the acceleration is mild. The equiprwtitioningfactors are tracking, but are not exactly equal; the beam is approximatelyequipartitioned, however. If we use the matching equations to predict the final longitudinal beam radius, rmsl2, from rmsll at 160 MeV, taking into account a growth in longitudinal rms emittance of about 2, we get: rmsl2 = Sqrt[(~lrms2/~lrms 1)(o11/o12)(y1/y2)*31 rmsll
1II.C. -19-
Also check the equipartitioning asymptotic emittance growth, assuming no contribution from non-uniform field energy: elfinal/elinitial= SqrtE1 - 2*(pinitial- 1)/(3*pinitial)] etfinal/etinitial= SqrtE1 + @initial - 1)/3] where pinitid= = ( (elrms)Y/(etrms)Y)) ( rmsrA2/rmslA2)
Using the CCLDYN numbers at 160 MeV for initial (the ratio is eln/em from here) and 1600 MeV for final: pinitial= ((1.82)*(.0839/.391))"2 = .152 elfinal = 2.16 elinitial = 2.16 ,655 = 1.41, compared to 2.06 ,655 = 1.35 from the CCLDYN run. etfinal = 0.85 etinitial, compared to 1.14 etinitial in the CCLDYN run. cclAPT = ( resetccl; type = ccl ; ccltype = sc; cellspercav = 2; lqibetalam = 1.5; energy = 20.6 ; curamp = 0.250 ; freq = 700; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgap[ccll =.; eO[ccl] = 1.; gapobl[ccl] = 0.2; phis[ccl] = -60 ; ifocus[ccl] = mag; filfac[ccl] = S;mult[ccl] = 1; field =.; a[ccl] = 1.4 ; bmrad = rmsr*N[Sqrt[S.lI ; bmlen = rmsl*N[Sqrt[S.ll ; rmsr = a[ccl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bdrmsl; runccl; ) (* NOTE:could not let rrnsl = bzbfac because this is recursive with definition of bz, which depends on sigl. So compute bz after sigl is found and then get lfac. *) Unset::norep: Assignment on vgap for vgap[ccll not found.
gamma 1.02195
FindRoot[sigOt == 70.9,{field,.5}] (field -> 0.6029161
field = 0.602916; runccl
facs = FindRoot[{etnrms*lOOO == 0.0257, elnmdrms == ,3842 }, {tfac,{l5,l6}},{lfac0,{5,6}}1 (tfac -> 16.464, lfacO -> 5.91109)
1n.c. -20-
N[ {sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,etn* 1000,etnrms* 1000,el,eln,elnmd,elnmdrms, elnms,elnmsrms,sigt/sigl,rmsl/rmsr,rmsl,rmsr,tfac,lfacO,lfac}]/. facs (70.9,
42.671,
0.1285,
0.601847,
0.0257,
0.0000015246,
29.4376,
0.00110686, 4.723,
2.92771,
9.03472,
0.00024356, 0.248955,
0.306911, 1.921,
0.000609895,
0.3842,
0.0850339,
16.464,
0.835188 1
cclAl'T = ( resetccl; type = ccl ; ccltype = sc; cellspercav = 6; lqibetalam = 1.; energy = 160 ; curamp = 0.250 ; freq = 700; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgaplccll =.; eO[ccl] = 1; gapobl[ccl] = 0.2; phis[ccll =: -40 ; ifocus[ccll = mag; filfac[ccll = .5; mult[ccll = 1; field =.; a[ccl] = 3.5 ; bmrad = rmsr*N[Sqrt[S.]] ; bmlen = rmsl*"[Sqrt[S.]] ; rmsr = a[ccl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bdrmsl; runccl; ) Unsat::norep: Assignment on vgap f r vgap[
11 not found.
gamma 1.17052
FindRoot[sigOt == 70.5,{field,.S}] {field
->
0.2607421
field = 0.260742; runccl facs = FindRoot[{etnrms*lOOO == 0.0265, elnmdrms == 0.6551, {tfac,{30,32}},{lfaco,(5,6}}1 (tfiic -> 35.7089,
lfacO -> 6 . 5 0 7 7 )
N[ {sigO t,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,etn*lOOO,etnrms* lOOO,el,eln,elnmd,elnmdrms, elnms,elnmsrms,sigt/sigl,rmsl/rmsr,rmsl,rmsr,tfac,lfacO,lfac~l /. facs
1II.C. -21-
0.00000762302, 5.91109,
t70.4999, 46.2614, 0.656191, 20.8488, 7.03765, 0.337557, 0.000217794, 0.1325, 0.0265, 0.00049815, 0.00041523, 3.275, 0.655, 0.000012996, 0.00000259921, 6.57341, 3.87751, 0.380053, 0.0980148, 35.7089, 6.5077, 1.11227 }
cclAPT = ( resetccl; type = ccl ; ccltype = sc; cellspercav = 10; lqibetalam = 1.; energy = 1000 ; curamp = 0,250 ; freq = 700; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgap[ccl] =.; eO[ccl] = 1; gapobl[ccl] = 0.2; phis[ccl] = -40 ; ifocus[ccl] = mag; filfac[ccl] = S; mult[ccl] = 1; field =.; a[ccl] = 3.5 ; bmrad = rmsr*N[Sqrt[S.l] ; bmlen = rmsl*N[Sqrt[5.11 ; rmsr = a[ccl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bdrmsl; runccl; ) Unset::norep:
Assignment on vgap f o r vgap[ccl] not found.
gamma 2.06576
beta 0.875021
FindRoot[sigOt == 70.2,{field,.5}] ( f i e l d -> 0.1190341
field = 0.119034; runccl facs = FindRoot[{etnrms*lOOO == 0.0291, elnmdrms == 1.2677 }, {tfac,{l4,15}},{lfac0,{6,7}}1 (tfac -> 40.9892, lfacO -> 11.66241
N[{sigOt,sigt,sigtosigO t,sigOl,sigl, siglosigO1,et,etn*lOOO,etnrms*1000,eI,eln,elnmd,elnmdrms, elnms,elnmsrms,sigt/sigl,rmsl/rmsr,rmsl,rmsr,tfac,lfacO,lfac}] /. facs i70.1998, 56.8911, 0.810416, 10.2804, 4.21176, 0.409689, 0.0000804944, 0.1455, 0.0291, 0.000803645, 6.3385, 1.2677, 0.0000251528, 0.00000503056, 13.5077, 4.18131, 0.357035, 0.0853883, 40.9892, 11.6624, 2.93621)
1II.C. -22-
cclA1’T = ( resetccl; type = ccl ; ccltype = sc; cellspercav = 10; lqibetalam = 1.; energy = 1600 ; curamp = 0.250 ; freq = 700; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgap[ccll =.; eO[ccl] = 1; gapobl[ccl] = 0.2; phis[ccl] = -40 ; ifocus[ccll = mag; filfac[ccll = .5; mult[ccl] = 1; field =.; a[ccl] = 3.5 ; bmrad = rmsr*N[Sqrt[5,]] ; bmlen = rmsl*N[Sqrt[5.]1 ; rmsr = a[ccl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bdrmsl; runccl; ) Unset::norep: Assignment on vgap for vgap[ccll not found.
gamma 2.70521
beta 0.929168
FindRoot[sigOt == 70.2,{fieId,S}] { f i e l d -> 0.1463451
field = 0.146345; runccl facs = FindRoot[{etnrms*lOOO == 0.0302, elnmdrms == 1.3514 {tfac,{l4,20)},~lfacO,{9,10}}]
},
{tfac -> 47.804, M a c 0 -> 13.9793)
N[{sigO t,sigt,sigtosigO t,sigOl,sigl, siglosig01,et,etn*10OO,etnrms*lOOO,el,eln,elnmd,elnmdrms, elnms,elnmsrms,sigt/sigl,rmsl/rmsr,rms~,rmsr,tfac,lfacO,lfac}] /. facs I70.2002, 61.3233, 0.873549, 6.65716, 2.54746, 0.382665, 0.0000600733, 0.151, 0.0302, 0.000856706, 6.757, 1.3514, 0.0000268135, 0.0000053627, 24:.0723, 4.32002, 0.316293, 0.0732156, 47.804, 13.9793, 3.07053 }
1II.C. -23-
Check on auerture factors usinp 4/91 BTA Design
0
Start with H. Yokobori's BTA run, using a Type 8 input - uniform in 3-D. Input transverse un-normalized total emittance, averaged over x & y = 2.55 cm-mrad;normalized = 0.166 cm.mrad. Dividing by 5 yields the normalized tranverse rms emittance = 0.033 cm.mrad. Similarly, for longitudinal, total un-normalized input was 15.2 cm.mrad; normalized = 0.992; divide by 5 gives normalized longitudinal rms emittance = 0.198 cm.mrad. cell 0 Cell 1 Cell 37 PARMILAgives 10.1728 2.00 2,1352 energy 0.1065 0.033 0.0336 tran rms emit 0.198 0.4312 0.4631 long rms emit 6 12.8 4.3 eln/etn 1.02 3.22 tran emit growth long emit growth 2.17 IC- 1.08 ->I 2.34 rms beam radius 0.1697 0.1874 0.3163 ## bore/(rms bm rad) 7.37 6.67 3.95 bore/(rms bm rad*Sqrt[psi] 5.59 5.06 3 .OO - accounts for flutter factor in calculation of transverse aperture factor.
#
Code results below give: tfac lfac0 sigtosigot siglosigOl
9.2 2.5 .5 1
.73
Cell 0 e's Cell 9.5 2.3 .53 .72
1 e's 10.2 1.9 .6 1 .85
Cell 0 e's Cell 37 e's 9.6 6.6 4.1 3.2 .58 .87 .61 .86
The rows marked ## should be equivalent. At the start (Cell 0) of the PARMILA run, one can put anything one likes. This code, however, computes a steady-state matched condition for the beam at the given energy. So there need not be any correspondenceat Cell 0, as there evidently isn't. By Cell 1, the PARMILA beam has changed some, but certainly not to an equilibrium. By Cell 37, the PARMILA aperture factor is smaller than that given by this code. This may be because there is strong emittance growth in this BTA design, as would be expected from the lack of equipartitioning, and the beam has spread and acquired a halo. The calculation of this code used the PARMILA emittances for its targets, but the results are still for a uniform, matched, equilibrium beam. At 10 MeV, a dtl is still too short for an equilibirum to have been reached; but the agreement here is reasonable. This example shows that great caution must be exercised when comparing transient to steady-state cases. (This is not just a comparison of analytical and numerical results. To check the effect of the input distribution shape, four types were run in PARMILA and the resulting emittances used as the target values in this code to get tfac and lfac: Cell 1 - 2.13 MeV Cell 37 - 10.17 MeV uans rms emit lone rms emit $& lfaccQ jran rrns emit lone rms emit b u t TVDe 8 .0336 .4312 10.2 2.3 .lo65 .4631 6.6 3.2 42 .0178 .156 10.3 2.7 .0562 .282 8.3 3.8 S538 .0935 S875 5 .0295 10.7 1.7 7.0 2.9 2 .0224 .2977 .0697 .3334 7.7 3.6 10.7 2.1 It is seen that tfac and lfac are somewhat insensitive to the emittance target.
1II.C. -24-
At the dtl input, Cell 0:
dtISHIJAERI = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 2, ; curamp = 0.100 ; freq = 201.25;
him :L: 1.0073 ; q = 1 ; cayt = 0.84 ; cayl = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] = 2.; gapohl[dtll = 2.328/9.863; phis[dtl] = -30.; ifocus[dtl] = mag; filfac[dtl] = 5.016/9.863; mult[dtl] = 1; field = .7692; a[dtl] = 1.25 ; bmrad = rmsr*N[Sqrt[S.ll ; bmlen = rrnsl*N[Sqrt[5.11 ; rmsr = a[dtl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bzhmsl; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtll not found.
{rmsr,rmsl,sigO t,sigt,sigtosigOt,sigOl,sigl,siglosigOl, etn,eln,elnms,tfac,lfacO,ctO,clO} /. Chop[FindRoot[{ etnrms == 0.033/1000 , elnrms == ,19811000 } , {tfac, 13, {IfacO, 1) I, 10"-4 ]
(0.136058, 0.327809, 59.5878, 30.3767, 0.509781, 42.6448, 31.2528, 0.732864, 0.000165062, 0.000990005, 0.0000309855, 9.18725, 2.46859, 1.75441, 0.6946161 At Call 1:
dtlSHIJAER1 = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 2.1352 ; curamp = 0.100 ; freq = 201.25; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cayl = 0.84 ; voltage = grad; vgapldtll =.; eO[dtlI = 2.; gapobljdtl] = 2,328/9.863; phis[dtl] = -30.; ifocus[dtl] = mag; filfac[dtl] = 5.016/9.863; mult[dtl] = 1; field = ,7692; a[dtl] = 1.25 ; bmrad = rmsr*N[Sqrt[S.l] ; bmlen = rmsl*N[Sqrt[5.]1 ; rmsr = a[dtl]/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bzhmsl; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtlI not found.
1II.C. -25-
{rmsr,rmsl,sigOt,sigt,sigtosigOt,sigOl,sigl,siglosigOl, etn,eln,elnms,tfac,lfacO,ctO,clO} 1. Chop[FindRoot[{ etnrms == 0.0336/1000 , elnrms == 0.4312/1000} , ( tfac, l}, { IfacO, 1 } I, 10"-4 ]
10.123177, 0,452726, 62.2845, 37.824, 0.607278, 41.9463, 35.6686, 0.850341, 0.00016848, 0.00215602, 0.0000674798, 10.148, 1.84668, 1.89413, 0.71108)
At Cell 37:
dtlSHIJAERI = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 10.1728 ; curamp = 0,100 ; freq = 201.25; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgapidtll =.; eO[dtl] = 2,; gapobl[dtll = 6.472l21.585; phis[dtl] = -30.; ifocus[dtll = mag; filfac[dtll = 10.88/21.585; mult[dtl] = 1; field = ,31374; a[dtl] = 1.25 ; bmrad = rmsr*N[Sqrt[S.ll ; bmlen = rmsl*N[Sqrt[S.]] ; rmsr = a[dtl]/tfac ; rmsl = bzO/IfacO ; tfac =.; lfacO =.; lz = bdrmsl; rundtl; ) Unset::norep: Assignment on vgap for vgapldtll not found.
{rmsr,rmsl,sigOt,sigt,sigtosigOt,sigOl,sigl,siglosigOl, etn,eln,elnms,tfac,lfacO,ctO,clO} /, Chop[FindRoot[{ etnrms == 0.1065/1000 , elnrms == 0.4631/1000) , ( tfac, 51, { lfac0, 3 1 3, 10"-4 ]
I0.1904, 0.570377, 56.9056, 49.6224, 0.872012, 27.3018, 23.5255, 0.861682, 0.000532634, 0.0023155, 0.0000724714, 6.56511, 3.17904, 2.87741, 1.52189}
1II.C. -26-
0
. ..
-
Check us-oned run. transverse sgace-charpe factor mt = 0.9.72cells, from 13 Dec 1980 runs. RAJ records, dtlFMIT = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 2. ;curamp = 0.120 ;freq = 80.; him = 2.0073 ;q = 1; cayt =: 0.84 ;cay1 = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] =.; gapobl[dtl] = 0.2; phis[dtl] = -30.; ifocus[dtll = mag; filfac[dtll = .5;mult[dtl] = 1; field (*Tesla*); a[dtl] = 2.54 ; bmrad = rmsr*N[Sqrt[S.ll ; bmlen = rmsl*N[Sqrt[S.]] ; rmsr = a[dtl]/tfac ; rmsl'= (17.53*(100.*betalam))/(N[Sqrt[511*360.) ; tfac =.; lfac0 =.; lfac =.; rundtl; )
:=.
Unsot::norep: Assignment on vgap for vgap[dtll not found. Unset::norep: Assignment on e0 f o r eO[dtlI not faund.
FindRoot[ {sigOt == 46.46, sigOl == 49,381, {field, A}, {eO[dtll, 111
(field -> 0.611585, eO[dtl] -> 1.46167)
.611585/2.54= .2408Tesla (* field gradient -- PARMZLAgot ((2336/.0461)+(2*2236/.0487)+(2124/.0512))/ ((1/.0461)+(2/.0487)+(1/.0512))= 2236 G average for quads -1, 1 and 2;difference may be Bessel approx? For eo, PARMILA uses eOT = 2.0*0.7318 = 1.4636.*)
field = ,611585; eO[dtl] = 1.46167; rundtl; (* The ellipse form-factor is less than 1, so used exact form for that case, *)
facs = FindRoot[ et == ,006, {tfac,E5,5.511 1 {tfzic
-> 6.38266)
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,el,el/et,et/el,etn,eln,eln/etn,etn/el~,rms~/rms~}
/. facs
{0.397953, 0.377146, 0.948727, 0.351348, 46.46, 15,0378, 0.323672, 4!3.38, 18.5737, 0.376138, 0.006, 0.00665608, 1,10935, 0.901432, 0.000277587, 0,000308599, 1.11172, 0.899506, 0.9477131 (* eve1 is 0.90; should be 0.96. The earlier numbers were calculated using the more accurate matrix equations, without the relativistic gamma factors. *)
-
mut = 1 .323672"2(* Design was for transverse space-chargefactor = 0.9 *) 0.895236
1II.C. -27-
(* At Cell 72, PARMJLA eOT = 2.*0.855 = 1.71, and quad average is (241.1 + 2*238.4 + 230.7)/4 = 237.15 G/cm over 3 cm, for field = .071145 Tesla. PARMILA got -25.14 for sigOt and 22.80 for sigOl; solving for these here gives somewhat different values for field, and 1.79 for eOt: *)
dtlFMIT = ( resetdtl; type = dtl ;dtltype = alvarez; energy = 65. ;curamp = 0.120 ;freq = 80.; him = 2.0073 ;q = 1 ; cayt = 0.84 ;cay1 = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] =.; gapobl[dtl] = 0.2; phis[dtl] = -30.; ifocus[dtl] = mag; filf'ac[dtl] = .5; mult[dtl] = 1; field =. (*Tesla*); a[dtll = 2.54 ; bmrad = rmsr*N[Sqrt[S.lI ; bmlen = rmsl*N[Sqrt[S.Il ; rmsr = a[dtl]/tfac ; rmsl = bzO/lfacO ; ffac =.; lfac0 =.; lfac = bdrmsl; rundtl; ) Unset::norep: Assignment on vgap for vgap[dtl] not found.
Unset::norep: Assignment on e0 for eO[dtl] not found.
FindRoot[ {sigOt == 25.14, sigOl == 22.8}, {field, A}, {eO[dtll, 111
{field -> 0,0584115, eO[dtll -> 1.91398)
t[dtll 0.935489
1.914
*
1.79055
0.9355
field = .0584115; eO[dtl] = 1.91398; rundtl;
(* PARMILA got sigt = 8 and sigl = 9.3 at LJe output; solving for these shows ..OW t.5 rmsr,rmsl, et, and e agree, Likewise, PARMILA got a.rms.out = Sqrt[(l.l6)(1.62)(.095 + .088)/2] = .4147; b.rms.out = (6/360)(.254)(375)Sqrt[.O83] = .4574; et.rms.out = (.0012)(.0461)(1.25)/(.254) = .000272, el.rms.out = (BO1153)(.0461)(1,18)/(.254) = .000247; and (et.rms.out.reaVa.rms.out - el.rms.outreal/b,rms.out = .000116, as a measure of the equipartitioningat the output (Cell 72). We see that the solutions for sigt & sigl and for e m s & elms agree with each other pretty well, with both giving values for rmsr & rmsl that are too large. The solutions for rmsr & rmsl exceed the space-chargelimits. (These were done with ff = 1/(3.*p) *)
facs = FindRoot[ {sigt == 8, sigl == 9.3}, {tfac,{4.4,4.5}},{lfacO,{ll,l2}}
]
{tfac -> 4.53247, lfac -> 12.2771)
1II.C. -28-
{rmsr,rmsl,p, If, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,etrms,el,elrms,etn,eln,el/et, rmsllrmsr, etrmdrmsr
- elrms/rmsl}
/. facs
t0.560401, 0.653777, 1.20718, 0.276126, 25.14, E., 0.318218, 22.8, 9.3, 0,407a95, o.ooii3ai5, 0.00022763, o.ooia0075, o.o0036015i, 0.302702, 0.000512804, 1.58218, 1.16662, -0.000144686}
facs = FindRootI {rmsr == .4147, rmsl == ,45743, {tPac,{4.4,4.5)),{lfacO,{ll,l2)} 1 {tfac -> 6.12491, lfac -> 17.548)
{rmsr,rmsI,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,etrms,el,elrms,etn,eln,ellet, rmsl/rmsr, etrmshmsr elrms/rmsl) /. facs
-
I0.4147, 0.4574, 1.14131, 0.292062, 25.14, 28.5998 I, 1.13762 I, 22.8, 26.0104 I, 1.14081 I, 0.00222814 I, 0.000445628 I, 0.0024652 I, Ov00O493039 I, 0,592596 I, 0.000702019 I, 1.10639, 1.10297, -0.0000033369 I}
facs = FindRoot[ {etrms == .000272, elrms == .000247}, {tfac,{4.4,4.5}},{lfacO,{ll,lZ}} I [tfac -> 4.41291, lfac -> 12.9505)
{rmsr,rmsl,p, ff, sigOt,sigt,sigtosigOt,sigOl,sigl, siglosigOl,et,etrms,el,elrms,etn,eln,el/et, rmsl/rmsr, etrmshmsr eIrms/rmsl} /. facs
-
IO .575584, 0.619782, 1.11422, 0.299163, 25.14, 9.0617, 0.360449, 22.8, 7,,09703,0.311274, 0.00136, 0.000272, 0.001235, 0.000247, 0.361705, 0.000351694, 0.908088, 1.07679, 0.0000740364)
Overall, the agreement seems good.
1II.C. -29-
0
Studies dtlGEN = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 2. ; curamp = 0,100 ; freq =.; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] =.; gapobl[dtl] = 0.2; phis[dtl] = -30.; ifocus[dtll = mag; filfac[dtll = S; mult[dtl] = 1; field =.; a[dtl] = 100*betalam/9 ; bmrad = rrnsr*N[Sqrt[S.Il ; bmlen = rmsl*N[Sqrt[S.Il ; rmsr = a[dtl]/tfac ; rmsl = bzOllfac0 ; tfac =.; lfac0 =.; lfac = bdrmsl; rundtl; )
Unset::norep: Assignment on vgap for vgap[dtll not found. Unset::norep: Assignment on e0 for eO[dtl] not found.
N[ {eO[dtl],etn,freq,field,sig0t,sigt,sigtosigOt,sigOl,sigl,siglosigOl, etn, eln,tfac,lfacO,sigt/sigl, rmsl/rmsr}] 1. {eO[dtl] -> 2., field -> l., freq -> 400., tfac -> 5, lfac0 ->2.4} (2.,
0.000227729, 400., l., 44.9893, 33.1139, 0.736038, 30.655,
20.9292, 0.682734, 0.000227729, 0.000352899, 5, 2.4, 1.58218, 1.5625}
tab1 = Table[ ( eO[dtl] = k; rundtl; N[~eO[dtl],etn,freq,field,sig0t,sigt,sigtosigOt,sigO~,sigl,sig~osigOl, etn,eln,tfac,lfac0,lfac,sigt/sigl,rms~rmsr,rmsr,rmsl}] /. FindRoot[{ sigOt == 50, etn == 0.02*5A(j-1)/1000 , sigt/sigl == bmlen*gamma/bmrad }, {field,{.5*freq/200,.51*freq/200}},
1,
{tfac,{5,6}},{lfacO,~2*Sqrt[2OO/freql,2.5*Sqrt[2OO/freql}}
{k,2,2},ti,3,3},{freq,200,800,200} I
1II.C. -30-
]
{{{{2., 0.0005, 200., 0.587209, SO., 36.8166, 0.736332, 43.3527, 31.247, 0.720762, 0.0005, 0.000589122, 5.03183, 3.20979, 2.50122, 1.17824, 1.17574, 0.215768, 0.2536871, [2., 0.0005, 400., 1.09126, 50.,
45.4549, 0.909097, 30.655,
26.9453, 0.878985, 0.0005, 0.000843466, 3.95348, 1.76144,
12., 0.0005, 600., 1.59314, 50., 47.7671, 0.955343, 25.0297, 23.2769, 0.929971, 0.0005, 0.00102606, 3.30909, 1.21197, 1.57225, 2.05213, 2.04776, 0.109366, 0 223956)I t2.,
0.0005, 800., 2.09442, 50.,
48.6802, 0.973604, 21.6764,
20.6625, 0.953226, 0.0005, 0.00117799, 2.89301, 0.922925, 1.25791, 2.35597, 2.35096, 0.0938217, 0.220571)}}}
(* Lcmk at some structure characteristics;field, aOtn, aOln and sigOl for sigOt == 70, vs eO[dtl] and frequency. *)
table1 = Table[ ( eO[dtl] = ktabl; rundtl;
N[{eO[dtll,freq,field,aOtn,aOln,sigO1}] /. Chop[ FindRoot[ sigOt == 70 , { field, .5 1 I, lo*-6 ] 1 9
{ktabl,1,5,2),{freq,200,400,50} ]
II1.C. -31-
{{{l., 200., 0.733689, 2.66192, 1.19092, 30.655},
{l., 250., 0.909051, 2.14131, 0.852152, 27.4187), {l., 300., 1.08436, 1.79103, 0,648254, 25.0297}, {l., 350.,
1.25965, 1.53925, 0.514428, 23.173},
{l., 400., 1.43492, 1.34953, 0.421053, 21.6764}},
{{3., 200., 0.7953, 2.52418, 2.06273, 53.096}, {3., 250., 0.971662, 2.05106, 1.47597, 47.4905), {3., 300., 1.14767, 1.72735, 1.12281, 43.3527}, { 3 . , 350.,
1.32347, 1.49191, 0.891016, 40.1368},
{3., 400., 1.49913, 1.31297, 0.729285, 37.5446}}, { I S . , 200., 0.85247, 2.40084, 2.66297, 68.5467},
250., 1.03048, 1.96873, 1.90547, 61.31},
IS.,
{5., 300., 1.20767, 1.66848, 1.44954, 55.9681), (S.,
350., 1.38435, 1.44772, 1.1503, 51.8164},
IS.,
400., 1.56071, 1.27856, 0.941503, 48.4698}})
(* Look at the conditions sigOt == 90,rmsl == a given fraction of the bucket width, and various transverse
emittances; at several values of eO[dtl] and vs frequency; solving for tfac and lfac0 (lfac0 will be bzO/rmsl by the definition of the problem). FindRoot may return an essentially real number, but as a complex number with a very small imaginary part; the small imaginary part can be Chop'ped off. Or,the solution from FindRoot may be truly complex, e.g. when the tune is depressed below zero. The plotting routines don't like complex numbers, so a Map'ping operation is introduced to change all comples numbers to 0. In order to save the table for manipulation in a later Muthemutica session without having to regenerate it, the result of the Map operation is cut and pasted into a variable definition -- now existing in InputForm. The same can be done with graphs using Inpuflorm. This is handy for changing the viewpoint, etc later without having to regenerate the plot. The plotting routine is now another layer deeper, since there are two parameters. Curves are generated for each table column in turn, storing them in pltlist until all are ready to be plotted. Options have been exercised: 1) to add a curve to the list to be plotted only if there is at least one valid point. 2) to change the GrayLevel and Dashing when the curves have more than one valid point. 3) to plot a point if the curve has only one valid point. *)
k =.; j
-. -.,
1II.C. -32-
tab1 = Table[ ( eO[dtl] = k; rundtl;
N[{eO[dtll,etn,freq,field,sigt,sigtosigOt,s~gOl,sigl,siglosigOl,eln,tfac,lfacO}] Chop[FindRoot[{ sigOt == 90, etn == 0.02*5A~-1)/1000, rmsl == (20/360)*(100*betalam) 3, { field, 1.5 1, { tfac,7 },{ IfacO, 1 1 ] 9 10"-5 1 1,
~k,1,3},0',1,3},~freq,200,400,50}I
-
alist = {{1,2,2,1 I, 3 + 4 1},0,3,5,6 7 I}}
({I, 2 . 2 , I, 3 + 4 I}, (1, 3 , 5, 6
-
7 111
qlist[Ul-] := If[ Re[lll] == 111,1ll,OI
Map[qlist,alist,2] {{l, 2 . 2 , 0, 01,
(0, 3 , 5 , 0))
Map[qlist,Qbl,4]
1II.C. -33-
/.
realtabl = (* paste in *) ( ( ( ( l., 0.00001978, 200..0.9269,15.96,0.1773,30.66,16.94,0.5526,0.001462,16.66,lS), (l., 0.00001996,250.,1.152,19.79,0.2199,27.42,10.23,0.373, 0.0007063,16.51,lS}, ( l . ,0.00001992,300.,1.378,23.24,0.2582,25.03,O., O.,O., 16.36,1.5). (l., 0.00001977,350.,1,603,26.37,0.293,23.17,O.,O.,O., 16.19,1.5),
(l., 0.00001997,400.,1.828,29.7,0.33,21.68,O.,O.,O., 15.99,lS)), ((l.,0.0001004,200., 0.9269,54.01,0.6001, 30.66,20.16,0.6578,0.001741, 13.6,lS), (l., 0.0001001,250.,1,152,59.47,0.6608,27.42,15.83,0.5775,0.001094, 12.78,lS), (l., 0.0001,300..1.378,63.59,0.7065, 25.03,12.38,0.4947, 0.0007126,12.07,lS), {l.,0.0001,350.,1.603,66.78,0.742,23.17,9.382,0.4049,0.0004628, 11.45,lS), ( l . , 0.0001,400., 1.828,69.31,0.7701,21.68,6.481,0.299,0.0002798,10.92,1.5)). ( ( l., 0.0005,200..0.9269,81.24,0.9027,30.66,25.43, 0.8296,0.002196,7.475,lS), (l., 0.0005, 250.,1.152,82.99,0.9221,27.42,22.07,0.8048,0.001524, 6.757,lS), (l., 0.0005, 300.,1.378,84.17,0.9352,25.03,19.57,0.7819,0.001126, 6.212,1.51, (1.. 0.0005,350.. 1.603,85.02,0.9447,23.17,17.62,0.7603,0.0008692,5.78,1.51, (l., 0.0005001,400., 1.828,85.67,0.9518,21.68,16.04,0.7398, 0.0006922,5.427,1.5))). ( ( (2., 0.00001979,200.,0.9519,15.96,0.1774,43.35,35.02,0.8079,0.003024,16.65,l.S), (2..0.00001997,250.,1.177,19.79,0.2199, 38.78,29.26, 0.7547,0.002021,16.51,1.5), (2.. 0.00001995,300.,1.403,23.27,0.2586,35.4,24.74,0.6989,0.001424,16.35,lS), (2.,0.00001982,350.,1.628,26.43,0.2936,32.77,20.96,0.6397,0.001034,16.19,lS), (2., 0,00001998,400., 1.854,29.71,0.3301,30.66,17.69,0.5772,0.0007637,15.99,lS)), ((2., 0.0001004,200.,0.9519,54.,0.6,43.35, 36.69,0.8464,0.003168, 13.6,1.5). {2., 0.0001001,250.,1.177,59.47,0.6608,38.78,31.66,0.8166,0.002187,12.78,lS), (2., 0,0001,300.,1.403,63.59,0.7065,35.4,27.92,0.7889, 0.001607,12.07,1.51, (2.,0.0001,350..1.628,66.78, 0.742,32.77,25., 0.7629,0.001233,11.45,1.51, (2.,0.0001,400., 1.854,69.31,0.7701,30.66,22.62, 0.738,0.0009766,10.92,lS)), ((2.,0.0005, 200.,0.9519,81.24,0.9027,43.35,39.83,0.9188,0.003439,7.475,lS), (2.,0.0005, 250.,1.177,82.99,0.9221,38.78, 35.2,0.9077,0.002431,6.757,lS), (2., 0.0005, 300.,1.403,84.17,0.9352,35.4,31.77,0.8976,0.001829, 6.212,1.5). (2..0.0005, 350.,1.628,85.02,0.9447.32.77, 29.11,0.8883,0.001436,5.78,lS), (2., 0.0005001,400.,1.854,85.67,0.9519,30.66,26.96,0.8796,0.002164,5.427,lS))), (((3.,0.00001979,200.,0.9764,15.97,0.1774,53.1,46.54,0.8766,0.004018,16.65,lS), (3.,0.00001997,250.,1.202,19.79,0.2199.47.49, 40.1,0.8444,0.00277,16.51,1.51, (3.,0.00001996,300.,1.428,23.29,0.2588,43.35, 35.19,0.8118,0.002025,16.35,lS), (3.,O.oooO1986,350.,1.653,26.48,0.2942,40.14, 31.25,0.7786,0.001542,16.18,lS), (3., 0.00001999,400., 1.879,29.72, 0.3302,37.54,27.98,0.7453,0.001208,15.99,1.5)). ((3.,0.0001004,200.,0.9764,54.,0.6,53.1,47.81,0.9005,0.004128,13.6,lS), (3.,O.OOO1001,250.,1.202,59.47,0.6607,47.49,41.88, 0.882,0.002893,12.78,lS), (3.,0.0001,300.,1.428,63.59,0.7065,43.35, 37.5,0.865,0.002158, 12.07,1.5), (3., 0.0001,350.,1.653,66.78,0.742, 40.14,34.09,0.8493,0.001682, 11.45,lS}, (3.,0.0001,400., 1.879,69.31,0.7701,37.54,31.33,0.8345,0.001352,10.92,lS)], ((3.,0.0005, 200.,0.9764,81.24.0.9027,53.1,50.26,0.9466, 0.004339,7.475,1.5), (3.,0.0005, 250.,1.202,82.99,0.9221,47.49,44.62, 0.9395,0.003081, 6.757,1.5). (3.,0.0005, 300.,1.428,84.17,0.9352.43.35, 40.45,0,933, 0.002328,6.212,lS), (3., 0.0005, 350.,1.653,85.02,0.9447,40.14,37.21,0.927,0.001836,5.78,lS), (3..0.0005002,400., 1.879,85.67,0.9519,37.54,34.6,0.9215,0.001493,5.427,1.5)))) ;
1II.C. -34-
For[b1=4,hc12, h++, (* a plot for each table column *) pltlist = {} ; For[p=l, pc4, p++, (* plot for each outer parameter *) Forrj=l, jc4, j++,(* plot each inner parameter *) For[k=l; blist = Q,kc6, k++, (* at each value of x-axis *) Ifl realtabl[[p,j,k,hll != 0, blist = Append[blist,{realtabl[[pj,k,3] J, realtab~[[p~,k,hll~lIl i If[ blist != 0, pltu] = Listplot[ blist, PlotRange -> All, PlotJoined -> IflLength[blist] > l,True,False], Plotstyle -> IflLength[blist] > 1, { GrayLevel[(p-l)*0.4], Dashing[{pA2*0.02,0.02}l I, { PointSize[0.02] } 1, DisplayFunction -> Identity 3; pltlist = Append[ pltlist, pltul 1 I 1 1 ; Show[pltlist,DisplayFunction -> $Displaylunction] ] Field vs frequency, at gradients of 1,2, and 3 MeV/m:
1. 1.
1. 1.
ot vs frequency:
1II.C. -35-
ot/aotvs frequency:
0. 0. ....
.......................
.,..,,,In
................................ ..............................
.............. ...............................
0. ............... .........
r..*c-
250
300
~
..,*..
4..c*"-'*
350
.,
*..W'~."~.
400
001vs frequency:
01 vs frequency
-.\_
\ -
...........
-.
1II.C. -36-
U
--
YT
250
300
350
Eln vs frequency:
tfac vs frequency:
1II.C. -37-
- A
400
dtlGEN = ( resetdtl; type = dtl ; dtltype = alvarez; energy = 2. ; curamp = 0.100 ; freq =.; him = 1.0073 ; q = 1 ; cayt = 0.84 ; cay1 = 0.84 ; voltage = grad; vgap[dtl] =.; eO[dtl] =,; gapobl[dtl] = 0.2; phis[dtl] = -30.; ifocus[dtll = mag; filfac[dtll = .5; mult[dtll = 1; field =.; a[dtl] = 100*betalam/9 ; bmrad = rmsr*N[Sqrt[5.11 ; bmlen = rmsl*N[Sqrt[5.]] ; rmsr = a[dtll/tfac ; rmsl = bzO/lfacO ; tfac =.; lfac0 =.; lfac = bzhmsl; rundtl; ) Unset::norep: Assignment on vgap f o r vgap[dtll not found. Unset::norep: Assignment on e0 €or eOCdtl1 not found.
tab1 = Table[( eO[dtl] = 3.; rundtl; N[{eO[dtl],etn,freq,field,sigt,sigtosigOt, sig01,sigl,siglosig0I,eln,tfac,lfacO}] 1. FindRoot[{ sigOt == 90, etn == 0.1/1000 , rmsl == (20/360)*(100*betalam) }, {field,l.7}, {tfac,7},{ IfacO, 1) 1 ), {freq,200,400,50}] {{3., 0.00010046, 200., 0.976363, 54.0263, 0.600292, 53.096, 47.8141, 0.900521, 0.00412785, 13.5987, 1.51, { 3 . , 0.000100156, 250., 1.20223, 59.48, 0.660888, 47.4905, 41.8853,
0.881972, 0.00289281, 12.7815, 1.51, {3., 0.000100034, 300., 1.4279, 63.5903, 0.706558, 43.3527, 37.5008, 0.865017, 0.00215833, 12.0716, 1.5}, {3., 0.000100005, 350., 1.65347, 66.778, 0.741977, 40.1368, 34.0882, 0.849299, 0.00168164, 11.4545, 1.5}, [3., 0.0001, 400., 1.87897, 69.308, 0.770089, 37.5446, 31.3327, 0.834547, 0.0013525, 10.916, 1.5}}
-
FindRootLO.4 == Sqrt[l+uA21 u, {u,l}l {U
-> 1.05}
1II.C. -38-
IV. RF Power Considerations for Transmutation-Driver Linacs
IV. RF Power Considerations for Transmutation-Driver Linacs A. Introduction
The rf system for an rf-powered linac may be built in thousands of ways, depending on the type of power amplifier, the size of the individual modules, the rf frequency, the decision to use pulsed or cw rf, and dozens of other factors. The major question is what is an optimum rf system for ATW applications, where the average beam current is from 10 to 250 mA, the output energy of the proton linac is from 800 to 1600 MeV, and the fundamental frequency, fl, is between 100 and 400 MHz? The major portion of the rf power is delivered at a frequency of 2*fl=f2. A second important question is how much will the rf system cost? The rf system is to be operated with a minimum of people, highly automated, and very reliable. Overall efficiency is also important. While it is impossible to answer these questions in a general way, some trends and guidelines are developed in this study to help future rf system designers start out in the right direction to find the minimum cost, maximum reliability and maximum efficiency solutions to these problems. The major rf power components of a generalized rf linac power system are shown in Fig. 1. The power system begins at the power line inputs at the upper left. A local power substation transforms the input power to the ac voltage required for the main and auxiliary power supplies, and also transforms the power for light, heat, etc. in the PiLW complex. The substation consists of transformers, circuit breakers, and possibly switches and fuses to safely and efficiently distribute the primary power to the various loads of the AIW complex. The power supplies transform the ac power into dc power, usually at a different voltage, to supply the rf amplifiers. For the case of the solid-state amplifier, ac power from the substation drives a number of low voltage, high current power supplies, while in the vacuum tube case, the substation drives a number of high voltage, relatively low current power supplies. The high voltage systems usually require a crowbar to protect the vacuum tubes from the high stored energy in the system. The power conditioning system may filter the output of the power supply and protect the power amplifier from the supplywhen the amplifier arcs. The power conditioning system is quite specific to the power amplifier, and a pulsed rf system requires a much more complex power conditioning system than does a cw rf system. The heart of the high-power rfsystem is the power amplifier, which is connected to the accelerator tank by the rftransmission system. The power amplifier may be solid state, or avacuum device, such as a gridded tube, a klystron, a klystrode, a magnicon, a gyrotron, or a gyrocon. The rf and power supply control racks consists of the control and protection circuits for these systems, plus any smaller power supplies required for solenoids or filaments associated with the rf power amplifier. A drive amplifier accepts a low power signal from the low level rf system and amplifiesit to the required level for the particular power amplifier. The drive amplifier is usually solid state.
w.-1-
FIG. 1. GENERIC RF POWER SYSTEM BLOCK DIAGRAM +
COklPVreR INTERFACE
-
MWER SUBsTATlON
RF
REFERENCE
To BUILDINGS
i
? O W TO T M G E F
I
4
'--
I
RF AND
mwer SUIILY coNmo18
C
1
ACCELERATOR
AMPLIFIER
CAVITY L
I
I
J
Near the center of the diagram are the computer interface and safety and interlock systems. These systems connect to all parts of the block diagram, so their interconnectionsare left out for readability of the diagram. There is a single rf reference system that can drive as many different frequencies as are required for the accelerator. An rf reference distribution system connects the various rf modules to the main reference. The low level rfsystem consists mainly of phase and amplitude (or in-phase and quadrature ) control modules and the electronicsfor the resonance controllers. The low level rf system is independent of frequency, power level, and type of high-power amplifier. The cooling system is also shown near the center of the diagram, since all the electronic systems require some cooling. Generally the high-power systems require water cooling, while the lower power systems require air cooling,The waste heat is eventually dissipated into the outside air in either case. High efficiency in the power system reduces the cost and complexity of the waste heat removal system. There are dozens of choices that must be made to define an rf system. These choices include type of rf generator, such as tetrodes, triodes, solid state, klystron, magnicon, gyrocon, or gyrotron. The choice of operating frequency is also important, but for proton machines, the frequencyrange is about from 100 to 1000 MHz. At these low frequencies,the gyrotron is not expected to be a serious contender, and it will not be discussed further. The optimum rfamplifier size is also important, with choices ranging from 50 kW to 4 MW for cw amplifiers, and. from 50 kW to 50 M W for pulsed amplifiers. The intent of this study is to find the optimum rf system parameters as function of frequency, power module size, and total power required for the total rf system.
B. Optimizing the Accelerator to Minimize RF Costs It is instructive to speculate on how to design an accelerator to minimize the costs of the rf system. The conventional wisdom is to utilize each rf system to the fullest, and to minimize the number of rf power amplifiers. The conventional wisdom is that the total costs of the rf power system decreases with the square root of the total number of rf amplifiers, for a given total output power. This philosophy maximizes the output power per rf amplifier, and also can lead to problems if the amplifier’s power output become too large. In a klystron system, the high voltage required becomes too high for good cost or reliability performance, while in a solidstate system the power supply current or the rf combining system become expensive or unreliable when the rf power becomes too large, For tube-type rf systems, the conventionalwisdom is roughly correct, provided that the high-voltage system remains under about 115 kV. This limit is based on the poor reliability experienced between 120 and 135 kV dc in the Free Electron Laser rf system at Los Alamos. This system operates reliably for voltages below 115 kV DC power transmission lines are operated at 500 kV and even higher voltages, with excellent reliability, even in the outdoor environment. Thus higher dc system voltages above 115 kV may well be practical, but large engineering expenses would be required to achieve good reliability.
w.- 2 -
The large power per module concept minimizes the rf costs in other ways than tube costs.
Some parts of the rf system, such as the computer interface, rf driver, and feedback controls, have costs that are completely independent of the rf generator size. Hence, costs are reduced by using fewer generators for a given rf power. In pulsed systems, the modulator costs are large, and the system cost is minimized by placing many generators in a single modulator. By similar reasoning, costs are saved by operating multiple generators from a single power supply and a single capacitor bank. After LAMPF was built, Don Hagerman of LAMPF thought that a larger size rf module would have been a better choice for that machine, but when it was built, he wanted to be able to adjust phase and amplitude at the 1MW power level.
The conventional wisdom is that the klystron or other vacuum tube costs are largely independent of frequency in the 300 to 1000MHz frequencyregion,but the cost estimatesfrom actual vendors show that the vacuum tube costs do increase with frequency over this frequency range. The CERN LEP klystron produces 1MW cw at 352 MHz, and it is available at a very low cost, since each of the two vendors has produced about 20 of these klystrons. Even if one ignores this low cost option, the vendors simply want more money per watt as the output frequency is increased. For the present state of the art, the lowest cost rf system would involve 352 MHz as the high frequency, or even better, as the only frequency. Due to the historical anomaly that CERN has 20 MW cw installed power at 352MHz, and two vendors are in headto-head competition, this frequency is a real bargain. The optimum amplifier size is a rather complicated result of several considerations. For the cw case, 1or 2 MW per accelerator feed is probably optimal. If we had a larger generator, it would be prudent to split the output power into 1 or 2 MW sections, and use high power, mechanical phase and amplitude adjustersto make up for any unbalances that are brought on by thermal effects. Some devices, such as the gyrocon and the magnicon, require at least 2 output ports that are inherently phase locked, and this is an advantage for these generators. By using larger generators, the reliability of the system improves, since we expect the reliability to decrease slowlywith amplifier size. With the current state of the art, a 2 MW generator size may well be optimal. There is some chance that a 4 MW amplifier would be a better choice, but much development is required before the choice can be made. There is also the possibility that very reliable, low power rf systems can be developed in which the mass produced prices would be a better solution than the other choices. Such generators do not exist now, but may be worthy of research efforts. In pulsed linacs, the optimum amplifier size is determined by beam dynamics, rather than generator considerations. Thus, the Fermilab upgrade is using 10 MW peak output power klystrons at 805 MHz on a proton machine, while SLAC uses 50 MW peak power klystrons for their electron linac, and several 100 MW peak tubes are being discussed for the next generation of linear electron colliders. C. Reliability
The reliability of the power system is perhaps its most important attribute, and the reliability
nr. - 3 -
requirements must be considered at each step of the design and manufacturing processes. The overall goals for an AlW system are 75% availability for operation in each calendar year. This availability goal is perhaps too high to meet without replacement of components, so we consider a maintained system, in which components are replaced as soon as they weaken. To realize this goal the overall system reliability budget is shown in n b l e 1. The power system must have no more than 250 hours per year of unscheduled down time. To achieve this goal, the power system must have more diagnostics than is usual, so that it can warn its supervisory computers that parts are approaching the extremes of their operational range. We anticipate operating the power systems with some scheduled down time each week (8 hrs/week in Table I); and failing components could be replaced in that period. LAMPF,for example, operates for 6 months in a row, 24 hours per day, but there is a 4-hr shift each week during which time weak components are replaced.This extra diagnostic method is the principal method proposed to obtain the excellent reliability required tor the AlW power system. In the LEP power system at CERN,1000 thermocouples are monitored for each pair of 1 MW cw klystrons and their accelerator cavities, while for an older system, such as LAMPF,only a few temperatures are monitored for each klystron. The added information can be used to anticipate failures, and the defective component can be changed during a maintenance period. A second method that will be used is to operate the least reliable components several percent below their maximum ratings. We have considered operating the power amplifiers at about 5 to 10% below their maximum ratings, for example. When the amplifier has lost most of this margin, the supervisory computer notifies the maintenance people to change the amplifier at the next scheduled maintenance period. A third method that is used often in space systems is to employ redundant components. This method does not seem feasible for m,since the costs of the major components are so high. Redundant methods will not be dismissed, and this possibility should be examined during the detailed design process.Certain types of power amplifiers such as solid-state, are inherently parallel, so that as transistors fail, the maximum output power gradually decreases. This phenomenon is called graceful degradation, and it is shared in tube type amplifiers as the cathode wears out or as a gap is eroding away. Graceful degradation is desired and will enhance the reliability of the system, while catastrophic failures, such as that from arcing must either be eliminated or be very rare. The failure rate for most components follows a bath-tub shaped curve, with high early failures due to infant mortality (manufacturingdefects), followed by a low failure rate, which may gradually rise as the components wear out. By conservative design and low loadings, the wear-out period may be pushed out in time. It is usual to screen components by operating them under carefully controlled conditions to eliminate the infant mortality section of the system would only receive comcurve. By screening or wearing-in the components, the ponents that are in the high reliability part of their life cycle. The LAMPF klystrons have shown an 80,000 hr mean-time between failures, and they are in the constant failure rate part of their life cycle. Another method that is being considered for AlW is to reward financially the vendors for long life components. Perhaps contracts could be written with payments for each year of continued operation above a guaranteed minimum, so that the cost savings of not N - 4 -
Table I V . 4 . Reliability Budget for RF System Subsystem Klystron Power Supply Power Conditiodog Law Level RF RF ~ S p O r L Water System
MTBF' Number k hours Inst.lled 50 150 100 100 150 20
482
80 80
482 482
80
Reventive Maintenance
Failures per Year 84 4 7 42 28 35
Percent Unanticipated Anticipated FailwwNear 75 50 50 50 50 85
21 2 4 21 14 5
T h e to
Hours Out Repair,hrs per Year 3
6
8 hrs/week
Total System Down me, hrslyr RF System Availability, %
5 2 4
5
63 12 20 42 56 25
416
634 93
replacing the component is shared between the ATW and the component manufacturer. Some vendors have expressed problems with receiving the extra payments years after a sale, but it will simply take many years to establish the reliability of the various components. The power level of the components also will effect the system reliability, and there is an optimum size for each component to achieve the best system reliability., This problem must be solved in detail during the design stage. Since so few high power components are now in use, testing and calculations will have to be done to wisely make this choice. D. Power Effciency
After reliability, the second most important attribute of the power system is its efficiency. High efficiency reduces the primary power demands, reduces the cooling requirements, and reduces both the capital and operational costs of the system. Sometimes the highest efficiency of a component may only be achieved by reducing the reliability or robustness of the device, In the klystron and klystrode, for example, the energy conversion efficiency increases as the intercepted beam power is increased by reducing the magnetic fields. A compromise must be reached between the beam interception, which effects the life of the device, and the energy conversion efficiency, which effects the capital and operating costs. Contracts have been writ-. ten to reward efficiency, as this can be measured at the factory. Thus, financial incentives should be applied to the critical component contracts, and in general, the most energy efficient designs, (consistent with good reliability) should be used. Informal discussions with klystron vendors on financial rewards for reliability have now been productive so far, since the reliability takes so many years to prove. For example, it took about 15 years for the LAMPF klystrons to show that their mean time to failure was 80,000 hrs. Many vendors are not interested in rewards so far in the future. There must be a way to give the vendors a financial incentive to produce such excellent lifetimes on a regular and consistent basis. E. Quantity Discounts High power systems are generally manufactured in small quantities. Hence the unit costs are usually high, and the non-recurring engineering costs are a substantial fraction of the total costs. The most powerful cwrfsystem built to date is the CERN LEP rf system, which now has 18 MW of installed power at 352 MHz, and will have 40 MW installed by 1994. Industrial products tend to become less expensive as the quantity is increased, and the unit price generally drops by 5 to 15% each time the accumulated production is doubled. We call this factor the learning factor for the industry. In industries that require much manual labor, the 5% rule holds, while for highly automated industry, the 15% rule applies. Of course, if very large quantities of anything were ordered, automation would be used to reduce the costs of the products. Based on informal estimates from power supply and power tube vendors, these industries are in the 5% learning coefficient range, while power semiconductors are estimated to be in the 10% learning coefficientrange, since their volume will never be at the level of logic or diode N.-5-
devices. The low-level rf system is estimated to have a 10% learning factor, since most of the hardware can be reduced to circuit boards. To obtain cost estimates, we place a quantity discount factor, QDklystron, for example, to reflect the quantity discount. The discount applies each time the total production is doubled, so there is a base number that must be estimated for each component. The base number is 20 for the 352 MHz, 1MW cw klystrons, and it is 5 for the other klystrons. For power supplies, low power chadsis, and most other components, the base number is 2. Thus the general form of the quantity discount factor is QD = (l-W)**(ln(NC)/ln(Base)) where LF is the learning factor expressed as a fraction, NC is the number of components used in the power system, and Base is the doubling number base for that component. We have used the 5% learning factor for all high-power components, and the 10% factor for all low-power components.
E Power Substation The power substation consist of the transformers, relays, contactors, and switches to reduce the power line input voltage to lower voltages for use in the ATW complex. The input voltage for the ATW facility would be at least 230 kV,with more than one circuit to provide redundancy. The usual practice is to transform the input power to 13 kVfor local distributionwithin the PirW complex. The cost of the substation is primarily a function of the number of output circuits and the total power transformed, The losses in the substation can be very low, less than 1%of the power transformed. G. Power Supply
The power supply takes the substation 3-phase ac power and transforms it into dc power at the appropriate voltage and current for the rf power amplifier. The cost of the power supply depends on the output power, and the output voltage. The output voltage is much higher for some types of vacuum tube amplifiers, such as the klystron, magnicon, etc. than for gridded tubes. Solid state amplifiers require the lowest voltages, often only 100 V, and for them, the current becomes a problem and a cost factor in higher-powered units. The decision on pulsed or cw operation of the rf system also effects the power supply. The losses in the power supply system are about 4% at the 3-MW level, and the percentage loss increases as the rating of the power supply becomes smaller. Another consideration for the power supply is the electrical noise that may be put on the power line by the power supply. The choice of controller for the power supply influences this noise, and many designers use variable transformersrather than silicon devices to regulate the supply to minimize the noise. The silicon regulator is much faster than the variable transformer, and the controller choice is complex The normal practice in dc power supplies is applicable up to about 3 MW dc output. Larger dc supplies are used for dc transmission lines, up to the GW power level, but this technology has not yet been
applied to accelerator projects. For simplicity, a maximum of 5 MW per power supply is considered in this report. H. Power Conditioning The power conditioning system can be very simple in a cw case, and it can be very complex and expensive in pulsed power systems. In the minimal, cw klystron case, the power conditioning system consists of a filter to reduce the power supply ripple, a crowbar to divert the power supply and filter energy in case of a fault, and a high voltage enclosure to keep all high voltages away from personnel. In the case of a modulating-anode pulsed klystron, the power conditioning system would consist of a capacitor bank to store many times the pulse energy, a crowbar, and an switching system called a modulator. The modulator may cost several times the cost of the power amplifier. To minimize modulator costs,several tubes are often place in the same modulator. This practice slightly increases the modulator rise and fall times, which increases operating costs, but reduces capital costs. I. Power Amplifier For an N W system that employs protons, the rfpower is required at frequenciesbetween 2Q0 and 800 MHz, while if deuterons were used, the frequencies would be multiplied by 1/2. Several types of rf power amplifiers have been proposed for the MW rf system. These include klystrons, gridded tubes, gyrocons, magnicons, and solid state amplifiers. The klystron is used in more large accelerators than any other amplifier, and its application is emphasized here. At LAMPF,where there are 4 triode rf systems at 201.25 MHz, and 44 Mystron rf systems at 805 MHz, the down time and maintenance effort on the two rf systems are approximately equal, but in recent years, the down time of the gridded systems has been significantly greater than that of the klystron systems. Thus the klystron rf systems are at least a factor of 11 more reliable than similar gridded systems, in this instance. This ratio is expected to hold true in any high average power rf system. J. Cost Estimates
The unit cost of any component of a high-power rf system generally is only weakly dependent upon the power of the component. This leads to the conventional wisdom that bigger systems are less expensive. Unless otherwise noted, all costs are in M$,all powers are in MW, and all voltages are in kM Substation A 15 M W addition to the LAMPF main substation was recently estimated to be $ 1.33 M.The cost per M W should decrease as the substation size increases, and we estimate a 0.4 exponent for the power law. Thus an estimate of the substation costs is w.-7-
CS=0.45 * P,**0.4 where C, is the substation cost in $M, and P , is the substation power, in MW. There is only one substation for the system, so there is no quantity discount factor. Power Supply
We have recently purchased a power supply for $380/kW at the 460 kW level at 92 kV and 5 A. The same vendor estimates that a similar supply at 30 A and 92 kV would cost $ 13:3.4/kW,but the vendor would not want to build a larger power supply. Larger power supplies do cost less per kW, but only very few companiesare interested in making them, since the total market is very small. Previous studies have shown that the voltage of the supply has a minor influence on the price, roughly as the fifth root. Thus we are lead to a cost estimate for the power supply of
C, = QD,,,*0.2415982*(P,)*
*0.4152965*(Vp/92)**0.2
where CpS is the power supply cost in M$, QD,,, is the power supply quantity discount factor, P, is the power supply size in MW, and Vp is the power supply voltage in kV This expression should be valid from 35 kV to 120 kV, and for powers between 0.5 and 5 MW. Very large power supplies, in the over 100 MW class are built for dc transmission lines, and the cost per watt decreases to under 0.1 M$/MW. Large power supplies are not mass produced, so the learning factor is about 5%.
Klystron The costs for klystrons is a function that depends strongly on average power, and weakly on everything else. The frequency dependence is noticeable over the 300 to 1000MHz frequency range, primarily because as the frequency goes down, the size power densities increase as the square of the frequency. Since the current price of the 1MW cw klystrons at 352 MHz is now about $M 0.29, and the price of 100 kW klystrons (quantity 12) at 850 MHz is about $M 0.15, we find the relation ckiy=
Q&~*0.027*P~~**0.412 1*(freq/m)**O.4
where Pkly is the klystron average output power in MW and freq is the frequency in MHz. The fixed costs for developing a new klystron are $M.5 to .75 for 1MW cw,and about $M0.25 to 0.5 for a 0.1 MW pulsed or cw klystron. This equation has several caveats, the most important being that it is valid only for output powers at or below 2 MW. On the spread sheets, we have used actual klystron costs whenever we had them, and we use the above equation only as an estimate for new frequencies and output powers. The cw power limit on the klystron is now
about 4 MW, but we could not even get a cost estimate from any vendor on a 4 MW klystron. Its development would have to be undertaken by a series of contracts, and possibly the vendors would not guarantee powers over 2 MW in a fixed price contract. The technology of the vendor is also important. One of the vendors would sell a 112 MW klystron for only 7% less than the price for a 1MW klystron, since they feel that 1 MW gives them no problems. If a given vendor has only produced 500 kW klystrons, then they would charge a much larger premium for a 1 M W device. The development of the windows and especially the collector, are the technology items that are most in need of development. As the collector gets larger, to dissipate more power, the density of resonant modes in the collector increases. The spent beam always has rf modulation on it, so the danger of exciting a collector mode either at the operating frequency or at a harmonic increases with collector size. In principle, these modes can be controlled, but the task is difficult, and it requires developmental efforts. One can save money on the klystron and similar generators by building a mini-collector, that will not handle the full beam power, but only the power left in the beam after the rf energy is extracted. This savings complicates the cavity conditioning problem. One possible solution is to have one or more special, pulsed rf systems that are used to condition each cavity. In this case, we have to trade the cost savings from the smaller collectors with the additional costs of the pulsed rf systems. Such an approach has been used on the LEP ring at CERN, where all cavities are conditioned in a special building with a very flexible rf system that can be operated both pulsed and cw.After conditioning, which takes about a week of 24 hrlday operation, the cavities are moved, under vacuum, to the main ring, and operated with cw rf from then on. Since the CERN LEP klystron has had a production history of about 20 klystrons from each vendor, the 5% learning is applied to doubling of 20. The price estimates are for quantity of 5 , so for the other klystrons, the doubling number is 5. Only one high average power pulsed klystron is now in production. It operates at 433 MHz, and produces 1 MW average, 4 MW peak. This klystron costs $M 0.95, and to change its frequency would cost about $M0.5. Based on estimatesfrom a single klystron manufacturer, the cost formula must be doubled for pulsed klystrons, for the high-duty factor cases that are usually considered for M.The best klystrons made to date have a dc to rf conversion efficiency of from 65 to 69%. The difference in price between a 50 and 60% efficient klystron is only about 5%, so AI" would always try to realize the highest efficiency.
The klystrode is a novel combination of a tetrode gridded current modulation system and a klystron output cavity. A schematic drawing of the klystrode is shown in Fig. 2. Less than 100 have been built, but more than 64 klystrodes are now installed in UHF television transmitters. The advantages of the klystrode are the very high efficiency of 70% and the fact that as the input drive is reduced, both the beam current and the output power decrease, so the efficiency tends to be constant over a broad range of output power. The disadvantage is a relatively low power gain of 20 dB, which requires a second klystrode as a drive amplifier. The recent sales price for a 250 kW cw klystrode at 267 MHz that is being developed now is $M
0.15, and the costs should scale as follows;
Magnicon The magnicon is a deflection-modulated rf amplifier shown schematically in Fig. 3. It is an improved version of the gyrocon, and the only magnicon produced to date has been a Soviet one that produced 2.8 MW at 915 MHz in the pulsed mode with a dc to rf conversion efficiency of 73%. Discussions with one of the inventors, Dr. Oleg Nezhevenko, have resulted in estimates that the production costs would be similar to those of the klystron. The first advantage of the magnicon is the very high efficiency,and the second is that the output interaction is distributed, hence very large pulsed or cw powers are possible, since the fields in the output cavity are much lower than those in a concentrated interaction device, such as the
klystron.
Solid State Amplifiers The present cost of a 65 kW, 200 MHz solid-state amplifier is about $M 0.5. The. costs are likely to increase with frequency, by about the cube root of frequency. This comes out to a cost of
C, = QDS*7.69*(freq/211)**0.33 where freq is the operating frequency in MHz. This cost will include all power supplies and monitoring equipment. For a pulsed system, the first factor is reduced by lo%, but the peak power must be used. Most solid-state amplifiers are designed for wide bandwidth and operate at low efficiency, For narrow band amplifiers, an efficiency of 60% may be possible, especially at or below 200 MHz, but the efficiency will decrease as the frequency is increased. Gridded =be Amplifiers The 211 MHz rf system in the proceeding paragraph was purchased as a gridded tube system, for a cost of $M 0.35 for the 65 kW cw at 211 MHz. These costs are likely to scale up with frequency, but remain essentially independent of power per system, due to complexity of the combiner. We estimate a cube root relationship to frequency: C, = QD*d*5.35*(freq/211)* *0.33.
As in the solid-state system, this includes all power supplies and monitoring equipment. For a pulsed system, the first factor may be divided in half, but the peak output power is used. The dc to rf efficiency for the tetrode is from 60 to 70% in Class C,but the amplifier efficiency is
about 10 percentage points lower. Low Level RF System
The low level rf system is estimated to have a non-recurring engineering(NRE) cost of $M 0.5, a capital cost of $M 0.15, and a learning factor of 10%. The rfreference system is taken to cost $M 0.15, plus $M 0.01 per rf module.The formula is then
where NRF is the number of rf modules in the system.
Power Conditioning The power conditioning block is built into the amplifiers for the solid state and gridded tube systems, but for klystrons, it is complicated, and made up of a energy storage system, a modulator, a crow bar, and the modulator itself. The learning factor for all these components is 5%, and the costs are discussed below. Energy Storage for Pulsed Systems If the system is pulsed, the pulsed energy is usually stored in a capacitor network. Two types of modulators are commonly used for high power pulsed systems: a modulating anode system, or a pulse-forming network (PFN) system. The modulating anode system is generally used for lower peak power klystrons, up to about 4 and rarely 6 MW peak, while the PFN system is optimum for higher peak powers, but lower average power. A third type of modulator, utilizes a series switch tube between a capacitor bank and a pulse transformer. This allows high peak and average powers at the same time. Each type of modulator requires a different ratio of stored energy to pulse energy, and higher quality capacitors are required for the PFN systems, since the capacitors are completely discharged during each pulse. The table below shows the appropriate energy ratios and capacitor costs for the three types of systems. Modulator Anode Modulation Pulse Forming Network Series Switch lbbe
Energy Ratio Times pulse Energy 10 1.2 , 2
N -11 -
Capacitor Costs ($M/MJ) .ll .25 .ll
Crow Bar System According to out GTA experience, we can estimate the crowbar costs at $M 0.1 per crow bar, for all capacitor banks up to 1 MJ. Modulator We estimate that the anode-modulator would cost about $M 0.4, the PFN modulator $M 0.36, and the series tube modulator would cost $M 0.3 each, plus $M 0.1 for the transformer, if required. The PFN modulator costs must be increased as the square root of the pulse length above 250 p,thus
C,b = 0.35*@ulse-len/250)* * O S where pulse-len is the pulse length in microseconds. This formula is only valid at or above 250 ps, A 5% learning factor is used with the modulators.
CW Power Conditioning For the cw case, the power conditioning consists of the crowbar, filter capacitors, and protective resistors inside an enclosure. The price estimate is $M 0.2, with a 5% learning curve, and Nps systems are used. The cost relation is then Ccwpc= QDpc*0.2*Nps
CW Shielding, Structure Support, and Socket Tank In the cw case, a tube support, with X-ray shielding, and a socket tank are all that is required to operate the rf system. This equipment is estimated to cost $M 0.15 per amplifier, but it is included in the amplifier estimates for solid state and tetrodes. The cost relation is C, = QDW*0.15*NRF where a 5% learning factor is used.
RF and Power Supply Controls These are only required for klystrons, and included in the price of the solid-state and gridded tube amplifiers. The estimate is $M 0.05 for each power supply and $M 0.075 for each klystron. A 10% learning factor is appropriate. The formulas are
+
Crfcont = QDcont*NRF*0.075 QDpscont*NPS*0.05
Iv-1 2 -
where NPS is the number of power supplies.
RF Driver The rf driver is required on the klystron, magnicon, solid-state, and klystrode rf generators and the cost is about $M 0.01 per system. Due to the low power gain of the klystrode, the driver is estimated at $M 0.11. A 10% learning factor is appropriate, RF ’kansmission System
For a typical waveguide transmission system for pulsed service, the cost is about $M 0.1 per cavity input, and the learning factor is 5%. The waveguide system costs are about 50% higher for cw power, and coaxial systems should be avoided in high-power cw applications. The table below lists the cw output power limits for coaxial lines at 100 MHz, and estimates the cost for a typical system. The cw limits decrease as the square root of frequency. Coaxial Size 9” 6” 3”
Power Limit, MW 0.4
0.18 0.04
Cost per run, $M 0.2 0.1
0.05
The cost of the rf window is included in the above estimates. For higher average powers, a waveguide power distribution system is required. The peak power capability of waveguide at 1000 MHz is -MW, and the high average powers are easily handled with water cooling on the waveguide surfaces. The window is the delicate component of the rf transmission system. In principle, this should not be a problem, since 1MW cw windows are made at 352 MHz, and every cw klystron has a single window that transmits all it power. Thus, 500 kW windows at 2450 MHz are available, and the limiting power scales like freq**2,so at least 2 M W cw should be available at 600 MHz, but the design has not yet been made. On vendor was willing to sell a 4 MW cw klystron, obviously with a window, two years ago for a firm fixed price, so they did believe that a 4 MW window was a reasonable development project. Cooling System The cost of cooling is roughly $M OSMW,with a 5% learning factor for each doubling of power above 1MW. We built a 1MW deionized water system with heat exchangers for $M 0.25 9 years ago, and the heat exchangers were obtained without charge from another program.The cost is Ccs = QDcs*Pps,
w.-13 -
where the base is 2 MW. The water system becomes a large part of the total costs. RF power amplifiers can be steam, rather than water cooled, and the cooling system requirements become lower. The problem is that water cooling is more robust than vapor-phase cooling. Thus, this trade must be carefully examined for each rf system. The large 1MW cw klystrons at 508 MHz at the llistan ring at KEK in Japan are examples of vapor-phase cooling. Computer Interface System We estimate this item to be $M0.05 per power amplifier, and the NRE is about $M 0.5. A 10% learning factor is appropriate. The cost is Ccif = QDcif*O.OS*NRF Safety and Interlock System The safety and interlock system must be made fail safe and redundant and hard wired in all matters where personnel safety or the environment are concerned. In the GTA power system, for example, the personnel and environmental safety systems are fail safe, so that is the safety systems are disconnected or shut down, the power system shuts down. These systems perform their tasks with hardware, and the computers only monitor their states. The safety systems are also designed such that and single component failure shuts the protected power component down. Where the hazards are high, redundant or even doubly-redundant safety and interlock systems are used. The safety and interlock system should cost about 4% of the total rf system costs. The NRE for this system will be high, and is difficult to estimate at this time. A few man years of effort are required for the safety and environmental efforts on a small accelerator, and a few tens of man years are required for a large accelerator. Thus the NRE for this system is between $M 0.75 and $M 7.5, with the high estimate valid for highpower systems (above 100 kW in the beam). Supervisory Computer System All modern accelerators are monitored and partially controlled by a supervisory computer, which in often distributed. The computers can range from pc's to mid-size. We estimate the cost of these systems to be 10% of the rest of the power system cost. Historically, the cost has been from 5 to 20%. Installation and Commissioning Costs The costs of installation and commissioning are estimated to be 35% of the hardware costs of the power system for cw accelerators, and 50% of the hardware costs for pulsed machines. The extra cost for the pulsed cases is due to the complex modulators that are re-
quired for the high-average power systems required for N W class accelerators. Building Area and Costs We use Don Reid’s estimates from his LACE code (Los Alamos Accelerator Cost Estimator) to obtain the power building area. For a long pulse system, Ried has used the building area of Abuild = 125*Pav+Nfl(212 + 30) + 800 The building area, in square feet is 125 times the average rfpower in MW, plus 212 square feet for each amplifier and modulator, plus 30 square feet for passageways for each rf module, plus 800 square feet. In the cw case, and for pulses greater than 5 ms, he uses a slightly different formula, Abuildcw= 125*Pav+Nrf*(132+30)+800 where the only difference is the use of 132 square feet for the power amplifier, since there is no modulator. We have increased Ried’s estimate of $125 per square foot building cost to-$150 to convert the areas into dollars.
K. Design Examples Using the cost estimates developed above, we can make cost estimates for several rf systems of interest to AIW accelerators. We consider module sizes of 50,250,500, 1000, 2000 and 4000 kW for a cw system, and frequenciesof 100,200,350, and 425 MHz for the low frequencypart of the linac, and twice the fundamental for the high frequencypart of the linac. We also consider total rfsystem powers of 1,2,5,20,50,100, and 200 MW. These costs are the hardware production, procurement, building, installation and commissioning costs, but do not include local NRE,installation, and commissioning. Each table of results is preceded by a table of component costs and their learning factors and doubling bases, since these estimates are very important in determining the system costs.
L, CW Klystron System Results We start with the CEFW LEP frequency,352 MHz cw due to the low cost estimatesof the LEP klystron. Component
LF
Base
Quantity Unit Cost
Power Supply Power Condition
.05 .05
2 2
NPS NPS N-15-
Power Amplifier Shield, Support,Sok RF&PS cont Transmission Sys Drive Amp Low Level RF Computer Interface
10 2 2 2 2 2 2
.OS
.05 .10 .OS
.10 * 10 .10
Nrf Nrf
0.29
Nrf&Nps Nrf Nrf Nrf
Nrf
The substation, cooling, safety, RF reference, supervisory computer control, building and commissioningsystems are not in the above table, since these components are used only once in each PiIW system. The detailed spreadsheet output that allocates the various component costs of the power system is labeled Case I in the Appendix.
Frequency MHz 352 352
352
352 352 352 352 352
Total Power MW
1 2 5 10 20 50 100 200
Power Module kW 1000 1000 1000 1000 1000 1000
1000 1000
Total Cost $M
CostlMW $M
4.54 7.18 15.10 27.36 50.58 113.56 214.01 405.10
4.54 3.59 3.02 2.74 2.53 2.27 2.14 2.03
-
We also have price estimates for 1 and 2 MW cw klystrons at 704 MHz, twice the LEP frequency. The 1MW case is summarized in the table below, and the details are labeled Case I1 in the Appendix. Frequency MHz
Total Power
704 704 704 704 704 704 704 704
1
MW 2 5 10
20 50 100 200
Power/Module kW 1000 1000 1000 1000 1000 1000 1000 1000
Total Cost $M
CostMW $M
6.19 9.10 17.80 31.29 56.88 127.70 239.93 453.74
6.19 4.55 3.56 3.13 2.84 2.55 2.40 2.27
2 MW cw klystrons are also possible at 704 MHz. The table below summarizes the power
w.-16 -
system costs for this case, and the detailed results are Case I11 in the Appendix. We have used 6 MW instead of 5, to optimize the usage of the klystrons. Frequency MHz 704 704 704 704 704 704 704
Total Power MW
2 6 10 20 50 100 200
Power/Module
kW
Total Cost $M
CostfMW $M
2000 2000 2000 2000 2000 2000 2000
7.84 17.69 26.12 46.87 104.18 194.93 367.5 1
3.92 2.93 2.61 2.34 2.08 1.95 1.84
These examples show that for very large systems, we can save $M 45 on a 100 MW system and over $M 86 on a 200 MW system by using 2 MW, rather than 1 MW klystrons.
At 850 MHz, a vendor gave us data on 0.5 and 1.0 MW klystron prices and performance estimates at two efficiencies, but the capital costs are almost equal. We present the low efficieney
case first, although we certainly do not recommend using such low efficiency klystrons for Airw purposes. The first example is 0.5 MW, 50% efficient klystrons at 850 MHz, and the details are Case W in the Appendix. Frequency MHz
Total Power MW
850 850 850 850 850 850 850 850
1 2
5 10 20 50 100 200
PowerModule kW 500 500 500 500 500 500 500 500
Total Cost $M
Cost/MW $M
7.00 11.67 24.71 45.40 84.69 195.92 372.04 693.99
7.00 5.83 4.94
4.54
4.23 3.92 3.72 3.47
A more interesting case is the 60% efficiency klystron, also at 500 kW and 850 MHz. This is Case V in the Appendix. The klystron development costs are higher, so the first MW is more expensive, but for all powers above 1 MW, even the capital costs of this system are better than those for the lower-efficiency klystron.
Frequency MHz
Total Power MW
PowerModule kW
Total Cost $M
CostMW $M
1350
1
850 850 850 850 850 850 850
2 5 10 20 50 100 200
500 500
500 500 500 500 500 500
7.04 11.30 23.61 43.17 80.37 184.79 350.02 666.74
7.04 5.65 4.72 4.32 4.02 3.70 3.50 3.33
We also have made system designs for a 1 MW, 50% efficient klystron at 850 MHz, but we recommend the higher efficiency version. The low efficiency klystron is Case VI. Frequency Total Power Powerh4odule Total Cost Cost/MW MHz MW kW $M $M
850
850 850 850 850 850 850 850
1 2 5 10 20 50 100 200
1000 1000 1000 1000 1000 1000 1000 1000
6.40 9.72 19.45 34.52 63.15 143.73 270.71 512.87
6.40 4.86 3.89 3.45 3.16 2.87 2.71 2.56
.
The costs are less for the 1MW,62% efficient klystron at 850 MHz, which is Case Vn in the Appendix. Once again, the klystron development costs are higher, but all the rf systems cost less than the low-efficiency counterpart, due to savings in the power supplies and cooling system. Frequency MHz
Total Power
850 850 850 850 850 850 850 850
1 2
MW 5 10
20 50 100 200
PowerModule
kW
1000 1000 1000 1000 1000 1000 1000 1000
Total Cost
$M
6.34 9.35 18.37 32.35 58.94 132.77 249.99 473.77
Cost/MW $M 6.34 4.68 3.67 3-23 2.95 2.66 2.50 2.37
With 1 MW klystrons, and 200 M W total rf power, we see that the cost per installed rf watt
varies from $2.03 at 352 MHz to $2.37 at 850 MHz. A graph of these costs are shown in Fig. 2, where the cost in $/W is plotted versus total rf system power for the three frequencies, using 1 MW klystrons. The cost rises if 500 kW klystrons are used, and the cost per watt will decrease to $1.84 (at 704 MHz) if a 2 MW klystron is developed. We expect additional savings of about $ 0.2 per Watt if a 4 MW klystron could be developed.
1. CW Klystron System Summary The 352 MHz 1.1 MW klystrons for the LEP project at CERN are the lowest cost options for cw klystron systems. The total system costs estimates, including commissioning, vary from 4.54 to 2.03 $/Was the total RF system power varies from 1 to 200 MW. The klystron costs will increase with frequency, and the range at 850 MHz is from 6.34 to 2.37 $/W for 1 MW klystrons the 1 to 200 MW total RF power level. The use of 500 kW klystrons at any frequency will raise the costs, and the use of 2 MW (or larger) klystrons will reduce the rf system costs. M. Pulsed Klystron System Results
We have examined two pulsed klystron systems so far, the first is for a 4 MW peak, 1 MW average klystron at 433 MHz, This klystron only has an efficiency of 45.6%, and it operates at. 148 kV The cost table is summarized below, but here the power corresponds to average power, and the peak power is 4 times higher. The details are in Case VIII of the Appendix. We see that the cost per average Witt is higher than for the cw systems, and we only use pulsed systems when there is some nonlinearity that we must find, such as high-energy physics applications, or free-electron lasers. Frequency MHz
Total Power MW
433 433 433 433 433 433 433
1 2
5 10 20 50 100
PowerModule kW 1000 1000
1000 1000 1000 1000 1000
Total Cost
$M
6.71 10.89 23.36 42.55 79.79 185.04 352.3 1
CostlMW $M 6.71 5.45 4.67 4.26 3.99 3.70 3 -52
The second pulsed rf system examined is the 100 kW average, 1.25 MW peak power klystron at 850 MHz. Once again, the costs per average M W are shown in the table below, and the peak power is 12.5 times the average power. The details are in Case IX of the Appendix, Frequency MHz
Total Power MW
PowerModule kW
Total Cost
$M
CostMW $M
850 850 850 850
850
850 850
1
2
5 10 20 50 100
1000 1000 1000 1000 1000 1000 1000
6.71 10.89 23.36 42.55 79.79 185.04 352.3 1
6.71 5.45 4.67 4.26 3.99 3.70 3.52
We see that the cost per average Watt is very high, but this is to be expected, since this particular klystron has a high ratio of peak to average output power, and this type of klystron is only used if we have to make relatively high peak powers, not high average power.
w.-20 -
N. Cost Spreadsheet Appendices
1. Case I. 1 MW CW Klystrons at 352 MHz ATW cost CW
352 MHz 1.1 MW klystrons
7/23/9 1
Total rf Power 1 Total dc Power 1.617647 1.1 Amplifier Effic. .68 Module rf Power Number Modules 1 Total ac Power 1.887365 Power Sup Voltage 87 Module Efficiency ,5828231 1 Number of PowSup 1.617647 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetydcint suprv. comp Instal & Condition Buildings Totals AlW cost CW
cost/rfwatt $M Cost QD factor 3304.402 .5804402 1 .29 15712 .2915712 1 .2 .2 1 .29 .29 1 .15 .15 1 .125 .125 1 .15 ,15 1 .01 .o 1 1 .15 .15 1 .16 .16 1 .05 .05 1 .8088235 .8088235 .1186334 .1186334 .1542234 ,1542234 1.133542 1.133542 .16305 ,16305 4.535284 4.535284 352 MHz 1.1 MW klystrons
2 Total dc Power 3.235294 Total rf Power Module rf Power 1.1 Amplifier Effic. .68 Number Modules 2 Total ac Power 3.774730 Module Efficiency ,5828231 Power Sup Voltage 87 1 Number of PowSup PowSup Size 3.235294
w.- 21 -
1
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals MW cost CW
cost/rfwatt $M Cost QD factor .3829477 .7658955 .1944780 ,3889560 1 .1 .2 1 -29 .58 1 .1425 .285 .95 .09625 .1925 .95 .1425 .285 -95 ,009 .018 .9 .135 .27 .9 .0845 ,169 .95 .0475 ,095 .95 ,7415149 1.483030 ,9167820 ,0946476 ,1892952 .1230419 ,2460838 .9043581 1.808716 .lo305 .2061
1
3.591288 7.182576 352 MHz 1.1 M W klystrons
Total rf Power 5 Total dc Power 8.088235 Module rf Power 1.1 Amplifier Effic. .68 Number Modules 5 Total ac Power 9.436825 Power Sup Voltage 87 Module Efficiency .5828231 2 Number of PowSup PowSup Size 4.044118 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref
costlrfwatt $M Cost QD factor
,2209915 .1621718 ,076 .29 ,1331579 .0855790 .1331579 ,0078299 1174480 ,0388772
.
1.104957 ,8108590 .38 1.45 ,6657897 ,4278949 ,6657897 .0391493 ,5872400 .1943860
.95 .95 1 ,8877196 A877 196 A877196 .7829867 .7829867 ,8877196
.95
comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals AlW cost CW
.0443860 .6929024 .0801001 ,1041301 ,7653561 ,06705
.2219299 .8877196 3.464512 3566793 .4005003 ,5206504 3.826781 ,33525
3.019138 15.09569 352 MHz 1.1 MW klystrons
10 Total dc Power 16.17647 Total rf Power Module rf Power 1.1 Amplifier Effic. .68 Number Modules 10 Total ac Power 18.~365 Module Efficiency S828231 Power Sup Voltage 87 Number of PowSup 4 PowSup Size 4.044118 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetytkint suprv. comp Instal & Condition Buildings Totals PiIW cost CW Total rf Power
costlrfwatt $M Cost ,1458000 ,1540632 1.540632 ,0722 .722 .2755 2.755 .1265000 1.265000 .0813000 .8130002 .1265000 1.265000 ,0070469 .0704688 ,1057032 1.057032 .0234333 .2343334 .0421667 .4216668 A582573 6.582573 .0727388 .0945605 .9456048 .6950195 6.950195 .OS05 SO5
QD factor 1.458000 .9025 .9025 95 .8433336 ,8433336 ,9025 A433336 ,7046880 .7046880 3433336 ,8433336 .8 138454 ,7273883
2.735840 27.35840 352 MHz 1.1 MW klystrons 20 Total dc Power
32.35294
Module rf Power
1.1
Amplifier Effic.
.68
Number Modules 20 Total ac Power 37.74730 Module Efficiency S82823 1 Power Sup Voltage 87 Number of PowSup 8 PowSup Size 4.044118 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf
rf ref
comp inter cooling safety&int suprv. comp 1:nstaI & Condition 13uildings Totals N W cost C W
cost/rfwatt $M Cost .0961921 1.923842 ,1463601 2.927201 .06859 1.3718 -2712787 5.425575 ,1201750 2.403501 .0772350 1.544700 .1201750 2.403501 ,0063422 .1268438 .0951329 1.902658 ,0155117 .3102334 .0400583 .am 1669 .6253444 12.50689 .0672958 1.345916 ,0874846 1.749691 .6430116 12.86023 .04905 .98 1
QD factor ,857375 357375 ,9354439 .8011669 .8011669 .857375 ,8011669 ,6342192 .6342192 .8011669 ,8011669 .773 1531
2.529237 50.58475 352 MHz 1.1 M W klystrons
50 Total dc Power 80.8823 5 Total rf Power ]Module rf Power 1.1 Amplifier Effic. .68 Number Modules 50 Total ac Power 94.36825 Module Efficiency .582823 1 Power Sup Voltage 87 Number of PowSup 16 PowSup Size 5.055147 substation power sup power cond power amp
cost/rfwatt $M Cost QD factor .0555105 2.775527 .1220471 6.102354 ,8145063 .0521284 2.60642 .8145063 .2657976 13.28988 ,9165435
.1122966 ,0691804 .1122966 .0055 176 .Of327642 .0104864 .0374322 Sa43479 .0603922 ,0785099 S770477 .04545
shield,support rf&ps cont trans sys drive amp lowlev rf rf ref cornp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals ATW cost CW
5.614828 3.459019 5.614828 ,2758807 4.138210 S243219 1.871609 29.21740 3.019611 3.925494 28.85238 2.2725
.7486438 .7486438 .8145063 .7486438 S517614 317614 .7486438 ,7486438 .7224665
2.271205 113.5603
352 MHz 1.1 MW klystrons
100 Total dc Power 161.7647 Total rf Power 1.1 Amplifier Effic. .68 Module rf Power Number Modules 100 Total ac Power 188.7365 Power Sup Voltage 87 Module Efficiency ~ 8 2 8 213 Number of PowSup 32 5.055147 PowSup Size cost/rfwatt $M Cost QD factor
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
.0366233 .1159447 .0495220 ,261725 ,1066817 .0657214 .lo66817 .0049659 .0744878 .0086121 .0355606 S551305 .0568663 .0739261 S433572 .04425
3.662330 11.59447 4.952198 26.1725 10.66817 6.572137 10.66817 .4965852 7.448779 .8612116 3.556058 55.51305 5.686627 7.392615 54.33572 4.425
.7737809 .7737809 .g025
.7112116 ,7112116.7737809 ,7112116 .4965852 ,4965852 ,7112116 .7112116 ,6863432
Totals
'4TW cost CW
2.140056 214.0056 352 MHz 1.1 MW klystrons
200 Total dc Power 323.5294 'rota1 rf Power ]Module rf Power 1.1 Amplifier Effic. .68 Number Modules 200 Total ac Power 377.4730 Module Efficiency S828231 Power Sup Voltage 87 Number of PowSup 64 PowSup Size 5.055147 substation power sup power cond power amp shield,support d&ps cont trans sys drive amp llowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
cost/rfwatt $M Cost ,0241624 4.832474 .1102475 22.02950 ,0470459 9.409176 .2577148 51.54296 ,1013477 20.26953 ,0624353 12.48706 .lo13477 20.26953 ,0044693 ,8938534 .0670390 13.40780 ,0075065 1.501302 .0337826 6.756510 .5273740 105.4748 .0537749 10.75498 .0699074 13.98147 ,5138191 102.7638 ,04365 8.73
QD factor ,7350919 -7350919 .8886717 ,6756510 .6756510.7350919 .6756510 .4469267 .4469267 .6756510 ,6756510 .6520260
2,025524 405.1048
2. Case 11. 1 MW CW Klystrons at 704 MHz p;Iw
cost CW
704 MHz 1 MW klystrons
1 Total dc Power 1.833333 'Total rf Power 1.1 Amplifier Effic. .6 Module rf Power Number Modules 1 Total ac Power 2.137107 Module Efficiency ,5147145 Power Sup Voltage 90 1 Number of PowSup PowSup Size 1.833333
7/23/91
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals ATW cost CW
codrfwatt $M Cost QD factor ,6100222 .ti100222 ,3092352 .3092352 1 .2 .2 1 1.26 1.26 1 .15 .15 1 .125 ,125 1 .15 .15 1 .Ol .o 1 1 .15 -15 1 .16 .16 1 1 .05 .05 ,9166667 .9166667 1 .1636370 .1636370 .2127281 .2127281 1.563551 1.563551 .16305 .16305
1
6.193890 6.193890 704 MHz 1 M W klystrons
Total rf Power 2 Total dc Power 3.666667 1.1 Amplifier Effic. .6 Module rf Power 4.274214 Number Modules 2 Total ac Power Module Efficiency S147145 Power Sup Voltage 90 Number of PowSup 1 PowSup Size 3.666667 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref
cost/rfwatt $M Cost QD factor .4024646 .8049291 1 .2062599 .4125199 .1 .2 1 1 .8164 1.6328 .95 .1425 ,285 .95 .09625 .1925 ,1425 ,285 .95 .009 ,018 .9 .9 ,135 .27 .95 .0845 ,169
1
comp inter cooling safety&int suprv. camp Instal & Condition Buildings Totals cost CW
,0475 ,8326357 ,1206004 .1567805 1.152337 ,10305
.095 .95 1.665271 ,9083298 .2412008 ,3135611 2.304674 ,2061
4.547778 9.095556 704 MHz 1 M W klystrons
Total rf Power 5 Total dc Power 9.166667 1.1 Amplifier Effic. .6 Module rf Power 5 Total ac Power 10.68554 Number Modules ]Module Efficiency S147145 Power Sup Voltage 90 Number of PowSup 2 4.583333 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys (driveamp lowlev rf rf ref comp inter cooling safetydkint suprv. comp Instal & Condition Buildings Totals p(Iw cost
CW
cost/rfwatt $M Cost .2322542 1.161271 .1719965 ,076 .38 .55024 2.7512 .1331579 .6657897 ,0855790 ,4278949 .1331579 ,6657897 ,0078299 .0391493 .1174480 .5872400 .0388772 ,1943860 .0443860 .2219299 ,7780495 3.890248 ,0947590 ,4737952 .1231868 ,6159338 .9054227 4.5271 13 .06705 ,33525 3.559395 17.79697 704 MHz 1 M W klystrons IV -
28
-
QD factor
.8599826 .95 1 ,8877196 .8877196 .8877196 ,7829867 .7829867 .8877196 ,8877196 .8487813
.95
.95
Total rf Power 10 Total dc Power 18.33333 Module rf Power 1.1 Amplifier Efic. .6 Number Modules 10 Total ac Power 2 1.37107 Module Efficiency .5 147145 Power Sup Voltage 90 Number of PowSup 4 4.583333 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals AIW cost CW
cost/rfwatt $M Cost .1532307 1.532307 .1633967 1.633967 ,0722 .722 ,444744 4.44744 .1265000 1.265000 .0813000 .8130002 .1265000 1.265000 .0070469 ,0704688 ,1057032 1.057032 ,0234333 .2343334 .0421667 .4216668 .7391470 7.391470 .0834147 .8341474 .lo84392 1.084392 ,7970279 7.970279 .OS05 SO5
QD factor .9025 ,9025 .95 .8433336 ,8433336 ,9025 .8433336 .7046880 .7046880 .8433336 A3433336 .8063422
3.129300 31.29300 704 MHz 1 MW klystrons
20 Total dc Power 36,66667 Total rf Power 1.1 Amplifier Effic. -60 Module rf Power 42.74214 Number Modules 20 Total ac Power Moduie Efficiency 5147145 Power Sup Voltage 90 8 Number of PowSup PowSup Size 4.583333 substation power sup power cond power amp
cost/rfwatt $M Cost QD factor .lo10945 2.021891 ,1552269 3.104537 .857375 ,06859 1.3718 .857375 .3942968 7.885936 ,9354439
shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int auprv. comp Instal & Condition Buildings Totals .p31w cost
CW
,1201750 ,0772350 ,1201750 ,0063422 .095 1329 .0155117 .0400583 ,7021897 ,0758411 ,0985935 ,7246619 .04905
2.403501 1.544700 2.403501 ,1268438 1.902658 .3 102334 ,8011669 14.04379 1.516822 1.971869 14.49324 .98 1
,8011669 8011669 ,857375 ,8011669 ,6342192 ,6342192 .8011669 .80 11669 .7660251
2.844175 56.88349 704 MHz 1 MW klystrons
'Total rf Power 50 Total dc Power 9 1.66667 1.1 Amplifier Effic. .6 Module rf Power 'Number Modules 50 Totai ac Power 106.8554 Module Efficiency ,5147145 Power Sup Voltage 90 18 Number of PowSup PowSup Size 5.092593 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
cost/rfwatt $M Cost .0583396 2.916981 ,1374586 6.872928 ,0581355 2.906776 .3600537 18.00268 ,1122966 5,614828 .0706822 3.534108 .1122966 5.614828 .0055176 ,2758807 .0827642 4,138210 .0104864 ,5243219 .0374322 1.871609 .6561553 32.80777 .0680647 3.403237 .0884842 4.424208 ,6503586 32.5 1793 .04545 2.2725
QD factor .8074379 .8074379 ,9165435 ,7486438 ,7486438 3074379 ,7486438 ,5517614 .55 17614 .7486438 .7486438 .7158058
Totals AI" cost CW
2.553976 127.6988 704 MHz 1 MW klystrons
Total rf Power 100 Total dc Power 183.3333 Module rf Power 1.1 Amplifier Effic. .6 213.7107 Number Modules 100 Total ac Power Module Efficiency S147145 Power Sup Voltage 90 Number of PowSup 36 PowSup Size 5.092593 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetykint suprv. comp Instal & Condition Buildings Totals ATW cost C W
cost/rfwatt $M Cost .0384898 3.848980 .1305856 13.05856 ,0552287 5.522875 ,3456875 34.56875 ,1066817 10.66817 ,0671481 6.714806 ,1066817 10.66817 ,0049659 .4965852 .0744878 7.448779 .0086121 A612116 ,0355606 3.556058 .6233476 62.33476 .0638991 6.389908 .0830688 8.306881 .6105557 61.05557 .04425 4.425 2.399251
QD factor ,7670660 .7670660 .9025
.7112116 ,7112116.7670660 .7 112116 .4965852 ,4965852 ,7112116 ,7112116 ,6800 155
239.9251
704 MHz 1 M W klystrons
Total rf Power 200 Total dc Power 366.6667 Module rf Power 1.1 AmpIifier Effic. .6 Number Modules 200 Total ac Power 427.4214 Module Efficiency S147145 Power Sup Voltage 90 Number of PowSup 72 PowSup Size 5.092593
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp 1:nstal & Condition Buildings Totals
cost/rfwatt $M Cost ,0253938 5,078759 .1240563 24.81 127 .0524673 10.49346 .3359403 67.18806 ,1013477 20.26953 ,0637907 12.75813 .lo13477 20.26953 ,0044693 ,8938534 ,0670390 13.40780 .0075065 1.501302 .0337826 6.7565 10 S921802 118.4360 .0603729 12.07457 ,0784847 15.69694 ,5768626 115.3725 .04365 8.73
QD factor .7287127 .7287127 ,8886717 ,6756510 .6756510.7287127 .6756510 ,4469267 ,4469267 .6756510 .6756510 A460 147
2.268691 453.7383 2 MW CW Klystrons at 704 MHz
AT" cost C W
704 MHz 2 M W klystrons
712319 1
Total rf Power 1 Total dc Power 1.833333 ]Module rf Power 1.1 Amplifier Effic, .6 1 Total ac Power 2.137107 Number Modules Module Efficiency S147145 Power Sup Voltage 90 IHumber of PowSup 1 PowSup Size 1.833333 substation power sup power cond power amp shield,support d&ps cont trans sys drive amp lowlev rf
cost/rfwatt $M Cost QD factor ,6100222 6100222 .3092352 ,3092352 1 .2 .2 1 1.26 1.26 1 .15 .15 1 .125 ,125 1 .15 .15 1 .o 1 .o 1 1 .15 .15 1
1
rf ref comp inter cooling safeiy&int suprv. comp Instal & Condition Buildings Totals
p;Tw
cost CW
.16 -05
,9166667 .1636370 .2127281 1.563551 .16305
.16 .05 .9166667 ,1636370 .2127281 1.563551 ,16305
1 1 1
6.193890 6.193890 704 MHz 2 MW klystrons
Total rf Power 2 Total dc Power 3.666667 Amplifier Effic. .6 Module rf Power 2.2 Number Modules 1 Total ac Power 4.259914 ModuIe Efficiency .5164423 Power Sup Voltage 95 Number of PowSup 1 PowSup Size 3.666667 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetykint suprv. comp Instal & Condition Buildings Totals AJW cost CW
cost/rfwatt $M Cost QD factor .4019254 .8038508 1 ,2085024 ,4170048 1 .1 .2 1 ,6625 1.325 1 .075 .15 .0625 .125 1 1 .075 .15 1 ,005 .o1 1 ,075 .15 1 .08 .16 1 .025 .05 ,9083298 3326357 1.665271 .lo4 1225 .2082451 .1353593 .2707186 ,9948909 1.989782 .081525 .16305 3.918961 7.837923 704 MHz 2 MW klystrons
w.-33 -
1
Total rf Power 6 Total dc Power 11 Module rf Power 2.2 Amplifier Effic. .6 Number Modules 3 Total ac Power 12.77974 Module Efficiency ,5164423 Power Sup Voltage 95 Number of PowSup 3 PowSup Size 3.666667 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling fafety&int suprv. comp Instal & Condition Buildings Totals ,MW cost CW
cost/rfwatt $M Cost ,2079087 1.247452 ,1922223 1.153334 .0921919 331514 -3858333 2.3 15 .0691439 .4148635 '0576199 ,3457 196 .0691439 .4148635 .0042310 ,0253862 ,0634654 ,3807927 ,0296096 .1776576 .0230480 .1382878 .7676226 4.605736 .0784816 .4708898 ,1020261 ,6121567 .7498920 4.499352 .041525 ,24915
QD factor .92 19190 ,9219190
1 .9219190 ,92 19190.92 19190 .92 19190 .8462060 ,8462060 .9219190 .9219190 .8374065
2.933965 17.60379 704 MHz 2 MW klystrons
'Total rf Power 10 Total dc Power 18.33333 Module rf Power 2.2 Amplifier Effic. .6 5 Total ac Power 21.29957 Number Modules Module Efficiency ,5164423 Power Sup Voltage 95 Number of PowSup 4 PowSup Size 4.583333 substation power sup power cond
cost/rfwatt $M Cost QD factor ,1530254 1.530254 .1651732 1.651732 .9025 ,0722 .722 .9025 N-
34-
power amp shield,support rf&ps cont trans sys drive amp lowiev rf rf ref comp inter cooling safetykint suprv, comp Instal & Condition Buildings Totals N W cost CW
.3305 .0665790 .OS13395 .0665790 .0039149 .0587240 .O 194386 ,0221930 .7391470 .0699525 ,0909383 .6683965 ,033525
3.305 .6657897 ,5133949 .6657897 .0391493 S872400 .1943860 .2219299 7.391470 ,6995254 .9093830 6,683965 .33525
1 ,8877196 ,8877196 .9025 8877196 .7829867 .7829867 .8877196 .8877196 ,8063422
2.611626 26.11626 704 MHz 2 MW klystrons
Total rf Power 20 Total dc Power 36.66667 2.2 Amplifier Effic. .6 Module rf Power Number Modules 10 Total ac Power 42.59914 Module Efficiency ,5164423 Power Sup Voltage 95 8 Number of PowSup PowSup Size 4.583333 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition
cost/rfwatt $M Cost .lo0959 1 2.019182 .1569145 3.138290 .06859 1.3718 .2778625 5.55725 .0632500 1.265000 ,0487725 .9754502 .0632500 1.265000 .0035234 .0704688 ,0528516 1.057032 .0117167 ,2343334 .0210833 .4216668 ,7021897 14,04379 .0628385 1.256771 .OS 16901 1.633802 .6004222 12.00844 IV- 35 -
QD factor .857375 ,857375 .95 8433336 .8433336 357375 .8433336 .7046880 .7046880 .8433336 ,8433336 ,7660251
Buildings Totals
N W cost CW
.027525
.5505
2.343439 46.86879 704 MHz 2 MW klystrons
%tal rf Power 50 Total dc Power 9 1.66667 Module rf Power 2.2 Amplifier Effic. .6 Total ac Power 106.4979 Number Modules 25 Power Sup Voltage 95 Module Efficiency .5 164423 18 Number of PowSup PowSup Size 5.092593 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf i f ref comp inter cooling safetydkint suprv. comp Hnstal & Condition Buildings Totals .AJw cost CW
cost/rfwatt $M Cost ,0582615 2.9 13074 .1389530 6.947651 .0581355 2.906776 ,2476594 12.38297 ,0591035 2.955173 ,0440856 2.204281 ,0591035 2.955173 ,0030653 .1532671 .0459801 2.299006 .0069402 .3470115 ,0197012 .9850576 ,6561553 32.80777 .0558858 2.794288 .0726515 3.632575 S339885 26.69942 .023925 1.19625
QD factor .8074379 $074379 ,9308055 ,7880461 ,7880461 3074379 .7880461 .6 130682 .6130682 .788046 1 .7880461 .7158058
2.083595 104.1797 704 MHz 2 MW klystrons
‘rota1rf Power 100 Total dc Power 183.3333 Module rf Power 2.2 Amplifier Effic. .6 Total ac Power 212.9957 Number Modules 50 Module Efficiency ,5164423 Power Sup Voltage 95
Number of PowSup Powsup Size 5.092593 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals pirw
cost CW
36 cost/rfwatt $M Cost .0384382 3.843824 ,1320054 13.20054 .OS2287 5.522875 .2355576 23.55576 .0561483 5.6 14828 .04 18813 4.188 133 .OS61483 5.6 14828 .0027588 .2758807 .0413821 4.138210 ,0052432 ,5243219 .O 187161 1.871609 ,6233476 62.33476 ,0522742 5.227423 .0679565 6.795649 .4994802 49.94802 .022725 2.2725
QD factor ,7670660 .7670660 .9165435 ,7486438 ,7486438.7670660 .7486438 SI7614 ,5517614 ,7486438 ,7486438 .6800155
1.949292 194,9292 704 MHz 2 M W klystrons
Total rf Power 200 Total dc Power 366.6667 Module rf Power 2.2 Amplifier Effic. .6 Number Modules 100 Total ac Power 425.99 14 Module Efficiency S164423 Power Sup Voltage 95 Number of PowSup 72 PowSup Size 5.092593 cost / h t t
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp
.0253598 ,1254051 .0524673 .2277601 ,0533409 .0397873 ,0533409 .0024829
$M Cost 5.07 1956 25.08102 10.49346 45.55201 10.66817 7.957453 10.66817 ,4965852
Iv -
37
-
QD factor .7287127 .7287127 .9025 ,7112116 .7112116.7287127 .7112116 .4965852
lowlev rf rf ref comp inter cooling safety&i nt suprv. comp Instal & Condition Eluildings Totals
.0372439 .0043061 .0177803 ,5921802 .0492582 ,0640356 ,4706619 .022125
7.448779 ,8612116 3.556058 118.4360 9.851637 12.80713 94.13239 4.425
,4965852 .7112116 ,7112116 ,6460147
1.837535 367.5071
4. Case Iv. 0.5 Mw, 50% Efficient, CW Klystrons at 850 MHz
ATW cost CW
850 MHz 0.5 MW klystrons Model M1
7/23/91
Total r€Power 1 Total dc Power 2 .5 Amplifier Effic. .5 Module rf Power Number Modules 2 Total ac Power 2.13 1263 Module Efficiency ,4692053 Power Sup Voltage 64 1 Number of PowSup I’owSup Size 2 substation power sup power cond power amp shield,support r.f&ps cont trans sys drive amp lowlev rf I+ ref comp inter cooling safetj&int suprv. comp Instal & Condition Buildings Totals
cost/rfwatt $M Cost QD factor .6093544 ,6093544 ,2994935 ,2994935 1 -2 *2 1 1.232 1.232 1 .285 .285 .95 .1925 ,1925 .95 ,285 ,285 .95 .018 ,018 .9 .27 .27 .9 .169 .169 .95 .095 .095 .95 .95 .95 .95 .1842139 1842139 ,2394781 ,2394781 1.760164 1.760164 .2061 ,2061 6.995304 6.995304
1
ATW cost C W
850 MHz 0.5
M W klystrons Model M1
Total rf Power 2 Total dc Power 4 Module rf Power .5 Amplifier Effic. .5 Number Modules 4 Total ac Power 4.262526 Module Efficiency ,4692053 Power Sup Voltage 64 Number of PowSup 1 PowSup Size 4 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals MW cost CW
cost/rfwatt $M Cost QD factor .4020240 ,8040480 1 ,1997622 .3995244 1 .1 .2 1 1.038 2.076 .9025 ,34295 .6859 .9025 1 ,160375 ,32075 .9025 .27075 ,5415 .81 ,0162 ,0324 .81 .243 .486 .9025 .09305 ,1861 .9025 .09025 .1805 .9025 .9025 1.805 .1543544 ,3087089 .2006608 ,4013216 1.474857 2.949713 ,1461 ,2922 5.834833 11.66967 850 MHz 0.5 MW klystrons Model M1
Total rf Power 5 Total dc Power 10 .5 Amplifier Effic. .5 Module rf Power Number Modules 10 Total ac Power 10.65632 Module Efficiency ,4692053 Power Sup Voltage 64 Number of PowSup 2 PowSup Size 5 substation
cost/rfwatt $M Cost QD factor .2320000 1.160000
Iv.- 3 9 -
power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling :iafety&int suprv. comp Instal & Condition Buildings Totals AlW cost CW
.1665782 .076 88362 ,3204668 .1455000 ,2530001 .0140938 .2 114064 .0468667 ,0843334 ,8433336 .13 10880 .1704143 1.252545 .1101
3328909 .38 4.4181 1.602334 ,7275002 1.265000 .0704688 1.057032 ,2343334 ,4216668 4.216668 ,6554398 ,8520717 6.262727 .SO5
.95 .95 .95 ,8433336 ,8433336 .8433336 .7046880 .7046880 ,8433336 ,8433336 3433336
4.941347 24.70673 850 MHz 0.5 M W klystrons Model M1
Total rf Power 10 Total dc Power 20 Module rf Power .5 Amplifier Effic, .5 Number Modules 20 Total ac Power 21.3 1263 Module Efficiency .4692053 Power Sup Voltage 64 Number of PowSup 4 5 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int
cost/rfwatt $M Cost ,1530629 1.530629 ,1582493 1.582493 .0722 .722 .8310389 8.310389 .3044434 3.044434 .1382250 1.382250 .2403501 2.403501 .0126844 ,1268438 ,1902658 1.902658 .03 10233 .3 102334 .0801167 A3011669 .8011669 8.011669 ,1205131 1.205131
QD factor ,9025 ,9025 .9354439 ,8011669 3011669 .9025 ,8011669 .6342192 .6342192 ,8011669 ,8011669 ,8011669
.95
.1566670 1.566670 1.151502 11.51502 .0981 .981
suprv. comp Instal & Condition Buildings Totals ATW cost CW
Total rf Power Module rf Power
4.539609 45.39609
850 MHz 0.5 MW klystrons Model Ml
20 .5
Total dc Power Amplifier Effic.
40 .5
Number Modules 40 Total ac Power 42,62526 Module Efficiency .4692053 Power Sup Voltage 64 8 Number of PowSup PowSup Size 5 cost/rfwatt $M Cost ,1009839 2.019677 ,1503368 3.006736 ,06859 1.3718 ,7984821 15.96964 ,2892213 5.784425 .1313138 2.626276 .2283326 4.566652 .0114159 .2283189 .1712392 3.424784 .0227222 .4544434 ,0761109 1.522217 .7611086 15.22217 .1123943 2.247886 .1461126 2.922251 1.073927 21.47855 .092 1 1.842
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
p;fw
QD factor .857375 357375 .9211108 ,7611086 .7611086 357375 .7611086 ,5707973 .5707973 ,7611086 ,7611086 .7611086
TotaIs
4.234391 84.68783
cost CW
850 MHz 0.5 MW klystrons Model M1
Total rf Power Module rf Power
50 .5
Total dc Power Amplifier Effic. IV- 4 1 -
100 .5
Number Modules 100 Total ac Power 106.5632 Module Efficiency .4692053 Power Sup Voltage 64 Number of PowSup 20 PowSup Size 5 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals AI'W cost CW
cost/rfwatt $M Cost ,0582758 2.913788 .1404810 7.024049 .0640934 3.204668 ,7702929 38.51465 -2702604 13.51302 ,1227051 6.135254 ,2133635 10.66817 ,0099317 ,4965852 .1489756 7.448779 ,0172242 ,8612116 .0711212 3,556058 .7112116 35.56058 .lo39175 5.195873 .1350927 6.754634 ,9929312 49.64656 .0885 4.425
QD factor .80 11669 .8011669 .9025 .7112116 .7 112116.80 11669 .7 112116 ,4965852 ,4965852 .7112116 .7112116 .7112116
3.9 18378 195.9189 850 MHz 0.5 M W klystrons Model M1
Total rf Power 100 Total dc Power 200 Module rf Power ,5 Amplifier Effic. .5 Number Modules 200 Total ac Power 213.1263 Module Efficiency .4692053 Power Sup Voltage 64 Number of PowSup 40 5 PowSup Size substation power sup power cond power amp shield,support rf&ps cont
cost/rfwatt $M Cost ,0384477 3.844766 ,1334569 13.34569 ,0608887 6.088869 .7543887 75.43887 ,2567474 25.67474 .1165698 11.65698
QD factor .7611086 ,7611086 .8886717 ,6756510 .6756510.7611086
trans sys drive amp f lowlev x r f ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals MW cost CW
,2026953 .0089385 ,1340780 .0150130 ,0675651 .67565 10 .0985776 .1281509 .94 19091 .0873
20.26953 ,8938534 13.40780 1.501302 6.756510 67.56510 9.857761 12.81509 94.19091 8.73
.6756510 .4469267 ,4469267 ,6756510 A756510 .6756510
3.720378 372.0378 850 MHz 0.5 MW klystrons Model M1
Total rf Power 200 Total dc Power 400 .5 Amplifier Effic. .5 Module rf Power Number Modules 400 Total ac Power 426,2526 Module Efficiency ,4692053 Power Sup Voltage 64 Number of PowSup 80 PowSup Size 5 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
c o s t / h t t $M Cost ,0253660 5.073200 .1267841 25.35682 ,0578443 11,56885 .7407503 148.1501 .1925605 38.51211 ,1107413 22.14827 .1925605 38.51211 .0080447 1.608936 .1206702 24.13404 ,0135874 2.717474 .0641868 12.83737 .6418685 128.3737 .0917986 18.35972 .1193382 23.86763 .8771355 175.4271 .0867 17.34 3.469937 693.9874
w.- 43 -
QD factor .7230532 .7230532 .8750553 .6418685 .64 18685.7230532 .6418685 .4022341 .4022341 .64 18685 .6418685 .6418685
5. Case V. 0.5 Mw, 60% Emcient, CW Klystrons at 850 MHz NW cost CW
850 MHz 0.5 MW klystrons Model M2
7/23/91
'Total rf Power 1 Total dc Power 1.666667 .5 Amplifier Effic. .6 Module rf Power Number Modules 2 Total ac Power 1.780386 Module Efficiency ,5616760 Power Sup Voltage 64 1 Number of PowSup PowSup Size 1.ti66667 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals AT" cost CW
cost/rfwatt $M Cost QD factor S670493 370493 .2776304 ,2776304 1 1 .2 .2 1 1.445 1,445 .285 ,285 .95 .1925 .1925 .95 .285 .285 .95 .018 ,018 .9 .9 .27 .27 ,169 ,169 -95 ,095 .95 .095 .8333333 A333333 1 .1855005 .1855005 .2411507 ,2411507 1.772457 1.772457 ,2061 ,2061 7.042722 7.042722 850 MHz 0.5 MW klystrons Model M2
Total rf Power 2 Total dc Power 3.333333 .5 Amplifier Effic. .6 Module rf Power Number Modules 4 Total ac Power 3.560772 Module Efficiency S616760 Power Sup Voltage 64 1 Number of PowSup PowSup Size 3.333333
N.- 44
-
1
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals ATW cost CW
cost/rfwatt $M Cost QD factor ,3741130 .7482260 .la51795 ,3703591 1 .1 .2 1 1.1675 2.335 1 .27075 S415 .9025 .160375 ,32075 .9025 1 ,9025 .27075 S415 .0162 .0324 -81 ,243 .486 .81 .09305 ,1861 .9025 .09025 $1805 .9025 .7622991 1.524598 ,9147590 .1493387 ,2986773 ,1941403 .3882805 1.426931 2.853862 ,1461 .2922 5.649977 11.29995 850 MHz 0.5 MW klystrons Model M2
Total rf Power 5 Total dc Power 8.333333 .5 Amplifier Effic. .6 Module rf Power Number Modules 10 Total ac Power 8.901930 Module Efficiency ,5616760 Power Sup Voltage 64 2 Number of PowSup PowSup Size 4.166667 substation power sup power cond power amp shield,support
rf&ps cont trans sys
drive amp lowlev rf rf ref comp inter
cost/rfwatt $M Cost .2158931 1.079466 .1544180 .7720898 .076 .38 .96095 4.80475 .2530001 1.265000 .1455000 .7275002 .2530001 1.265000 .0140938 ,0704688 .2114064 1.057032 .0468667 .2343334 .0843334 .4216668
w.- 45 -
QD factor .95 .95 .95 3433336 A433336 .8433336 .7046880 .7046880 A433336 A433336
.95
cooling safety&int suprv. comp Hnstal & Condition Buildings
,7123241 .1251114 ,1626449 1.195440 .1101
,8547889
4.72 1082 23.60541
Totals “W cost CW
3.561620 .6255571 3132243 5.977198 ,5505
850 MHz 0.5 MW klystrons Model M2
‘rota1 rf Power 10 Total dc Power 16.66667 Module rf Power .5 Amplifier Effic. .6 Number Modules 20 Total ac Power 17.80386 ]Module Efficiency S616760 Power Sup Voltage 64 4 Number of PowSup 4.166667 IPowSup Size cost/&att ,1424363 .1466971 .0722 3909178 .2403501 ,1382250 .2403501 ,0126844 ,1902658 .0310233 .0801167 ,6767079 1144790 .1488227 1.093847 ,0981
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp Iowlev rf rf ref comp inter cooling c;afety&int csuprv. comp Instal & Condition Buildings
.
Totals AW cost CW
Total rf Power
$M Cost 1.424363 1.466971 ,722 8.909178 2.403501 1.382250 2.403501 ,1268438 1.902658 .3 102334 8011669 6.767079 1.144790 1.488227 10.93847 .98 1
QD factor ,9025 .9025 .935 4439 3011669 ,8011669 ,9025 ,8011669 ,6342192 .6342 192 ,8011669 BO11669 3120495
4.317223 43.17223
850 MHz 0.5 MW klystrons Model M2 20
Total dc Power
33.33333
Module rf Power .5 Amplifier Effic. .6 40 Total ac Power 35.60772 Number Modules Module Efficiency S616760 Power Sup Voltage 64 Number of PowSup 8 PowSup Size 4. 166667 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals MW cost CW
cost/rfwatt $M Cost .0939729 1.879459 .1393622 2.787244 .06859 1.3718 3492939 16.98588 .2283326 4.566652 .13 13138 2.626276 .2283326 4.566652 .0114159 .2283189 .1712392 3.424784 .0227222 ,4544434 .0761109 1.522217 .6428725 12.85745 ,1065423 2.130847 ,1385051 2.770101 1.018012 20.36024 .0921 1.842
QD factor A57375 357375 .9211108 ,7611086 .7611086 357375 ,7611086 S707973 ,5707973 ,7611086 .7611086 ,7714470
4.018718 80.37436 850 MHz 0.5 MW klystrons Model M2
Total rf Power 50 Total dc Power 83.33333 .5 Amplifier Effic. .6 Module rf Power Number Modules 100 Total ac Power 89.0 1930 Module Efficiency ,5616760 Power Sup Voltage 64 18 Number of PowSup PowSup Size 4.629630 substation power sup power cond power amp shield,support
c o s t / h t t $M Cost QD factor ,0542299 2.711495 .1234099 6.170493 3074379 .0581355 2.906776 ,8074379 .8151928 40.75964 .9025 .2133635 10.66817 .7112116
w.-
47
-
rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals MW cost CW
,1212156 .2133635 .0099317 ,1489756 .O 172242 .07 11212 ,6007269 .0978756 .1272383 ,9352014
.OW
6.060781 10.66817 .4965852 7.448779 .8612116 3.556058 30.03634 4.893780 6.361914 46.76007 4.425
.7112116,8074379 .7112116 .4965852 ,4965852 ,7112116 ,7112116 ,7208722
3.695705 184.7853
850 MHz 0.5 MW klystrons Model M2
Total rf Power 100 Total dc Power 166.6667 .5 Amplifier Effic, .6 Module rf Power Number Modules 200 Total ac Power 178.0386 Module Efficiency S616760 Power Sup Voltage 64 Number of PowSup 34 PowSup Size 4.901961 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp instal & Condition Buildings
cost/rfwatt $M Cost .0357784 3.577839 ,1138695 11.38695 ,0523816 5.238158 .7969632 79.69632 .2026953 .1144430 11,44430 .2026953 20.26953 .0089385 ,8938534 .1340780 13.40780 .0150130 1.501302 ,0675651 6.7565 10 S706905 57.06905 .0926045 9.260446 .1203858 12.03858 ,8848356 88.48356 .OS73 8.73
A?- 48
-
QD factor .7703173 .7703173 .8886717 20.26953 .6756510 .6756510.7703 173 .6756510 ,4469267 .4469267 ,6756510 ,6756510 .6848286
Totals ATW cost CW
3.500237 350.0237 850 MHz 0.5 MW klystrons Model M2
Total rf Power 200 Total dc Power 333.3333 .5 Amplifier Effic. .6 Module rf Power Total ac Power 356.0772 Number Modules 400 Module Efficiency ,5616760 Power Sup Voltage 64 Number of PowSup 66 PowSup Size 5.050505 cost/rfwatt $M Cost .0236049 4.720987 .lo65408 21.30816 .0484057 9.681 143 ,7818522 156.3704 .1925605 38.51211 .lo838 17 2 1.67634 .1925605 38.51211 .0080447 1.608936 .1206702 24.13404 .0135874 2.717474 .0641868 12.83737 S421560 108.4312 ,0881021 17.62041 ,1145327 22.90654 ,8418152 168.3630 ,0867 17.34
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
.7334199 .7334199 .8750553 .6418685 ,6418685.7334199 .6418685 .4022341 ,4022341 .64 18685 .64 18685 .6505872
3.333701 666.7403
6. Case VI. 1 p;Iw cost CW
QD factor
50% Efficient CW Klystrons at 850 MHz
850 MHz 1.0 M W klystrons Model P1
Total rf Power 1 Total dc Power 2.2 1.1 Amplifier Effic. .5 Module rf Power Number Modules 1 Total ac Power 2.56 1668 Module Efficiency .4294076 Power Sup Voltage 78 Number of PowSup 1 PowSup Size 2.2
Iv-
49
-
7/23/91
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetytkint suprv. comp Instal & Condition Buildings Totals NW cost CW
costlrfwatt $M Cost QD factor .6558799 .6558799 .3241751 ,3241751 1 .2 .2 1 1.22 1.22 1 .15 .15 1 ,125 .125 1 .15 .15 1 .o 1 .01 1 .15 .15 1 .16 .16 1 .05 .os 1 1.037656 1.037656 .9433232 ,1693084 .1693084 .2201009 ,2201009 1.617742 1.617742 ,16305 .16305
1
6.402912 6.402912 850 MHz 1.0 MW klystrons Model P1
Total rf Power 2 Total dc Power 4.4 1.1 Amplifier Effic. .5 Module rf Power Number Modules 2 Total ac Power 5.123337 Module Efficiency .4294076 Power Sup Voltage 78 Number of PowSup 1 IPowSup Size 4.4 substation power sup power cond power amp shield,support d&ps cont trans sys drive amp lowlev rf rf ref
cost/rfwatt $M Cost QD factor A327193 ,8654387 1 .2 162249 ,4324497 1 .l .2 1 ,836 1.672 .95 .1425 .285 .95 .09625 .1925 .95 ,1425 .285 .9 .009 ,018 .9 .135 .27 .95 .0845 .169
1
comp inter cooling safe@&int suprv. comp Instal & Condition Buildings
p;Tw
,0475 ,9857728 ,1291187 ,1678543 1.233729 .lo305
.095 .95 1-971546 .896 1571 ,2582374 ,3357086 2.467458 ,2061
Totals
4.861719 9.723438
cost CW
850 MHz 1.0 MW klystrons Model P1
Total rf Power 5 Total dc Power 11 Module rf Power 1.1 Amplifier Effic. .5 Number Modules 5 Total ac Power 12.80834 Module Efficiency .4294076 Power Sup Voltage 78 Number of PowSup 2 5.5 PowSup Size substation power sup power cond power amp shield,support
rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
p;Iw
cost/rfwatt $M Cost .2497137 1.248568 .1803061 .9015305 .076 .38 .6056 3.028 ,1331579 .6657897 ,0855790 ,4278949 ,1331579 ,6657897 .0078299 .0391493 .1174480 .5872400 ,0388772 .1943860 .0443860 .2219299 .9211472 4.605736 .lo3728 1 .5 186406 .1348465 ,6742327 .99 11221 4.9556 11 .06705 .33525
QD factor
.95 .95 1
,8877196 ,8877196 ,8877196 ,7829867 .7829867 A3877196 3877196 3374065
Totals
3.889950 19.44975
cost CW
850 MHz 1.0 MW klystrons Model P1
w.- 5 1 -
.95
Total rf Power 10 Total dc Power 22 Module rf Power 1.1 Amplifier Effic. .5 Number Modules 10 Total ac Power 25.61668 Module Efficiency .4294076 Power Sup Voltage 78 Number of PowSup 4 PowSup Size 5.5 substation power sup power cond power amp shield,support rE&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetydcint supw. comp Instal & Condition E3uildings Totals AW cost CW
cost/rfwatt $M Cost ,1647496 1.647496 .17 12908 1.712908 .0722 .722 SO846 5.0846 .1265000 1.265000 .0813000 ,8130002 .1265000 1.265000 ,0070469 ,0704688 ,1057032 1.057032 ,0234333 ,2343334 ,0421667 .4216668 3750898 8,750898 ,0921776 .9217762 ,1198309 1.198309 A3807571 8.807571 .OS05 SO5
OD factor .9025 ,9025 .95 .8433336 .8433336 ,9025 ,8433336 .7046880 ,7046880 .8433336 .8433336 ,7955362
3.452256 34,52256 850 MHz 1.0 MW klystrons Model P1
Total rf Power 20 Total dc Power 44 Module rf Power 1.1 Amplifier Effic. .5 Number Modules 20 Total ac Power 5 1.23337 Module Efficiency .4294076 Power Sup Voltage 78 8 Number of PowSup PowSup Size 5.5 substation power sup power cond power amp
cost/rfwatt $M Cost QD factor .lo86942 2.173884 ,1627263 3.254525 357375 ,06859 1.3718 357375 .4626796 9.253592 .9354439 Iv. - 52 -
shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&i nt suprv. comp Instal & Condition Buildings Totals ATW cost CW
,1201750 ,0772350 ,1201750 .0063422 .0951329 . O W 1 17 .0400583 .8313353 ,0843462 .lo96501 .8059282 .04905
2.40350 1 1.544700 2.403 501 ,1268438 1.902658 .3 102334 ,8011669 16.62671 1.686924 2.193002 16.11856 .98 1
.8011669 .BO11669 .857375 3011669 .6342192 .6342192 ,8011669 .8011669 ,7557594
3.157630 63.15260
850 MHz 1.0 MW klystrons Model P1
Total rf Power 50 Total dc Power 110 Module rf Power 1.1 Amplifier Effic. .5 Number Modules 50 Total ac Power 128.0834 Module Efficiency ,4294076 Power Sup Voltage 78 Number of PowSup 20 5.5 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
cost/rfwatt $M Cost .0627252 3.136262 .1520582 7.602910 ,0640934 3.204668 .430392 1 2 1.51961 .1122966 5.614828 .072 1716 3.60858 1 .1122966 5.614828 .0055 176 .2758807 .OB27642 4.1382 10 .0104864 ,5243219 ,0374322 1.871609 .7768344 38.84 172 .0767627 3.838137 ,0997916 4.989578 .7334680 36.67340 ,04545 2.2725 N.- 53 -
QD factor ,8011669 .8011669 .9165435 .7486438 .7486438 BO11669 .7486438 S517614 ,5517614 ,7486438 ,7486438 ,7062131
. .
h3[w
Totals
2.87454 1 143.7270
cost CW
850 MHz 1.0 MW klystrons Model P1
100 Total dc Power 220 Total rf Power Module rf Power 1.1 Amplifier Effic. *5 Number Modules 100 Total ac Power 256.1668 Module Efficiency .4294076 Power Sup Voltage 78 Number of PowSup 40 PowSup Size 5.5 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int
suprv. comp Instal & Condition Buildings Totals .ATW cost CW
costjrfwatt $M Cost ,0413832 4.138322 .1444553 14.44553 .0608887 6.088869 .4160507 41.60507 ,1066817 10.66817 .0685630 6.856304 .lo66817 10.66817 .0049659 .4965852 .0744878 7.448779 ,0086121 ,8612116 .0355606 3.556058 .7379927 73.79927 .0722529 7.225294 .0939288 9.392882 ,6903768 69.03768 .04425 4.425
QD factor .76 11086 ,7611086 ,9025 ,7112116 .7112116.7611086 ,7112116 ,4965852 .4965852 .7112116 .7112116 .6709024
2.707132 270.7132 850 MHz 1.0 M W klystrons Model P1
'Total rf Power 200 Total dc Power 440 Module rf Power 1.1 Amplifier Effic. .5 Number Modules 200 Total ac Power 512.3337 Module Efficiency .4294076 Power Sup Voltage 78 80 Number of PowSup PowSup Size 5.5 Iv.- 54
-
substation power sup power cond power amp shieI d,suport rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv, comp Instal & Condition Buildings Totals
cost/rfwatt $M Cost ,0273027 5.460549 ,1372325 27.44651 ,0578443 11.56885 ,4057712 81.15424 ,1013477 20.26953 .065 1349 13.02698 ,1013477 20.26953 .0044693 .I3938534 .0670390 13.40780 .0075065 1S O 1302 .0337826 6.7565 10 .7010930 140.2186 .0683949 13.67897 .0889133 17.78266 A5535128 130.7026 ,04365 8.73
QD factor .7230532 .7230532 .8886717 .6756510 .6756510.7230532 .6756510 .4469267 .4469267 .6756510 .6756510 .63735 73
2.564342 512.8685
7. Case Vn. 850 MHz, 1.0 Mw, 62% Efficient, CW Klystrons AlW cost CW
850 MHz 1.0 M W klystrons Model P2
7/23/91
Total rf Power 1 Total dc Power 1.774194 Module rf Power 1.1 Amplifier Effic. .62 1 Total ac Power 2.06862 9 Number Modules Module Efficiency ,5317531 Power Sup Voltage 78 Number of PowSup 1 PowSup Size 1.774194 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf
cost/rfwatt $M Cost .6021272 .602 1272 .2964413 .2964413 .2 .2 1.41 1.41 ,15 .15 .125 .125 .15 .15 .01 .01 .15 .15 Iv.- 5 5
-
QD factor
1 1 1 1 1 1 1 1
1
rf ref
comp inter cooling safety&int suprv. comp Tnstal & Condition Buildings Totals ATW cost CW
.16 .05 ,8870968 .1676266 .2179146 1.601672 .16305
.16 .05 .8870968 .1676266 .2 179146 1.601672 .16305
1 1
1
6.340929 6.340929
850 MHz 1.0 MW klystrons Model P2
Total rf Power 2 Total dc Power 3.548387 ‘Module rf Power 1.1 Amplifier Effic. .62 ‘NumberModules 2 Total ac Power 4.137259 Power Sup Voltage 78 Module Efficiency .5317531 1 Number of PowSup PowSup Size 3.548387 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp llowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals .W cost CW
cost/rfwatt $M Cost QD factor .3972558 ,7945115 ,1977264 .3954528 1 .1 .2 1 1 ,9425 1.885 .1425 .285 .95 ,09625 .1925 .95 .95 ,1425 .285 .9 ,009 .018 ,135 .27 .9 .95 ,0845 ,169 .95 ,0475 .095 ,8077340 1.615468 .9 105366 ,1240986 ,2481973 ,1613282 .3226565 1.185763 2.37 1525 ,10305 ,2061 4,676706 9.353411
850 MHz 1.0 MW klystrons Model P2
. .
1
Total rf Power 5 Total dc Power 8.870968 Module rf Power 1.1 Amplifier Effic. .62 Number Modules 5 Total ac Power 10.34315 Module Efficiency .53 17531 Power Sup Voltage 78 Number of PowSup 2 4.435484 PowSup Size substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetylkint suprv. comp Instal & Condition Buildings Totals ldirw cost C W
cost/rfwatt $M Cost ,2292483 1.146242 ,1648806 ,8244029 .076 .38 .662 3.31 .133 1579 ,6657897 ,0855790 ,4278949 ,1331579 .6657897 ,0078299 .0391493 .1174480 ,5872400 .0388772 .1943860 .0443860 .2219299 .7547804 3.773902 .0978938 .4894690 ,1272620 ,6363098 ,9353753 4.676877 .06705 .33525
QD factor .95 .95 1 .8877196 .8877196 .8877196 .7829867 ,7829867 .8877196 .8877196 .8508433
3.674926 18.37463 850 MHz 1.0 M W klystrons Model P2
Total rf Power 10 Total dc Power 17.74194 Module rf Power 1.1 Amplifier Effic. .62 Number Modules 10 Total ac Power 20.68629 Module Efficiency .5317531 Power Sup Voltage 78 4 Number of PowSup PowSup Size 4.435484 substation power sup power cond
cost/rfwatt $M Cost QD factor ,1512475 1.512475 ,1566366 1.566366 .9025 .0722 ,722 .9025 Iv.- 57
-
.95
power amp shield,support rf&ps cont
trans sys
drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals N W cost CW
,547125 ,1265000 .0813000 .1265000 ,0070469 ,1057032 ,0234333 .0421667 .7 170413 ,0862760 .1121588 ,8243674 .OS05
5.47125 1.265000 .8 130002 1.265000 .0704688 1.057032 ,2343334 ,4216668 7.170413 .8627602 1.121588 8.243674 ,5505
.95 ,8433336 .8433336 .9025 ,8433336 ,7046880 ,7046880 ,8433336 .8433336 .8083012
3.234753 32.34753 850 MHz 1.0 MW klystrons Model P2
20 Total dc Power 35.48387 Total rf Power Module rf Power 1.1 Amplifier Effic. .62 Number Modules 20 Total ac Power 41.37259 Power Sup Voltage 78 Module Efficiency .5317531 Number of PowSup 8 PowSup Size 4.435484 substation power sup power cond power amp shield,support xf&ps cont trans sys drive amp lowlev rf if ref comp inter woling safetydcint suprv. comp Instal & Condition
cost/rfwatt $M Cost ,0997861 1.995723 ,1488047 2.976094 .06859 1.3718 .4926191 9.852381 .1201750 2.403501 ,0772350 1.544700 .1201750 2.403501 ,0063422 .1268438 ,0951329 1.902658 .OM117 .3102334 ,0400583 .8011669 ,6811893 13.62379 .0786248 1.572496 .lo22122 2.044244 .7512597 15.02519
QD factor .857375 357375 .9354439 ,8011669 ,8011669 .857375 ,8011669 ,6342192 .6342192 .8011669 ,8011669 .7678861
Buildings Totals PilTw cost CW
.04905
.981
2.946766 58.93532 850 MHz 1.0 MW klystrons Model P2
50 Total dc Power 88.70968 Total rf Power 1.1 Amplifier Effic. .62 Module rf Power Number Modules 50 Total ac Power 103.43 15 Module Efficiency .5317531 Power Sup Voltage 78 Number of PowSup 18 PowSup Size 4.928315 substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp Iowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals PiTw cost CW
cost/rfwatt $M Cost ,0575846 2.879229 1317715 6.588577 .0581355 2.906776 ,4548510 22.74255 .1122966 5.614828 .0706822 3.534108 .1122966 5.614828 .0055176 ,2758807 .Of427642 4.138210 .0104864 ,5243219 .0374322 1.871609 ,6365317 31.82658 .0708140 3.540700 .0920582 4.6029 10 ,6766278 33.83 139 .04545 2.2725
QD factor 3074379 ,8074379 ,9165435 .7486438 ,7486438 ,8074379 .7486438 S517614 .5S 17614 .7486438 ,7486438 .7175448
2.655300 132.7650 850 MHz 1.0 M W klystrons Model P2
Total rf Power 100 Total dc Power 177.4194 Module rf Power 1.1 Amplifier Effic. .62 Number Modules 100 Total ac Power 206.8629 Module Efficiency .5317531 Power Sup Voltage 78 Number of PowSup 36
w.-59 -
I?owSup Size
4.9283 15
substation power sup power cond power amp shield,support rf&ps cont trans sys drive amp lowlev rf if ref comp inter cooling safety&int suprv, comp Instal & Condition Buildings Totals MW cost CW
cost/rfwatt $M Cost ,0379917 3.799 165 .1251830 12.51830 .0552287 5.522875 .4385006 43.85006 .lo66817 10.66817 .0671481 6.7 14806 .lo66817 10.66817 .0049659 ,4965852 .0744878 7.448779 .0086121 .8612116 .0355606 3.556058 ,6047051 60.47051 .0666299 6.662988 .0866188 8.66 1884 ,6366485 63.66485 .04425 4.425
QD factor ,7670660 .7670660 ,9025 .7112116 ,7112116 ,7670660 .7112116 .4965852 ,4965852 .7112116 ,7112116 ,6816675
2.499894 249.9894 850 MHz 1.0 M W klystrons Model P2
Total rf Power 200 Total dc Power 354.8387 Module rf Power 1.1 Amplifier Effic. .62 4 13.7259 Number Modules 200 Total ac Power Power Sup Voltage 78 Module Efficiency .53 17531 Number of PowSup 72 IPowSup Size 4.9283 15 substation power sup power cond power amp shield,support d&ps cont trans sys drive amp Xowlev rf
cost/rfwatt $M Cost .0250651 5.013029 .1189238 23.78476 .OS24673 10.49346 .4270585 85.41169 .lo13477 20.26953 ,0637907 12.75813 .lo13477 20.26953 ,0044693 ,8938534 ,0670390 13,40780
QD factor .7287127 .7287227 .8886717 .6756510 .6756510.7287127 .6756510 ,4469267 .4469267
rf ref
comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
.0075065 ,0337826 S744698 .0630907 ,0820179 ,6028318 .04365
1.501302 .6756510 6.756510 .6756510 114.8940 .6475842 12.61814 16.40359 120.5664 8.73
2.368858 473.7717
8. Case VIII. 4 MW Peak, 1 M W Average Power Klystrons at 433 MHz
cost PP 433 MHz 4 MW peak/l MW ave klystrons
7/23/91
Total Ave rf Power 1 Total dc Power 4 Amplifier Effic. .458 Peak rf Power Ave Module rf Pow 1.1 Total ac Power Number Modules 1 Power Sup Voltage 148 Module Efficiency .3935219 Number of PowSup Number Modulators 1 PowSup Size 1 modules/modulator
2.401747
pizw
substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings
2.795270 1 2.401747
costlrfwatt $M Cost QD factor .6791796 .6791796 1 ,3821689 .3821689 1 .95 .95 .4
.1 ,00968 .15 .125 .15 .o 1
.15 .16
.05 1.125481 ,1776604 .2309585 1.697545 .16305
.4 .1 .00968 .15 .125 .15 .01
.15
.16 .05 1.125481 3372183 .1776604 .2309585 1.697545 .16305
1 1
1 1
1 1 1 1 1
1
Totals p;Iw
cost PP
6.710723 6.710723 433 MHz 4 M W peak11 M W ave klystrons
2 Total dc Power Total Ave rf Power Peak rf Power 8 Amplifier Effic. .458 Ave Module rf Pow 1.1 Total ac Power Number Modules 2 Power Sup Voltage 148 Module Efficiency .3935219 Number of PowSup Number Modulators 1 PowSup Size modules/modulator 2 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals .pirw cost PP
4.803493 5.590540 1 4.803493
cost/rfwatt $M Cost QD factor ,4480914 .8961829 .2549068 ,5098135 1 .935 1.87 1 1 .2 .4 1 .05 .1 .00968 ,01936 .95 ,1425 ,285 .95 .09625 I925 .1425 ,285 .95 .9 ,009 ,018 .9 ,135 .27 .OB45 ,169 .95 ,0475 .095 .95 1.069206 2.1384 13 .89035 74 .1449654 .2899308 ,1884550 ,3769100 1.385144 2.770289 ,10305 .2061
.
5.445749 10.89150 433 MHz 4 M W peak/l
Total Ave rf Power Peak rf Power 20 Ave Module rf Pow
M W ave klystrons
5 Total dc Power Amplifier Effic. ,458 1.1 Total ac Power
12.00873 13.97635
1
Number Modules 5 Power Sup Voltage 148 Module Efficiency ,3935219 Number of PowSup 3 1 PowSup Size 4.002911 Number Modulators modules/modulator 5 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cone trans sys drive amp lowlev rf rf ref comp inter cooling safetylkint suprv. comp Instal & Condition Buildings Totals AlW cost PP
costlrfwatt $M Cost QD factor .2585846 1.292923 .26 14177 1.307089 .92 19190 1 ,926 4.63 .08 .02 ,00968 .1331579 .0942365 .1331579 .0078299 .11744&0 .0388772 ,0443860 .9991111 .1249555 .1624421 1.193950 ,06705
.4 .1 .0484 .6657897 .4711827 .6657897 .0391493 .SI372400 .1943860 .2219299 4.995556 .6247774 .8122106 5.969748 ,33525
1 1 .8877196 .8877196.9219190 ,8877196 ,7829867 ,7829867 ,8877196 ,8877196 .8319871
4.672284 23.36142 433 MHz 4 M W peakll M W ave klystrons
Total Ave rf Power 10 Total dc Power 24.01747 40 Amplifier Effic. ,458 Peak rf Power Ave Module rf Pow 1.1 Total ac Power 27.95270 10 Power Sup Voltage 148 Number Modules Module Efficiency .3935219 Number of PowSup 5 Number Modulators 2 PowSupSize 4.803493 rnoduleslmodulator 5 substation power sup
cost/rfwatt $M Cost QD factor .1706022 1.706022 .2262857 2.262857 .8877196
power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf r-f ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals ATW cost PP
A816
8.816
,076 ,019 .00968 .1265000 .OM4430 .1265000 .0070469 ,1057032 .0234333 .0421667 .949 1556 ,1139647 .1481541 1.088932 .05505
.76 .19 ,0968 1.265000 ,8544301 1.265000 .0704688 1.057032 ,2343334 .4216668 9.491556 1.139647 1.481541 10.88932 ,5505
$95 .95 .95 ,8433336 ,8433336 ,8433336,8877196 ,8433336 .7046880 .7046880 ,8433336 A433336 ,7903877
4.255218 42.55218 433 MHz 4 MW peak/l MW ave klystrons
20 Total dc Power 48.03493 Total Ave rf Power Peak rf Power 80 Amplifier Effic. .458 Ave Module rf Pow 1.1 Total ac Power 55.90540 Number Modules 20 Power Sup Voltage 148 Module Efficiency .3935219 Number of PowSup 10 4.803493 Number Modulators 4 PowSup Size 5 modules/modulator substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&pS cont trans sys
cost/rfwatt $M Cost QD factor ,1125555 2.251110 .2149714 4.299429 3433336 ,8650780 17.30156 ,9354439 .0722 1.444 ,01805 ,361 .00968 .1936 .1201750 2.403501 .OS 11709 1.623417 ,1201750 2.403501
.9025 .9025 8011669 ,8011669 A011669 3433336 A3011669
drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals M W cost PP
.0063422 .0951329 ,0155117 .0400583 .9016978 .lo691 19 .1389855 1.021544 .04905
.1268438 1.902658 .3 102334 ,8011669 18.03396 2.138239 2.77971 1 20.43087 .981
.6342192 ,6342192 ,8011669 .BO1 1669 .7508683
3.989290 79.78580 433 MHz 4 M W peak11 MW ave klystrons
Total Ave rf Power 50 Total dc Power 120.0873 200 Amplifier Effic. ,458 Peak rf Power Ave Module rf Pow 1.1 Total ac Power 139.7635 Number Modules 50 Power Sup Voltage 148 Module Efficiency .3935219 Number of PowSup 24 Number Modulators 10 PowSup Size 5.003639 5 modules/modulator substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont
trans sys
drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition
cost/rfwatt $M Cost QD factor .0649535 3.247676 ,1967374 9.836872 ,7904303 3453556 42.26778 .9165435 ,0674667 ,0168667 .00968 .1122966 ,0751186 ,1122966 .0055176 .OS27642 .0104864 .0374322 .8425840 .0991822 ,1289369 ,9476864
3.373335 .I3433336 .484 5.614828 3.75593 1 5.614828 .2758807 4.138210 S243219 1.871609 42.12920 4.959112 6.446846 47.38432
A433336 .8433336 .7486438 .7486438 .7486438.7904303 ,7486438 .55 17614 S517614 .7486438 .7486438 .7016427
.04545
Buildings
3,700812 185.0406
Totals AXW cost PP
2.2725
433 MHz 4 MW peak/l MW ave klystrons
100 Total dc Power 240.1747 Total Ave rf Power Peak rf Power 400 Amplifier Effic. ,458 1.1 Total ac Power 279.5270 Ave Module rf Pow Number Modules 100 Power Sup Voltage 148 Module Efficiency .3935219 Number of PowSup 48 Number Modulators 20 PowSup Size 5.00363 modules/modulator 5 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv, comp Instal & Condition Buildings Totals
MHz
cost/&att ,0428533 ,1869006 .83 1497
$M Cost QD factor 4.285334 18.69006 ,7509088 83.1497 .9025
,0640934 .0160233 ,00968 .lo66817 ,0713627 .lo668 17 .0049659 .0744878 ,0086121 .0355606 ,8004548 .0943942 .1227125 .go19365 .04425
6.409336 1.602334 .968 10.66817 7.136268 10.66817 ,4965852 7.448779 ,8612116 3.556058 80.04548 9.439420 12.27125 90.19365 4,425
,8011669 3011669 .7112116 .7112116 .7112116.7509088 .7112116 ,4965852 ,4965852 ,7112116 ,7112116 .6665605
3.523 148 352.3 148
9. Case IX. 100 kW Average, 1.25 MW Peak Power Klystrons at 850
Pirw cost PP
850 MHz 1.25 MW peak/.l MW ave klystrons
IV- 66-
7/23/91
Total Ave rf Power .1 Total dc Power 1.25 Amplifier Effic. .55 Peak rf Power Ave Module rf Pow .1 Total ac Power 1 Power Sup Voltage 85 Number Modules Module Efficiency .4892666 Number of PowSup Number Modulators 1 PowSup Size modules/modulator 1 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
p;rW
cost PP
.1818182 .2043876 1 .1818182
cost/rfwatt $M Cost QD factor 2.385596 .2385596 1 1.169679 .1169679 1 1.5 .15 4 1 .03025 1.5 1.25 1.5
.4 .1 .003025
$15 .125 .15 .01 .15 16
.1
1.5 1.6 .5 .9090909 ,7577846 .9851200 7.240632 1.6305
1 1 1
.os
.0909091 ,0757785 ,0985120 .7240632 ,16305
29.55865 2.955865 850 MHz 1.25 MW peak/.l MW ave klystrons
Total Ave rf Power .5 Total dc Power 6.25 Amplifier Effic. .55 Peak rf Power Ave Module rf Pow .1 Total ac Power 5 Power Sup Voltage 85 Number Modules Module Efficiency ,4892666 Number of PowSup Number Modulators 1 PowSup Size modules/modulator 5
w.-
67 -
.9090909 1.021938 1 .9090909
substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv, comp Instal & Condition 13uildings Totals rl;rw
cost PP
costlrfwatt $M Cost QD factor .9082699 ,4541349 1 ,4567723 .2283862 1.5 .75 1 .8 .2 .03025 1.331579 .7657897 1.331579 .0782987 1.174480 ,3887720 ,4438598 ,9090909 .4127497 ,5365746 3.943823 ,6705
.4 .1 ,015125 .6657897 ,3828949 .6657897 ,0391493 S872400 .1943860 ,2219299 .4545455 .2063748 .2682873 1.971912 ,33525
1 1 ,8877196 ,8877196 .8877196 .7829867 .7829867 .8877196 8877196
1
1
15.88239 7.941195 850 MHz 1.25 M W peakl.1 M W ave klystrons
Total Ave rf Power 1 Total de Power Peak rf Power 12.5 Amplifier Effic. .55 Ave Module rf Pow .1 Total ac Power Number Modules 10 Power Sup Voltage 85 Module Efficiency .4892666 Number of PowSup Number Modulators 2 PowSup Size modules/modulator 5 substation power sup power amp power conditioning modulator cro bar
1.8 18182 2.0438 76
1 1.818182
cost/rfwatt $M Cost QD factor ,5992347 ,5992347 1 .3046672 .3046672 1.4325 1.4325 .95 .76 .19
.76 .19
.95 .95
capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
p;Tw
cost PP
,03025 1.265000 .6825002 1.265000 .0704688 1.057032 .2343334 ,4216668 .9090909 .3688698 ,4795307 3.524551 ,5505
.03025 1.265000 ,6825002 1.265000 .0704688 1.057032 .2343334 .4216668 .9090909 .3688698 .4795307 3.524551 SO5
.8433336 .8433336 .8433336 ,7046880 ,7046880 .8433336 .8433336
1
1
14.14520 14.14520
850 MHz 1.25 MW peak/.l MW ave klystrons
Total Ave rf Power 2 Total dc Power 25 Amplifier Effic. .55 Peak rf Power Ave Module rf Pow .1 Total ac Power Number Modules 20 Power Sup Voltage 85 Module Efficiency ,4892666 Number of PowSup Number Modulators 4 PowSup Size modules/modulator 5 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter
3.636364 4.08775 1 1 3.636364
costlrfwatt $M Cost QD factor ,3953474 .7906949 ,2032131 .4064262 1 1.408008 2.816015 ,9354439 .722 .1805 .03025 1.201750 ,6258’752 1.201750 ,0634219 ,9513289 ,1551167 .4005835
1.444 .361 .0605 2.40350 1 1.251750 2.403501 .1268438 1.902658 ,3102334 .8011669
w.-69 -
.9025 ,9025 .8011669 .8011669 .8011669 .6342192 ,6342192 ,8011669 .8011669
1
cooling safety&int suprv. comp Hnstal & Condition Buildings Totals cost PP
.8262617 .3346163 .4350012 3.197258 ,4905
1.652523 .9088878 ,6692325 .8700023 6.394517 .98 1
12.82278 25.64557
850 MHz 1.25 M W peakl.1 M W ave klystrons
5 Total dc Power 9.090909 Total Ave rf Power Peak rf Power 62.5 Amplifier Effic. .55 Ave Module rf Pow .1 Total ac Power 10.21938 Number Modules 50 Power Sup Voltage 85 Module Efficiency ,4892666 Number of PowSup 2 Number Modulators 10 PowSup Size 4.545455 moduleslmodulator 5
substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont
trans sys
drive amp lowlev rf
rf ref
comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals
cost/rfwatt $M Cost QD factor .2281471 1.140735 .95 .1694558 .8472792 1.377319 6.886595 ,9165435 .6746669 .1686667 .03025 1.122966 S804828 1.122966 .0551761 ,8276421 .lo48644 .3743219 .7720934 ,3043607 .39566a9 2.908 167 ,4545
3.373335 ,8433336 ,8433336 ,8433336 .15125 5.614828 ,7486438 2.902414 .7486438 5.614828 ,7486438 .2758807 ,5517614 4,138210 -5517614 S243219 .7486438 1.871609 .7486438 3.860467 .8493027 1.521804 1.9~~45 14.54083 2.2725
11.67171 58.35857
.95
AW cost PP
850 MHz 1.25 MW peakl.1 MW ave klystrons
Total Ave rf Power 10 Total dc Power 18.18 182 Peak rf Power 125 Amplifier Effic. .55 Ave Module rf Pow .1 Total ac Power 20.43876 Number Modules 100 Power Sup Voltage 85 Module Efficiency .4892666 Number of PowSup 4 Number Modulators 20 PowSup Size 4.545455 modules/modulator 5 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safety&int suprv. comp Instal & Condition Buildings Totals AW cost PP
cost/rfwatt $M Cost .1505209 1.505209 .1609830 1.609830 1.355213 13.55213
OD factor
6.4093 36 1.602334 .3025 10.66817 5.334087 10.668 17 .4965852 7.448779 ,8612116
.8011669 ,8011669
.6409336 ,1602334 .03025 1.0668 17 ,5334087 1.066817 .0496585 .7448779 .0861212 .3556058 .7334887 .2853972 .37 10163 2.726970 A425
3.556058 7.3 34887
.9025 ,9025
.7112116 ,7112116 .7112116 .4965852 .4965852 .7112116 .7112116 .SO68376
2.853972 3.7 10163 27.26970 4.425
10.96081 109.6081 850 MHz 1.25 MW peakl.1 M W ave klystrons
20 Total dc Power 36 36364 Total Ave rf Power Peak rf Power 250 Amplifier Effic. .55 Ave Module rf Pow .1 Total ac Power 40.8775 1 Number Modules 200 Power Sup Voltage 85 Module Efficiency ,4892666 Number of PowSup 8
w.- 71 -
Number Modulators rnodules/modulator substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf if ref comp inter cooling safety&int suprv. comp Instal & Condition ]Buildings Totals ,ATw cost PP
40 5
PowSup Size
4.545455
cost/rfwatt $M Cost QD factor ,0993068 1.986136 ,1529339 3.058678 .857375 1.333843 26.67685 ,8886717 .6088869 .1522217 .03025 1.013477 SO67383 1.013477 ,0446927 ,6703901 ,0750651 ,3378255 ,6968143 .2694368 ,3502679 2.574469 ,4365
12.17774 3.044434 .605 20.26953 10.13477 20.26953 .8938534 13.40780 1.501302 6.756510 13.93629 5.388737 7.005358 51,48938 8.73
.7611086 .7611086 ,6756510 ,6756510 .6756510 ,4469267 ,4469267 .67565 10 .6756510 .7664957
10.36659 207.3319 850 MHz 1.25 MW peak/.l MW ave klystrons
‘rota1Ave rf Power 50 Total dc Power 90.90909 625 Amplifier Effic. .55 Peak rf Power Ave Module rf Pow .1 Total ac Power 102.1938 Number Modules 500 Power Sup Voltage 85 Module Efficiency ,4892666 Number of PowSup 18 Number Modulators 100 PowSup Size 5.050505 modules/modulator 5 substation power sup power amp power conditioning
cost/rfwatt $M Cost QD factor .0573080 2.865398 .1354280 6.771402 ,8074379 1.306462 65.32312 3707163
modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf rf ref comp inter cooling safetydkint suprv. comp Instal & Condition Buildings Totals
pirw
cost PP
S689693 .1422423 ,03025 .9470347 .4735174 .9470347 .0388820 3332295 .0661356 ,3156782 .6511323 .2505322 .3256918 2.393835 .4329
28.44846 7.112116 1.5125 47.35174 23.67587 47.35174 1.944098 29.16147 3.306782 15.78391 32.55661 12.52661 16.28459 119.6917 21.645
.7112116 ,7112116 .63 13565 .63 13565 .63 13565 .3888197 ,3888197 .6313565 .63 13565 .7162455
9.666263 483.3 132 850 MHz 1.25 M W peakl.1 M W ave klystrons
Total Ave rf Power 100 Total dc Power 181.8182 1250 Amplifier Effic. .55 Peak rf Power Ave Module rf Pow .1 Total ac Power 204.3876 Number Modules 1000 Power Sup Voltage 85 Module Efficiency .4892666 Number of PowSup 36 Number Modulators 200 PowSup Size 5.050505 modules/modulator 5 substation power sup power amp power conditioning modulator cro bar capacitors shield,support rf&ps cont trans sys drive amp lowlev rf
cost/rfwatt $M Cost QD factor ,0378092 3.780915 ,1286566 12.86566 .7670660 1.286276 128.6276 .857375 ,5405208 ,1351302 .03025 .8996830 .4498415 ,8996830 ,0349938 ,5249065
54.05208 13.51302 3.025 89.96830 44.984 15 89.96830 3.499377 52.49065
w.- 7 3 -
.6756510 .67565 10 ,5997887 S997887 ,5997887 .3499377 ,3499377
rf ref comp inter cooling safetytkint suprv. comp Instal & Condition Buildings Totals
,0614789 .2998943 A185757 .2379080 ,3092804 2.273211 .4317
6.147887 ,5997887 29.98943 S997887 61.85757 ,6804332 23.79080 30.92804 227.3211 43.17 I
9,199799 919.9799
. .
w.-7 4 -
V. Coupled-Cavity Linac Characterization and Costing
V. COUPLED-CAVITY LINAC CHARACTERIZATION AND COSTING V.A.
INTRODUCTION:
The cost optimization of a high power CW CCL requires the characterizationof an operating regime defined by physical limits as well as costing algorithms for equipment and operation. In the area of mechanical design of the rf cavities, the heat flux to the cavity wall, due to rf power dissipation, can be a limiting factor. A preliminary study of the peak heat flux in a CCL as a function of various cavity operating frequencies and acceleration gradients has been conducted. The shunt impedance for the cavities has been maximized on the basis of the optimum gap to cell length ration ( G / W 2 ) . The cavity bore radius is determined by beam dynamics requirements
p n p n
based on beam current and transmission requirements. Several bore radii, including 21c and 9 , have been selected for preliminary study. This should provide initial guidance as to shunt impedance and heat flux sensitivities to bore radii in the cavity design. A family of heat flux curves, based on cavity frequencies of 200, 700, 1300 Mhz, which represent the peak heat flux parameter space for the CCL cavity design can then be generated. It is also necessary to define the cavity geometry over a range of particle energies. This has been done for several energies between 50 Mev and 1600 MeV. Limits must be applied to the heat flux curves to define the operational regime. These limits are based on allowable thermal stresses (ay), electric fields (Ekp), coolant channel fluid velocities (VC),frequency shifts due to thermal expansion (Af(T)), pressure drops (AP),etc. These limits are defined by defining a specific coolant channel geometry for a given cavity design and performing a finite element analysis to determine the limiting heat flux for a specific limiting acceleration gradient for that geometry. These limits are then applied to the heat flux curves to define an operational regime. Shown below is a schematic for this process.
v. -2-
q
'1
A
A-
'AILX
Figure V.A.l Given the operational regime based on peak heat flux, it is possible to test a given set of accelerator design parameters Le., current as a function of radial aperture (I(Rb)), effective accelerating gradient (Eon,frequency (f), and shunt impedence (Z'IT), to determine if a particular CCL design can be adequately cooled. (i.e. fits within operational regime.) Once this determination has been made, the following costs can be estimated. W structure cost
Cooling System cost Vacuum System costs Costing algorithms are being developed for these areas (but are not complete and therefore not presented in this study). These algorithms will ultimately take the form of cost curves such as:
v. -3-
Figure V.A.2 These cost curves are being initially developed for capital costs only. Operational cost curves are desirable ultimately and will be developed as time and funding permit. To summarize: In order to estimate and optimize the cost associated with construction and operation of a CCL, it is necessary to determine acceptable design limits. The dominant mechanical design limit is characterized by the heat flux to the cavity due to rf power dissipation in the cavity wall. The operational regime for the cavity based on peak heat flux is being defined along with specific operational limits based on a finite element analysis of point designs. Once a specific accelerator design criteria has been established, which conforms to the operational regime for peak heat flux in the cavity, cost curves which are being developed may be used to estimate RF structure, cooling system, and vacuum system costs.
v. -4-
V.B. COUPLED-CAVITY DESIGN OPTIMIZATION V.B.1
A typical coupled cavity (CC) geometry and its parameters are shown in Figure V.B. 1. This figure is a two-dimensional drawing that is symmetrical about the r-axis and
axisymmetrical about the z-axis, and can be described by the listed parameters. The only parameter that is known initially given the beam energy (Te) and frequency is the cell length (ph/2) (Eq. V.B.l).
ph = c [ 1 - (m~/(mp+Te))~]*~ /f where
(Eq. V.B.l),
mp = particle mass (proton = 938 MeV), c = speed of light (cm/s), f = frequency (Hz) p = v/c = [ 1 - (mp/(mp+Te))2]*5,and h = c/f (cm).
All other parameters must be determined by optimizing effective shunt impedance with structural, thermal, and frequency shift considerations, (Note: The optimum 277'means the maximum ZTT value. Z is shunt impedance, and T is the transit time factor for a specified CC design.) ZTT is optimized to reduce the rf power required to operate the coupled cavity. In order to satisfy most of the structurally, and thermal considerations, four geometrical constraints were applied to the shunt impedance optimization. The first constraint was to allow 1.27 cm between the cavity structures for cooling channels, second rillow a small flat (.05*bph/2)along the cavity radius for machining and assembly purposes, third the minimum nose thickness of 0.5 cm to allow for cooling channels, and fourth to minimize concentrated heat fluxes along the nose surface, R3/R4 = 3. V.B.2 EffectiveecS -
OD-
. . .
All other parameters are determined iteratively by using the SUPERFISH codes and optimizing at a given frequency and beam energy. Table V.B.l shows the frequency trends as specific parameter magnitudes are increased (as a rule, frequency decreases as cavity volume increases), as well as their ZTI' optimization trend. An optimization code was written to iterate the cavity's geometrical parameters, and dewmine its optimum ZTT for a given beam energy and frequency. The SUPERFISH codes were used to determine ZTT.This optimization code starts with initial guesses to all parameters and then it iterates the cavity radius, maximizes R1, at a given gap to cell length ratio to converge to the specified frequency; at frequency convergence, Z'IT is determined. ZTT was computed over a range of gap to cell length ratios from $1to .8.
v -5-
-
R1 I
I
I .635em
R2
R3
R4 I -
G/2 -4
Figure V.B. 1. Coupled Cavity Geometry Table V.B. 1 Frequency Trends as Specific Parameters Are Increased and Their Required Action to Optimize ZIT. Parameter Freauencv Trend Cavity Radius, Rc decreases Cell Length, ph/2 deClWtSeS Radial Aperture, Rb increases Cavity-Side Radius, R1 Side-Nose Radius, R2 Nose Tip Radius, R3 Nose-Bore Radius, R4 Nose Face angle, a Gap, G
increases increases increases increases increases increases
V -6-
timum state
minimize at a given f and T calculated at given f and T minimize (to maximize ZTT but constrained by maximum beam envelope) maximize (produces best fields) minimize (maximizesZ'IT) minimize (cooling constraint) minimize (cooling constraint ) minimize (cooling constraint ) imtetomaximizeZlT
..
V.B.3 -terG-
The cavity radius initial guess was based on a radius of a pill box cavity as shown in Eq. V.B.2. RC = 2.405~/(2~f)
(Eq. V.B.2).
The initial guess for the largest radial aperture was selected such that the transit time factor was penalized by no more than 20%. The transit time factor is dependent on the gap and the radial aperture components as shown in Eq. V.B.3a-b
T = [gap component] * [aperture component]
where
(Eq. V.B.3b),
G = gap (em) Io = Bessel function of the zeroth order = 1+ xA2/4+... x = 27cRb/phy = 1. (for 20%T penalty), and y = (1- l/p2).5 [Lloyd Smith, 19591.
rhus the radial aperture is,
Rb = phy/(2~)
(Eq. V.B.3c).
The aperture size calculated using Eq. V.B.3c produces a low shunt impedance and an aperture which is much larger than required by beam dynamics considerations, so the largest aperture considered for further study was defied by Rb = Ph/(2n)
(Eq. V.B.3d).
The transit time factor is maximized along with the shunt impedance. Therefore, the gap effect was iterated while executing the SUPERFISH codes to determine the optimum ZTT. The minimum radial aperture is dependent on beam dynamics considerations such as the beam current, beam energy, allowable emittance, and focusing lattice. Quantifying the effect of radial aperture on ZIT, heat flux and frequency, and frequency sensitivity allows these effects to be considered in the optimization of the cavities. Theoretically, smaller radial apertures produce better Z'IT. V.B.4 Jelet-ose
. .
Geometry to
. .
This cavity optimization set at a constant radial aperture of ph/2n was used to optimize all of its geometric parameters (except for Rb) at beam energies of 50 MeV, and 1600 MeV, and at frequencies of 200 MHz, 700 MHz, and 1300 MHz. The variable geometric parameters are R2, R3, and a. All other parameters were determined in the SUPERFISH runs as required to converge on a solution on a specific frequency based on
v -7-
the variable parameters. (Note: Table V.B. 1 shows how all parameters change with respect to frequency) Initial guesses were made for R2,R3, and a to create realistic CC geometry and to maximize ZTT for these six cases. Then, R2, R3, a,and ZTT were scaled on the basis of frequency so that the maximum ZTT could be compared. The optima based on maximum Znrr for the variable geometric variables are R2= R3= 0.55 cm for a frequency of 1300 MHz, and a = 30 O for all frequencies.
V.B.5 Scaling With Res-pect To Freauencv
The following scaling relationships are used to scale with frequency scale directly from a known cavity design (marked with a subscript of 1) [J. McKeown and J. P. Labrie, 19831. Rc2 = (fl/f2)*Rc1 A2 = (f2/f1)2*A1 Z T T ~= (f2/f1).5*ml 92 = ( f ~ P * q 1 PD2 A (f2/f1)-'*5*PD1
(all geometric parameters)
(A = cavity surface area)
(q = peak & average heat flux) (PD = total power dissipated)
(Eq. V.B.4) (Eq. V.B.5) (Eq. V.B.6) (Eq. V.B.7) (Eq. V.B.8)
Parameters independent of frequencyare nose face angle, accelerating gradient, and transit time factor. V.B.6 ZTT nC -
With Resmct to
After the nose geometry was optimized, four different radial apertures were considered: ph/l8x, pU18, pU9,and fW2x. The optimization code was run at each aperture to find the geometry associated with the maximum ZTI' for six different energies and one frequency, 1300 MHz. The energies of interest were 1600, 1300, 1O00, 700, 400,and 50 MeV. Since the frequency was constant throughout these calculations, the same nose geometry was used with each energy and aperture to allow a comparison of the ZTT optimization plots. The optimization of 27" is particularly interesting for minimizing the rf power losses per cavity as shown by Eq 9.
(P= power)
p = (EoTP*
(Eq. V.B.9)
Figure V.B.2 shows the location of the maximum 2"with respect to the gap to cell length
ratio for 1600 MeV. At large apertures, such as ph/2x and PW,ZTI' has not yet reached a maximum value at a gap to cell length ratio of 0.7. However, at smaller apertures, such as PW18 and pA/18x, ZTI' has reached a maximum value at a gap to cell length ratio of .6 and .3 respectively. From Figure V.B.3, which was run at 400 MeV, ZTI' reached a maximum for all four apertures. This indicates that at high energies and large radial apertures, a cavity nose is not necessary. Figures V.B.2 and V.B.3 also indicate that at high energies p approaches 1 and thus ZIT becomes constant. This can be attributed to the small changes in the cavity length which cause the shunt impedance to maximize.
v -8-
Figure V.B.4 shows a plot of ZTT vs the radial aperture. This figure (range 0 S Rb 4 4) or the following equations can be used to find ZTI' for any aperture at 1300 MJAz and 11600, 1300, 1000,700, or 50 MeV. (Note: Once ZTT is found at 1300 MHz, it can be scaled to a desired frequency using Eq 6.) ZIT(Rb) = 34.588 - 4.8599"RRb - 8,8528*Rb2 ZTT(Rb) = 86.001 - 27.741"Rb - 2.3926*Rb2 ZTI'(Rb) = 89.145 - 26.223"Rb - 2.2547*Rb2 ZTT(Rb) = 89.620 - 25.354"Rb - 2.2627*Rb2 ZTT(Rb) = 89.827 - 24.982"Rb - 2.2738*Rb2 Zl'T(Rb) = 89.706 - 24.415"Rb - 2.2010*Rb2
@ 50 MeV @ 400 MeV @ 700 MeV @ lo00 MeV @ 1300 MeV @ 1600 MeV
(Eq. V.B.lO)
Figure V.B.5 illustrates the relation between ZTI' and beam energy. At energies greater than or equal to 400 MeV, ZTI' remains essentially constant at its maximum value. This indicates that at a constant gradient, rf power losses per cavity (Eq. V.B.8) are primarily dependent on the cavity length. At energies below 400 MeV, this figure may indicate that using a coupled cavity linac with a nose is not as desirable as a drift tube linac. However, to further locate the transition point from a DTL to a CCL with this optimization, different CCL nose geometries should be analyzed at low energies. The maximum ZTT vs gap to cell length ratio for a radial aperture of bl/18 at 1300 A4Hz and all six energies is shown in Figure V.B.6. At energies greater than or equal to 900 MeV, the maximum 23" values occur at the same gap to cell length ratios. For beam energies between 700 MeV and 50 MeV, the optimum gap to cell length ratio point and . maximum ZTT value decrease. This further illustrates how at some low energy, the nose geometry and cavity constraints are affecting the optimization. These calculations can be compared to the results of Nagle used in designing the 805 MHz coupled cavity linac at LAMPF [Nagle, 19751. Nagle's results show ZTT values of 48 MW/m at 400 MeV and 53 MW/m at 700 MeV for radial apertures around 1.91 cm. Using this aperture with proper scaling and the appropriate second order equation shown above, the ZTI' values at 805 MHz are 48 MW/m at 400 MeV and 51.5 MW/m at 700 MeV. This provides a baseline comparison between Nagle's point design of CCL and our more general results.
v -9-
Effective Shunt Impoedance vs Gap to Cell Length Ratio Freq. = 1300 MHz Beam Energy = 1600 MV 90
80
-a
70
$
50
c
40
3
E c.r
60
30
20 10
0 0.0
I
0.1
I
0.2
Radial Apertures: __Q_)
PU181t
I
I
0.3
0.4 Gap to Cell Length Ratio
-
Bb18
__P_
I
I
0.5
0.6
f%9
Figure V.B.2 Effective shunt impedance vs gap to cell length ratio for various apertures at 1600 MV and 1300 MHz.
0.7
Bhnlr
Effective Shunt Impedance vs Gap to Cell Length Ratio Beam Energy = 400 MV Freq. = 1300 MHz
50
-
40
-
30
-
20
-
I
0.3
0.2
Radial Apertures:
-
Y
$n/lSz
I
I
I
I
0.4
0.5
0.6
0.7
- -
0.8
Gap to Cell Length Ratio
$All8
paJ9
"---e--
Figure V.B.3 Effective shunt impedance vs gap to cell length ratio for various apertures at 400 MV and 1300 MHZ.
pmz
Effective Shunt Impedance vs Radial Aperture Freq. = 1300 MHz Beam Energy = 50-1600 MV 100
1
t
90
h
-z
E a 0
80
70
60
zso N
40
30
20 10
0 Radial Aperture (cm)
Beam Energies:
e 50 MV Cavity m 400MV Cavity 700 MV Cavity 9 lo00 MV Cavity
*
P b
1300 MV Cavity 1600 MV Cavity
ZlT(Rb) = 34.588 - 4.8599*Rb - 8.8528*RW2 ZlT(Rb) = 86.001 27.741*Rb + 2.3936*RW2 zIT(Rb) = 89.145 - 26.223*Rb + 2.2547*RW2 ZIT(Rb) = 89.620 - 25.354*Rb + 2.2627*RW2 ZlT(Rb) = 89.827 - 24.982*Rb + 2.2738*Rb"2 ZlT(Rb) = 89.706 - 24A15*Rb + 2.201PRW2
-
Figure V.B.4 Effective shunt impedance vs radial aperture for various beam energies at 1300 MHz.
Effective Shunt Impedance vs Beam Energy 90
80
-
I
Y
Y
70 60 50
40
30 c.
Y
20 10
1
0 0
200
400
600
-
800
1000
1200
Beam Energy (MV/m)
Radial Apertme.~: Y
$h/l8z
$All8
1$n/9
1400
-
1600
p1v2.rc
Figure V.B.5 Effective shunt impedance vs beam energy for four radial apertures.
Effective Shunt Impedance vs Gap to Cell Length Ratio Freq. = 1300.0 MHz Radial Aperture =OX /18
c I
w
P
0.2 I
0.1
0.3 I
Beam Energies: A
16OOMVCavity 700MVCavity
-
I
I
I
0.4 0.5 Gap to Cell Length Ratio'
--W-
1300MVCavity 4OOMVCavity
0.6
--b--Q-
1mMVCavity 50MVCavity
Figure V.B.6 Effective shunt impedance vs gap to cell length ratio for various energies at a radial aperture PA /18 and 1300 Mhz
0.7
V.B.7 Power CoThe total power dissipation (PD)determines the mass flow rate per cavity (M) of cooling required to maintain a constant coolant temperature rise during steady state operation of the linac. The amount of cooling per cavity is determined as follows:
where
Cp = specific heat of the cooling fluid (J/kg*K), Ti = input fluid temperature (K), and TO= output fluid temperature (K) [Incropera and DeWitt, 19851.
The total power dissipated, peak heat flux and average heat flux at a given beam energy were found at a frequency of 1300 MHz, an accelerating gradient of 1 MeV/m, and an aperture of ph/18 as shown in Figure V.B.7. The power dissipated per cavity can be scaled to any frequency using Eq. V.B.8, and scaled to an accelerating gradient using Eq. V.B.9 (rf power = power dissipated). The maximum allowable accelerating gradient is dependent on the heat flux limitations (as discussed in Section V.C.). The peak heat flux (qp) is dependent on the magnetic field (H), at a constant accelerating gradient ( h T ) and material resistance (R,) as shown in Eq. V.B.12 [Panofsky and Phillips, 19551.
(Eq.V.B.12)
qp = .5*Rs* Hp2*(EoT/1MV)2
where Hp = peak magnetic field at the inside surface of the coupled cavity. The average heat flux (qf) was determined by integrating Eq, V.B.12 along the inside surface of the cavity. The average and peak flux was determined in the SUPERFISH computer code. Material resistance is dependent on its temperature dependent resistivity (a) and rf current skin depth (6) as shown in Eq. V.B.13 [Panofsky and Phillips, 19551.
This study assumed constant room temperature resistivity of 1.7e-8 Q-m (resistivity of Cu). Rf current skin depth (6)is dependent on the fiequency, material's permeability (p0) and resistivity as shown in Eq.V.B. 14 [Panofsky and Phillips, 19551, Heat flux in an optimized cavity varies with beam energy and constant accelerating gradient as shown in Figure V.B.7. Figure V.B.7 shows the flux remains constant as does the effective shunt impedance with energies greater than 400 MeV, Again, the flux at beam energy less than 400 MeV could possibly be improved as discussed above. Heat flux dependence on the accelerating gradient is described in Eq.12 and plotted in Figure V.B.8. Figure V.B.8 shows the average heat flux vs EoT at beam energy of 700 MeV for the frequencies of 1300,700, and 200 MHz. This plot indicates ELS shown
V -15-
that operation at increased frequency results in increased heat flux. Thus a lower accelerating gradient may be required to maintain the same level of required cooling. The heat flux dependence on aperture follows a second order polynomial (as shown in Figure V.B.9), and is also inversely proportional to ZTT by comparing Figure V.B.4 and V.B.9. Figure V.B.9 shows that the average flux as a function of aperture at beam energies of 50,400,700,1000,1300, and 1600 MeV. The heat flux and ZTT trends with respect to radial aperture suggest two approaches that can be taken made when optimizing an accelerator. The first approach is to maintain the same operating power and increase the accelerating merit to decrease the total accelerator length to reduce cost in manufacturing cost. The second approach is to keep the same accelerator length and reduce the accelerating gradient to reduce cost in power and cooling. V.B.8 Tcical Heat Flux and Freauencv Sensitivitv Alonp the Cavitv Surface All of the coupled cavities optimized with respect to ZTl" have the same heat flux
and frequency sensitivity trends along the inside surface of the cavity. These trends are shown in Figure V.B.lO. Figure V.B.10 shows that heat flux at a beam energy of 1600 MeV, frequency of 700 MHz, and an accelerating gradient of 4.7 MeV/m is fairly constant along the cavity radius, peaks along the top surface of the nose and then approaches zero in the aperture. The temperature distribution in the cavity determines the its thermal expansion. Movements in the radial or axial direction will cause a frequency shift as shown in Figure V.B.lO. The frequency sensitivity in the radial direction along the cavity radius decreases the frequency as the radius increases, but the frequency increases with a radial increase at the nose. The frequency sensitivity in the axial direction is close to zero along the cavity radius and increases the frequency at the tip of the nose. Therefore, temperature control at the cavity radius and the nose needs to be tailored to mitigate the resultant frequency shifts.
v -16-
I
References P. P. Incropera and D, P. DeWitt, Fundamental of Heat and Mass Transfer, 2nd ed.. Publised by John Wiley & Sons, 1985. J. McKeown and J. -P. Labrie, "Heat Transfer, Thermal Stress Analysis and the Dynamic Behaviour of High Power RF Structures", IEEE Transaction on Nuclear Science, Vol. Pis-30, NO. 4, August 1983, p. 3593.
D.E. Nagle, "High Energy Proton Linear Accelerators", 6th International Conference, Santa Fe and Los Alamos, NM. Proceedings, June 1975, p. 403.
W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism. Published by Addison - Wesley Publishing Company, Inc., 1955.
Lloyd Smith, "Linear Accelerators", In Handbuch der Physik, Band XLIV (Springer, Berlin), 1959, p. 344.
V -17-
Peak Flux, Avg. Flux, and Power Dis. at 1 MV/m vs Beam Energy 3.00 2.75 2.50 2.25 2.00
< I
1.75
c-r
40
1.50 1.25 1.00
0
*
.
1
1
200
1
1
400
1 1
1
1
1000
1200
1
600
800
1
1400
1600
Beam Energy (MVlm)
Peak Flux (W/cm*2) __f_
Avg. Flux ( W J d 2 )
1PowerDis.(lcW)
Figure V.B.7 Peak flux, average flux, and power dissipation at 1 MV/m vs beam energy.
Average Flux vs Accelerating Gradient Radial Aperture = 81 /18 Beam Energy = 700 MV 50
40
I
30
20
10
0
0
1
2
Frequencies: I
Y
1300 MHz
3
4 EoT (MV/m)
700MHz
5
__p_.
6
200MHz
Figure V.B.8 Average flux vs accelerating gradient for various frequenciesat a radial aperture of 81/18 and a beam energy of 700 MV.
7
Average Flux vs Radial Aperture Accelerating Gradient = lMV/m Freq. = 1300 MHz
