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DESIGN OF A 3-MEV PARTICLE ACCELERATOR

EPHEDYN LIN LIKAI

A fuller understanding of p −73 Li nuclear fusion yields possible applications as it circumvents the neutron-irradiating complications associated with most fusion reactions. Quantum-mechanical corrections are suggested for the Gamow potential well approach for transmission below the classical limit. Possible alternative reaction pathways are considered, and the hypothetical semileptonic weak interaction cross-sections are calculated. The construction of a particle accelerator is proposed for the explicit verication of these models. It is shown that the validity of the WKB approximation can be demonstrated from the proposed experiment. The design and operating principles of a 3 MeV cyclotron are presented. A discussion of the continuity and maintenance of the cyclotron suggests future research uses.

Abstract.

Key words and phrases. cyclotron, aneutronic nuclear fusion, tunnelling, weak interaction cross-section, spin, coupling, Gamow potential, WKB approximation. 1

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

2

Contents List of Symbols

Part 1. 1.

Basis of research

Introduction

Part 2.

Phyiscal principles of the cyclotron design and operation

4 6 6 7

2.

Resonant frequency of oscillating electric eld at non-relativistic speeds

3.

Field-enhanced thermionic emission and Schottky eect (incomplete)

9

4.

Numerical analysis of path length

9

5.

Optimization of mean free path of residual gas

6.

Flexure, Fatigue, shear failure and safety factor

Part 3. 7.

Design of a 3-MeV particle accelerator

Inventory and equipment lists

7

9 11 12 13

7.1.

Equipment

7.2.

Sealants and mounting in vacuum

13 16

7.3.

Tools

16

8.

Summary of design specications

16

9.

Vacuum chamber

17

9.1.

Chamber wall

17

9.2.

End plates

19

9.3.

Base plates (incomplete)

20

9.4.

Electrodes

23

10.

Inlet ports and feedthroughs (incomplete)

24

RF: Radio frequency oscillator feedthrough

26

VP: Vacuum pump gate

27

H2: Hydrogen gas feedthrough

27

MP: Multipin electrical feedthrough

27

TG: Thermocouple gauge

27

IG: Thermionic ionization gauge

27

RG: Residual gas analyser (or blank port)

27

VW: View port

27

11.

Vacuum pump, ventilation and exhaust system

27

12.

Radio frequency power supply (incomplete)

12.1.

Impedance matching between RF system and signal (incomplete)

30 31

13.

Electromagnet (incomplete)

14.

Instrumentation

31 32

15.

Thermionic emission source

33

16.

Chemicals

33

16.1.

Isolating hydrogen, hydrogen molecule ions, protons and alpha

16.2.

Isolating depleted boron and lithium-7

36

16.3.

Extracting deuterium

36

particles

Part 4.

Handling procedures of the particle accelerator

33

36

17.

Electrical hazards

36

18.

Chemical hazards

37

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

3

19.

Radiation hazards

37

20.

Conclusion

38

References

Part 5.

Appendix

38

39

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

List of Symbols

o permittivity of free space Λ Lagrange function λ mean free path of residual gas λL Lagrange multiplier ω angular frequency of particle's circular motion σavg average stress on 1 bolt σU T S ultimate tensile strength of bolt Ab eective cross-sectional area of bolt AP area characterised by the minor diameter of end plate Ap relative atomic mass of projectile particle At relative atomic mass of target particle B magnetic ux d diameter of residual gas particles Def f eective diameter of bolt Dmajor major diameter of bolt E maximum producible energy of cyclotron e elementary charge of an electron F Faraday's constant F maximum shear stress on each end plate f frequency of oscillating electric eld f (p, λ) constraint function at pressure p and mean free path λ F oS factor of safety i ionisation eciency of thermionic emission lament source I (p, λ) beam current at pressure p and mean free path λ k Boltzmann's constant L Avogadro's constant m mass of particle nH 2 number of moles of hydrogen molecules p pressure in vacuum chamber P (x) collision factor at distance travelled x po atmospheric pressure q charge of particle R molar gas constant r radius of orbit in cyclotron rn radius of nth semi-circular orbit Ro residual range of colour force SP pitch size of bolt T average temperature in vacuum chamber t time taken to travel a semi-circular arc TE period of oscillating electric eld U Coulomb barrier for a system of 2 particles Up−11 B classical barrier of p −11 B fusion Up−7 Li classical barrier of p −7 Li fusion V volume of residual gas v tangential velocity of particle x distance travelled by particle xo path length of proton beam

4

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Zp Zt

atomic number of projectile particle atomic number of target particle

5

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

6

Part 1. Basis of research This section discusses the basis of, and the procedures which will undertaken to study, the quantum mechanical description of weak interaction in

p −73 Li

nuclear

fusion.

1.

Introduction

Linear accelerator designs generally require a large vacuum volume and direct high applied voltages. As such, producing a relatively energetic beam of ions from a linear accelerator is a dicult and costly task. Lawrence & Livingston [1] demonstrated a method for the repeated acceleration of light ions to high speeds by resonance with an oscillating electric eld, a development credited with the 1939 Nobel Prize in Physics. In particular, a cyclotron relies on the Lorentz force acting on charged ions as a magnetic eld is normal to the plane of circular motion of the ions to circulate ions back and forth from the interior of one electrode to the interior of another in spiral orbits, overcoming the diculties faced in linear accelerator designs. In his 1994 and 1995 Intel Science and Engineering Fair (ISEF) entries, Niell [2] laid out plans for the design of an aordable cyclotron with relative ecacy for the experimentation of resonance spectral analysis. This design has been adapted for our use. The cyclotron avails the acceleration of light ions to speeds suited for nuclear excitation. Considering the possible uses of a beam of protons and other light ions, there are a few promising directions for experimentation with the design ascribed. It is infeasible to perform a research on most fusion reactions because of the considerable Coulomb barrier even between the lightest nuclei, the storage and the availability of fusile materials in high isotopic purity. However, two reactions may be feasible: (1) (2)

p +7 Li p +11 B

 

2

4

3

4

He + 17.2 MeV, He + 8.7 MeV

and

We consider if these reactions are energetically feasible with our resources. For nuclear excitation of a target nuclei with a beam of protons, the bombarding protons must possess sucient energy to surmount the Coulomb barrier that surrounds the target nuclei to a distance where the attractive nuclear potential eectively replaces the repulsive Coulomb potential; and the residual colour force pulls the nuclei together.

This distance,

Ro

is taken to be approximately

1.5 × 10−15

m.

Enge [3] notes the following empirical formula used to estimate, to within 1 MeV, the Coulomb barrier for a system of 2 particles:

U=

(1.1)

where

e and 4π1 o

e2 Zp Zt (Ap + At )  1  1 4πo Ro Ap3 + At3 At

are the constant for electronic charge and the Coulomb constant

respectively; subscript

p

denotes the projectile; subscript

t

denotes the target;

Z and A are the relative atomic mass and atomic number respectively.

e = 1.60 × 10−19

C,

1 4πo

= 8.99 × 109

expression that:

Up−7 Li ≈ 1.13

MeV, and

2

N m

−2

C

Taking

, we calculate from the above

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Up−11 B ≈ 1.62

7

MeV

Imposing an uncertainty of

±1MeV, Up−11 B ≈ (2 ± 1)

MeV rounded up to the

same number of signicative gures as that of the uncertainty.

7

11

Also, it must be noted that 3 Li has a smaller nuclear cross-section than 5 B , and results would dier from expectation values based on a one-dimensional discussion of a proton-target collision; more specically, the to occur.

p −73 Li

reaction is less likely

Nevertheless, a high focusing action is suited for the task of nuclear

excitation given small nuclear cross-sections. Reaction (1) proceeds with alarming ease of detection. The nuclear transmutation of lithium-7 to an unstable beryllium-8 nuclide veries a successful collision. The beryllium-8 nuclide subsequently decomposes to 2 alpha particles, releasing a distinctly energetic, 17.2 MeV prompt gamma photon. Moreover, the discharge of alpha particles also results in a net increase in the partial pressure of helium in the vacuum chamber. This in turn, can be veried by an erroneous decrease in pressure reading on a thermionic ionisation pressure gauge calibrated for air (the ionisation gauge is insensitive to the presence of helium in the gauge). Based on these reasons, it would be prudent to build a cyclotron that is capable of producing a 3 MeV proton beam (subsuming the range of interest) with a high focusing action for such a study.

Semi-classical approximation.

The probability that an incident proton penetrates

the Coulomb barrier is unity when the energy of the incident proton is larger than the Coulomb barrier. However, there is a non-zero probability of transmission of an incident proton with energy less than the Coulomb barrier. Cockroft and Walton found evidence supporting this when they were able to transmute a sample of lithium-7 to beryllium-8 with 300 keV protons, far below the classical limit, verifying the quantum mechanical description of weak force interaction cross-sections. A further discussion of the research procedure will take us too far aeld from the focus of this paper, and is hence not discussed here.

Part 2. Phyiscal principles of the cyclotron design and operation This section discusses the physical principles of the design and operation of a cyclotron, with emphasis on the areas which require mathematical treatment. 2.

Resonant frequency of oscillating electric field at non-relativistic speeds

We rst determine a master equation for cyclotron frequency. For an ion of mass

m undergoing circular motion with orbit r in the electrode with tangential velocity v , the Lorentz force on the moving charge provides for the centripetal acceleration:

(2.1) where

B

is the magnetic ux in

mv 2 = Bqv r teslas and q

is the charge of the ion. The time

taken for the ion to travel a semi-circular arc of distance

(2.2)

t=

πr πm = v Bq

πr

is

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

8

The oscillating electric eld is at the peak value at the beginning of a semicircular path of the ion, and at the minimal value at the end of the path. Hence, the oscillation of the electric eld has period

TE = 2t =

(2.3)

2πm Bq

Therefore, the frequency of the oscillation of the electric eld is

f=

(2.4)

1 Bq = TE 2πm

This equation would be useful to calculate theoretical resonant frequency of the electric eld to be applied between the electrodes. We next determine the theoretical maximum producible energy as a function of magnetic eld and radius of the electrodes to nd the dimensions required for our cyclotron. It is clear that an ion with angular frequency

ω=f

is in resonance with

the oscillating electric eld, and that the theoretical maximum producible energy

E

is realised when an ion is in resonance with the electric eld on the cirucmference

of the electrodes,

i.e.

1 mv 2 2

E=

(2.5)

From eq. 2.2, we have the velocity of the ion

v=

(2.6)

Bqr m

Hence, the maximum producible kinetic energy from a cyclotron, assuming nonrelativistic speeds, is

E=

(2.7)

(Bqr)2 2m

Supposing we want to produce protons with

≥

3 MeV and a clearance of 1cm

(subsuming the thickness of electrodes and width of the ion beam) from the cirucmference of the electrodes, say, then

E=

(2.8)

B 2 q 2 (r − 0.01)2 2m

and in eV,

(2.9) Solving, we have

E=

eB 2 (r − 0.01)2 = 3 × 106 2m

B(r − 0.01) = 0.250. B =

ingston [1] that a magnetic ux of

It was suggested by Lawrence and Liv1.4T can be sustained for considerable

periods of time without overheating. This gives us a cyclotron of external radius 17.957cm.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

9

Field-enhanced thermionic emission and Schottky effect (incomplete)

3.

4.

Numerical analysis of path length

We consider a numerical method for determining the path length of the proton beam

xo ,

which would be necessary for determining the mean free path of the

residual gas and hence the desired ultimate pressure. Since a proton in the cyclotron receives an increase in energy of 2500 eV at the end of each semi-circular path travelled, and makes 1200 semi-circular orbits, then from eq 2.6, we have

mv r= = Bq

(4.1)

r

√

2mE Bq

(4.2)

1 rn = B

(4.3)

750 X 1 πrn = π xo = B n=1 n=1

2nmV e

750 X

r

2nmV e

A for-loop algorithm was written on MATLAB to compute the radii semi-circular path, and store the result in a matrix array

r(n).

rn of

each

The accelerating

potential of 2500V is specied. The element corresponding to the last arc length, 0.17875m, veries that the proton will at least acquire 3 MeV of energy within the internal diameter of electrodes specied.

%%for-loop algorithm for radii r of protons in a cyclotron with accelerating potential 2500V in MATLAB, written by Ephedyn Lin Likai, 2009 for n = 1:1200; r(n)=sqrt(n*2*2500*1.67e-027/1.6e-19)/1.4; end L=pi*sum(r) clear n

As such, it is determined that the path length of the proton beam will be

xo =

449.52m. 5.

Optimization of mean free path of residual gas

Koeth [4] suggests an experimental method for determining the optimal, ultimate pressure in the vacuum chamber.

A high pressure of hydrogen in the vacuum

chamber is desirable for increasing the availability of hydrogen for the formation of ions from the thermionic heater element, and hence increase the collected beam. However, a low pressure of hydrogen in the vacuum chamber is also desirable for increasing the mean free path of the protons, and hence reducing losses to the collected beam. It is often suggested that the average distance between successive impacts travelled by each proton in the vacuum, proton,

i.e. λ ≥ xo .

λ

should be at least the path length of the

However, the mean free path cannot be arbitrarily increased

by decreasing the pressure in the vacuum chamber. Thus, we need to maximise the collected beam as a two-variable function of pressure and path length to determine the optimal pressure at the end of pumpdown.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Neglecting focusing action, the collected beam number of hydrogen molecules

i,

eciency of the lament

nH 2

I

10

is given by the product of the

passing through the lament, the ionization

and the probability of passing through the interval

dened by the path length without undergoing collision,

1 − P (xo ).

These can be

expressed mathematically:

 dQ = nH 2 Le × i × [1 − P (xo )] dt =

(5.1)

λ= √

(5.2) where

L

is Avogadro's constant,

mann's constant,

T

F = Le p

 iF [1 − P (xo )] dt

kT 2πd2 p k denotes Boltzd denotes the diameter of the particles

is Faraday's constant,

denotes temperature and

collided against by the protons, and

pV RT

denotes the pressure within the chamber.

From the Beer-Lambert law,

dP (x) 1 x = e− λ dx l

(5.3)

ˆ

xo 1 x − e− λ dx = 1 − e− λ l [0,xo ]

P (xo ) = −

(5.4)

 ∴ I (p, λ) =

(5.5)

pV RT



h  i  xo  xo pV iF 1 − 1 − e− λ = iF e− λ RT

Since the mean free path of protons in vacuum chamber maintains a xed relationship with the pressure and hence free hydrogen molecules in the vacuum chamber, the possible values of

and

λ

are constrained by the function

kT f (p, λ) = pλ − √ =0 2πd2

(5.6)

I

p

and

f

have continuous rst partial derivatives and

For the maximum of

I (p, λ)

λL

Solving for

(5.10)

at any point.

denotes the Lagrange multiplier. Consider the Lagrange function,

Λ (p, λ, λL ) = I (p, λ) + λL f (p, λ)

(5.8)

(5.9)

∇p,λ f 6= 0

f (p, λ),

∇I (p, λ) = −λL ∇f (p, λ)

(5.7) where

to exist on

p

and

λ, ∇p,λ,λL Λ (p, λ, λL ) = 0 ∂Λ = ∂p



iV F RT



e−

xo λ

+ λL λ = 0

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

∂Λ = ∂λ

(5.11)

iV F xo RT λ2



pe−

xo λ

+ pλ = 0

∂Λ kT =0 = pλ − √ ∂λL 2πd2     xo iV F xo iV F xo 1 − xλo e = e− λ =⇒ 2 = =⇒ λ = xo 2 RT λ RT λ λ λ

(5.12)

(5.13)

∴p= √

(5.14) Hence,



11

λ = xo

kT kT =√ 2 2πd λ 2πd2 xo

to produce a proton beam with maximum beam current for the

specied path length.

Desired ultimate pressure, composition of residual gas and maximum tolerable pumpdown time. As we have determined, xo = 449.52m. Assuming room temperature ≈ 300 K); and that the constituent particles of the vacuum are mostly hydrogen 1 with diameter, d ≈ 74 pm, from eq. 5.14, the desired ultimate pres−6 −4 sure attained from the vacuum pump is found to be 2.85 × 10 Torr = 3.79 × 10

(T

gas molecules Pa.

This should be reached in practice within 2 hours of pumpdown. The composition of residual gas is either air (gas supply valve closed), or largely hydrogen, deuterium, helium or nitrogen, depending on the experiment. Controlled supply of the gas should bring the pressure up to

3.79 × 10−4

Pa (for

hydrogen). 6.

Flexure, Fatigue, shear failure and safety factor

Extra care is taken to the design of the mounting of the end plates since this is one of the few areas where we are not following a prescribed industrial standard. Unlike aluminium alloys, stainless steels have a distinct fatigue limit, therefore they do not fail regardless of the number of cycles of stress subjected to the bolts, so long as the amplitude of cyclic stress is below the fatigue limit. As such, stainless steel does not have a fatigue life; and we only consider if the maximum stress results in shear failure of the bolts. The load on the mounting bolts arises from the pressure dierence between the internal and external surfaces of the end plates. Assuming all of the atmospheric force applied at a normal to the surface of the end plate applied results in shear, and that the load is static, the total load on each end plate

F

and hence shear

stress on the mounting bolts should be the product of atmospheric pressure, the area characterised by the minor diameter of the end plate

Def f

and

of each bolt is the diameter of the imaginary cylinder

coaxial with the thread of the bolt, and can be found from the nominal size (bolt major diameter) and pitch size 1

po

Quantiatively,

F = p o AP

(6.1) The eective diameter

AP .

Sp

Dmajor

from the relationship

This assumption is valid as the ionisation eciency of the lament source is 10−3

m is sucient

to ensure adequate insulation up to 5000V. [5] With our specied radial clearance, the vacuum chamber is safely insulated from the D electrode. 9.2.

End plates. The at sections of the vacuum chamber require large tolerances

for withstanding greater atmospheric forces than the cylindrical section of the chamber. The material must possess a low rate of outgassing per unit surface area to attain the desired vacuum pressure at aordable pump capacity.

To circumvent

eld distortion, the end plates should be made of a material that has a relative magnetic permeability of approximately 1 (that of vacuum) 9.2.1.

Material and dimensions.

The end plates will be machined from aluminium

6061-T6 alloy plates of 1/2" thickness, to major diameter 42.994cm and minor diameter 37.914cm (with a housing joint of cross-sectional dimensions 2.540cm by 0.635cm around). 9.2.2.

Mounting hardware.

M6

×

1 metric size-pitch, hexagonal socket head bolts

M6

× 10 may also be

of length 30mm and matching nuts and washers will be used to mount each end

known as .250-28 or

plate.

1/4 - 28 UNF

The mounting hardware is made of type 304 stainless steel.

The bolts,

sourced from MDC Vacuum Products Corporation, have a recommended torque of 16.2 N m. Unthreaded holes specied for M6 bolts are drilled at angular separation of 20 degrees between each hole starting from 5 degrees anticlockwise from the axis through the centre of chamber to the centre of the VP port, on a bolt circle diameter of 41.565cm on both end plates.

Hence, the end plates can be mounted using a

ange and O-ring assembly with 18 sets of bolts, nuts and washers.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Note.

20

The existing design can be improved upon in the future by replacing the

aluminium end plates with Pyrex. Hence, a better view of the vacuum chamber during the experiment than available from view ports on the side can be obtained. Moreover, this can be done at lower cost than increasing the number of the view ports. The windows are clamped by 6 aluminium C-clamps of 2" opening placed in a hexagonal formation. Two thin acrylic rings are used as 'swivel pads' on both sides of the clamp so as distribute the pressure of the clamps more evenly. Due to the dierence in stinesses of the steel of the ange and the glass plate, the glass plate could crack. As such, the acrylic rings are used on both sides, and not merely the glass-side.

The cams of the C-clamps have to be shortened to t under the

ange of the vacuum chamber. However, this design was not implemented due to the availability of aluminium C-clamps from local hardware supplies

9.3.

Base plates (incomplete). Two base plates are required for the mounting

of two separate electrodes while maintaining a gap between the base plates for the lament leads and ion production in the centre of the cyclotron. The base plates are also required to insulate the electrodes. Again, to circumvent eld distortion, the base plates should be made of a material that has a relative magnetic permeability

e.g. Pyrex

of approximately 1. Borosilicate glass (

or

Klimax )

is very suitable for

these purposes, and has a low outgassing rate of . It is convenient to produce the I-side base plate out of a conductive material with a relative permeability of approximately 1,

e.g.

copper, to ensure a consistent

ground on the I electrode and vacuum chamber. However, this would disable the glow discharge of the electrodes

in situ

as a high voltage will have to be applied to

the entire vacuum chamber at the same time. Instead, the I-electrode is grounded through a...

9.3.1.

Material and dimensions.

The D-side base plate is made from Pyrex glass

to length 10.600cm, width 10.600cm and height 1.270cm. There are two reccesses of diameter 1.500cm and depth 1.000cm in the base plate, centred at the 1.750cm and 8.850cm intervals on the longitudinal axis of symmetry of the base plate. (Figure 9.3) These reccesses accommodate the aluminium sleeves described in .

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 9.3.

21

Technical drawing of D electrode base plate

The I-side base plate is made from Pyrex glass to length 10.600cm, width 3.500cm and height 1.270cm.

There are two reccesses of diameter 1.500cm and

depth 1.000cm in the base plate, centred at the 1.750cm and 8.850cm intervals on the longitudinal axis of symmetry of the base plate. These reccesses also serve the beforementioned purpose of accommodating aluminium sleeves. Two straight bores of 0.300cm diameter run parallel through the width of the base plate (perpendicular to the reccesses), starting at points 3.650cm and 6.950cm along the length, and centred at height 0.635cm, of the base plate. These bores will house the aluminium rods that act as lament leads. Lastly, a third straight bore of 1.000cm diameter is produced exactly between, and runs parallel to, the previous two straight bores. This bore will house the copper pipe that is used to deliver hydrogen to the centre of the cyclotron.

As such, there will be a 1.000cm lateral distance along the

longitudinal axis of symmetry between each intrusion. (Figure 9.4)

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 9.4.

9.3.2.

22

Technical drawing of I electrode base plate

Mounting and height adjustment mechanism.

on the base plate by means of

2 countersunk M6 allen bolts each. A third countersunk M6 allen bolt is also used to ground the I electrode on the ground wire housed in the base plate. The bolts would be ush with the surface of the electrode when fastened. The use of allen bolts is also necessary as the bolts are in a conned space, and is most suited to be fastened by an allen key.

This simple design is also useful:

washers of known stack height can therefore be used as spacers to readjust the height of the electrodes without the need for rebuilding, should the proton beam deviate from the plane of acceleration signicantly on one electrode side.

Note.

The original design of the electrodes was based upon a stem mount.

The

problem with this design was that a component in the connection had to be insulated from the high voltage radio frequency source. It was originally suggested that a pair of anodised bolts are used as the insulated connection. However, this design is unsafe as the anodised layer of the bolt cannot be ascertained to be consistent, or suciently thick. The bulk of the bolt (underneath the oxide layer) is electrically conductive and hence posed a huge risk. It also could not be conrmed that aluminium oxide had no radiation-induced electrical conductivity properties. The stem mount also occupied much space, and therefore was conclusively rejected when considerations were made to the availability of large O-rings (discussed above). Three hollow M3 bores run through the base plate feed the pair of ion source lament leads and the ground wire.

The central bore housing the ground wire

terminates on a female M5 thread. Two additional female M5 threads are produced for the mounting bolts. As such, each element can be laterally separated by 15mm of glass (hence a total width of 8.100cm). 9.3.3. 9.3.4. ers.

Outgassing properties of anodised fasteners (incomplete). Thread seizure and melting (incomplete). Problems associated

with fasten-

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

9.4.

23

Electrodes. The electrodes are mounted in a coplanar and diametrically ad-

jacent arrangement, forming an imaginary circular plane in which the particles undergo acceleration. Due to the shape of the electrodes, individual plates of its material have to be welded together.

As such, among the commonly available grades of aluminium

alloy, 6061-T6 is preferred over 7075-T6 due to its weldability.

9.4.1.

Material and dimensions.

A quasi-semi-circular (D-shaped), hollow elec-

trode is to be machined from 0.159cm thick 6061-T6 aluminium alloy plates with external diameter 35.914cm and external height 2.540cm. A solid aluminium rod of diameter 0.635cm and length 8.620cm is welded onto the electrode along the axis of symmetry of the electrode to allow a complete connection between the radio frequency oscillator feed and the electrode. (Figure 9.5)

Figure 9.5.

Technical drawing of D electrode

A second hollow electrode (I-shaped) is also machined from 0.159cm thick 6061T6 aluminium alloy plates to width 3.500cm and external height 2.540cm such that it ts the circular plane of acceleration perfectly while a lateral gap (diametrical region) of 2.000cm is maintained between the two electrodes. (Figure 9.6)

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 9.6.

24

Technical drawing of I electrode

9.4.2.

Magnetic permeability and shimming action (incomplete).

9.4.3.

Electric glow discharge and chemical mitigation of outgassing (incomplete). 10.

Inlet ports and feedthroughs (incomplete)

Metal-metal joints for the inlet ports will be arc welded using a non-consumable tungsten electrode in an argon atmosphere, specifying heliarc

a.k.a.

TIG (tungsten-

inert-gas) welding. The dimensions of the chamber wall will be slightly altered from welding, hence the chamber wall should be trued after welding on the inlet ports. The inlet ports are represented by the centre of their holes, of which the angular positions are denoted in degree measure on a modied Cartesian plane where angles above the horizontal axis are positive, and angles below the horizontal axis are negative, starting from

0◦

on the positive side of the horizontal axis.

Most of our inlet ports use the ISO standard quick release ange,

i.e.

Klein

Flange (KF). In particular, only DN16KF and DN25KF anges and ttings (nom-

MDC Vacuum Prod-

inal inner diameters of 16mm and 25mm respectively) are used. The ttings and

ucts produces these

anges are fabricated from type 304 stainless steel.

standard

ttings

Note.

under

Kwik-

The only exception is the use of the ISO LF anges and ttings for the

turbomolecular pump, which will later be discussed.

the

Flange trademark

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

25

The ISO KF standard provides economical vacuum ttings with some compromise in lowest attainable pressure: KF assemblies are usable down to as compared to

−13

1 × 10

Figure 10.1.

1×10−8

Torr,

Torr for ConFlat anges. (Figure 10.1)

ConFlat ange with a knife-edge compatible O-ring.

In comparison, the Conat ange per se is costlier, and requires a special-shaped O-ring (to accommodate the knife-edge reccess on the ange), multiple bolts, nuts and washers which cost more than the KF assembly. Moreover, KF ttings were found to be suitable for our vacuum chamber as the desired ultimate pressure is

2.85 × 10−6

Torr.

Each KF installation requires

compatible anges, an O-ring, a centering ring, a wing-nut and a hinged aluminium clamp for interfacing. These components are reusable and can be reassembled as desired; and are relatively cheap to replace if damaged. The ttings are installed by compression of the O-ring on the centering ring between mating anges, followed by nger-closure of the wing nut on the aluminium clamp. (Figure 10.2)

Figure 10.2.

Installation; and dimensions with ISO industry

cross-references for ttings to be used. Dimensions in mm.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

26

K40

RF: Radio frequency oscillator feedthrough. The electric oscillations have to be applied to the electrodes through an insulated electrical connection. This is done

refers

to

a

DN40KF compatible tting.

by means of a hollow tube conductor through a KF-anged ferrule. The feedthrough is housed in an alumina-based ceramic to insulate it from the metal ttings, while ensuring a ceramic-to-metal vacuum seal.

(Figure 10.3)The conductor is rated 2

for a maximum voltage and current of 5000V DC and 150A respectively .

The

hollow, tubular construction of the conductor enables a secure connection to the D electrode by means of an interference t. The dimensions and thickness of the

The interference t

tube are designated for a t with a solid rod of 0.635cm diameter. For the stated

may also be referred

8.62cm rod length on the electrode and accounting for the 1.000cm radial clearance,

to as a press t

the tube is occupied through 3/4 of its length when fully connected.

Figure 10.3.

Electrical feedthrough with KF-anged ferrule and

ceramic housing used for radio frequency oscillator. Vacuum side = 4.12; air side = 3.13. Dimensions in inches.

The RF port is placed at

0◦ .

2 The feedthrough is capable of exceeding 150A current rating if a cooling system is installed but this is unnecessary for our uses.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

27

Diusion pump, backing pump and ventilation port.

VP: Vacuum pump gate.

A valve system connects three conductance pipes for the diusion pump, backing pump and vent to a main pipe; and allows separate use of these. A port leads the main pipe to the vacuum chamber. The VP port is placed at

90◦ .

H2: Hydrogen gas feedthrough. The H2 port is placed at

Deector feed ; target multimeter feed;

MP: Multipin electrical feedthrough.

on source feed.

i

135◦ .

The lament leads of the ion source have to enter the vacuum

chamber from an external circuit.

180◦ .

The MP port is placed at

TG: Thermocouple gauge. The TG port is placed at

−30◦ .

IG: Thermionic ionization gauge. The IG port is placed at

−60◦ .

RG: Residual gas analyser (or blank port). The RG port is placed at

−90◦ .

VW: View port. A window are desired such that the plasma glow can be observed during the stage of outgassing from surfaces of the electrodes and the complete removal of adsorbed gases can be conrmed from a cease in the glowing phenomenon. The VW port is placed at

−135◦ .

Vacuum pump, ventilation and exhaust system

11.

Gas load on the pumps from outgassing. pressure

Pmind

of

3.79 × 10−4

Pa =2.85

Given that we have to maintain a base

× 10−6 torr,

we can calculate the required

pump capacity, or pumping speed:

Table 9.

Gas load and pump capacity specications

Main component

−1

Outgassing rate [torr

l

s

Pmin [l

s

−1

Gas load at

−2

cm

−2

cm

]

]

Borosilicate glass

AL 6061-T6

End plate

End plate

Chamber wall

Electrodes

8.0 × 10−9

7.0 × 10−9

6.0 × 10−9

6.0 × 10−9

2.81 × 10−3

2.46 × 10−3

2.11 × 10−3

2.11 × 10−3

1129

1129

756

727

3.17

2.78

1.60

1.53

34.9

30.6

17.6

16.9

2

Surface area [cm ]

304 stainless steel

Required pump capacity in

l

s

−1

in % of total

−1

Hence, a pumping speed of at least 10.1 s

is required. This is a low gure as we

have made an improvement to the conventional design of cyclotrons by specifying the use of 304 stainless steel for the electrodes.

This was previously impractical

as machining stainless steel was dicult, but has now become viable. In contrast, brass electrodes in the manner of Lawrence and Livingston would have entailed an apnmproximate outgassing rate of is in the order of

l

s

−1

3

10

4.0 × 10−6

torr

l

s

−1

−2

cm

of surface area, which

larger, and would thereby require a pumping capacity of 1020

for the electrodes alone.

3

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 11.1.

28

Cross-sectional diagram of suggested pump system. [5]

A parallel diusion vacuum pump system is built as illustrated. (Figure 11.1) Modications have been made to the design to run the vent, foreline and diusion pump line in series.

This reduces the number of required inlet ports for the en-

tire system, which we have identied to be the most likely source of leakage. As illustrated, two thermocouple gauges are required: along the foreline and at the vacuum chamber. The diusion pump used has a ANSI /ASA specication of 2 inches.

Hence,

the main pipeline connector is made of a stainless steel pipe of diameter 5.080cm. The pipe is contracted to a diameter of 2.540cm and terminates with a 7.620cm diameter ange with a thickness of 0.635cm before the point of connection with the inlet port. The dimensions allow us to mate the main pipeline connector with the inlet port perfectly.

The connector has 3 branch pipes of 5.080cm diameter

which are regulated by pneumatic valves. Branch pipe ends on the main pipeline connector terminate with anges of 10.160cm diameter, 0.635cm thickness, and 8.412cm bolt circle diameter, with 6 bolt holes in a hexagonal arrangement. The rst valve from the inlet port opens to the diusion pump, and is thereby acting as the gate valve. The second valve from the inlet port opens to the backing pump, and is thereby acting as the roughing valve. The third valve from the inlet port opens to the room, and is thereby acting as the vent valve.

Backing pump and diusion pump.

The backing pump is a regular mechanical

pump which operates at atmospheric pressure down to somewhere
0.5W

to overheat in vacuum.

It is necessary to place these in vacuum-tight,

air-lled boxes that are in thermal contact to the vacuum wall or coolant pipes. The pressure will also have to be monitored while the magnetic eld is o.

Thermocouple gauges.

The thermal conductivity of air decreases from some con-

stant to almost 0, as the air pressure changes from 133 to 0.133 Pa. Furthermore, temperature depends on the rate of heat loss to the surrounding gases, which is proportional to the thermal conductivity of the surrounding gases. Hence, assuming a linear behaviour for the

e.m.f., pressure readings can be found from the temperature

parameter, and this method will be useful down from 133 to 0.133 Pa. Two thermocouple gauge tubes are installed, along the foreline pipe; and in direct access to the vacuum chamber at the TG inlet port and heated to low temperature by a constant current, and a bi-metallic thermocouple is placed in thermal contact with each lament. The temperature, and consequently the pressure, at each position is then determined from the electromotive force (

e.m.f.)

produced by each

thermocouple. The thermocouple gauges are standard NPT nominal size male 1/8-in with 3 pins, which can be read by a Varian 845 ionisation guage controller which has 3 ports: for two thermocouple gauges, and 1 thermionic ionisation gauge.

Thermionic ionisation gauge.

To support pressure measurements below 0.133Pa, a

thermionic ionisation gauge is used. The thermionic ionisation gauge has a standard Kwik Flange nominal size 40 and 6 pins, which can also be read by the Varian 845 controller. The gauge is secured by means of a KF40-CP clamp and wing nut with a KF40-CR centering O-ring.

Note.

The indicated pressure is proportional to the ionisation cross-section, which

varies with the gas. Thus, the ionisation gauge has to be calibrated dierently for air, hydrogen and helium for dierent experimental phases of the project.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 15.1.

Leakage detector.

33

Output polarity-inverting buck-boost topology.

Leak detection is carried out in the operating pressure range of

the thermionic ionisation gauge.

This is done by spraying a small jet of helium

on the surfaces of the vacuum chamber during pumpdown of air.

A thermionic

ionisation gauge calibrated for air pressure readings is less sensitive to helium and

sic.)

would pick up a sudden and rapid decrease (

in pressure reading if helium is

being introduced into the chamber. Heliarc welding is employed to seal the leaks. Alternatively, the leaks can be sealed with a tube of Loctite 1C Hysol resin sealant, which is eective down to 15.

≈ 10−7

torr at room temperature.

Thermionic emission source

A negative voltage has to be applied across the lament leads that run through the I-side base plate. As such, the lament is heated to a temperature upon which it begins to discharge electrons. Nichrome will be used for the lament wire as other options, e.g. tungsten, tend to be oxidized at these temperatures. 0.26mm diameter nichrome wire was tested extensively for this usage. The wire has a resistivity of 26.80Ω/m. The lament has to have a total resistance of 4.0Ω, which translates to a length of 0.1492m. There are two options for generating a negative voltage from the power grid. The rst is to construct a rectier circuit with a center-tapped transformer. The other option is to run a +24VDC rail through a polarity-inverting circuit.

The

second option is chosen for its lower cost. A circuit is designed based on a Linear Technology LT3758 high voltage inverting controller. (Figure 15.1) A computer-generated circuit layout (Figure 15.2) shows that the circuit is kept

◦

within its maximum operating temperature of 125 C. (Figure 15.3) The minimum

◦

◦

temperature observed is 57 C, while the maximum temperature observed is 107 C. 16.

Chemicals

Isolating hydrogen, hydrogen molecule ions, protons and alpha particles. It may not be necessary to extract hydrogen, helium or nitrogen as large 16.1.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

Figure 15.2.

34

Circuit design of output polarity-inverting buck-

boost topology.

Figure 15.3.

Thermal simulation for output polarity-inverting

buck-boost topology under steady state. Ambient temperature and air pressure, unidirectional airow.

quantities are stored at most institutions of higher learning and support can be established with these institutions for use of their facilities.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

•

35

A tank of hydrogen can be commercially purchased but would require a regulator, which would be costly. Puried, industrial grade hydrogen, helium and nitrogen gas can be obtained from National Industrial Gases Pte. Ltd. (NIG) distributors and dealers at Ubi or Bedok Reservoir Road. The regulator for hydrogen would also have to be mated with the experimental apparatus.

•

Alternatively, as a contingency measure, hydrogen gas can be produced in large quantities by ourselves and helium gas can be acquired by renting balloon gas.

Note.

Balloon gas has a mixture of air and nitrogen which would alter experimental

results, and is considered the least desired alternative. However, it is very aordable and the most easily available option. Nonetheless, the contingency plan is very simple: hydrogen gas can be produced in large quantities through electrolysis of water or acid decomposition of zinc, then separated from other gases through a dehydrating agent and cold trap. The decision for the sourcing of hydrogen gas will be based on cost-eectiveness. For acid decomposition, the acid reagent used has to be hydrochloric acid, which is easiest to procure.

The products are in dierent phases, hence the separation

techniques required to purify the collected hydrogen gas will be simple. We know

3

that 2 dm

of

H2

is required - this corresponds to 0.0833mol of hydrogen gas at

room temperature; and a 2 mol dm

−3

solution of hydrchloric acid is suggested.

Based on the stoichiometric coecients from

Zn + 2HCl → ZnCl2 + H2 given

Ar

of zinc = 65.4, in theory, at least 83.3 cm

3 needed. Hence, we can react 83.3 cm of

HCl

3

of

HCl

and 5.45g of zinc is

and 5.45g of zinc in an Erlenmeyer

ask. For electrolysis of water, the method is similar to that of extracting deuterium. Using 100g of

Al2 Cl6

dimer in 2000cm

3

of distilled water as an electrolyte, and

0.953cm diameter copper pipes as electrodes, apply a current from a e.m.f. source of 2.2 kW and 100V direct current between the electrodes. The hydrogen is collected through a cold trap built around an Erlenmeyer ask held at 203.15 K. Protons, hydrogen molecule ions and helium-4 nuclei can be produced from hydrogen and helium gas respectively. The protons have to be delivered to the diametral region between the electrodes with low components of velocity normal to the plane of the accelerators.

A hot

cathode is installed at the centre of this region. The lament is placed above and normal to the plane of the accelerators. A current is passed through the lament, and as such, a large number of electrons undergo thermionic emission along the direction of the magnetic eld. Hydrogen gas introduced to the vacuum chamber would be ionised through collisions with electrons here and drawn out sideways by the electric eld, undergoing acceleration. The electron beam is highly collimated and not drawn out due to their small radii of curvature under the electromagnetic eld. The process for producing a beam of nitrogen molecule ions and nitrogen nuclei is also similar to that for hydrogen molecule ions and protons, although these ions may be unnecessary for the research.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

36

Regardless of the source of the gas, it should be stored in a lecture bottle. 16.2.

Isolating depleted boron and lithium-7. Boride and lithium-7 ions can

be easily produced if the pure material is put in place of the hot cathode used to generate protons and hydrogen molecule ions. Ions of metallic elements with atomic mass < 25 are also easily produced by replacing the lament in the above setup with a strip of the particular metal. Metal strips with a minimal tarnish (oxide layer) could be pre-prepared by dry sanding and storage under mineral oil. The ion beam produced has a signicant radii of curvature under the electromagnetic eld and is drawn out sideways by the electric eld, thereby also undergoing acceleration. While experimentation with depleted boron may be ideal, a major limitation is faced. A sample with a high concentration of depleted boron can be produced by chemical vapour deposition, but neither the process nor the product is easily accessible. 16.3.

Extracting deuterium. Isotopic fractionation has to be addressed to ensure

accurate results. A high isotopic fraction of deuterium can be extracted from highly puried heavy water with ease.

Non-industrial quantities of heavy water can be

procured from United Nuclear Scientic Supplies, LLC., claimed to be 99.999% pure and shipped via vPOST. As the item is not controlled for export by the Nuclear Suppliers Group, it is not necessary to obtain an export license from the U.S. Department of Commerce. Deuterium oxide has chemical properties that are similar to dihydrogen oxide and can undergo electrolysis to isolate deuterium. Using 100g of

3

2000cm

Al2 Cl6

dimer in

of heavy water as an electrolyte, and 0.953cm diameter copper pipes as

electrodes, apply a current from an

e.m.f.

source of 2.2 kW and 100V direct current

between the electrodes. The deuterium is discharged at the electrode connected to the negative terminal of the e.m.f. source (cathode). The deuterium is collected through a cold trap built around an Erlenmeyer ask held at < 203.15K.

Part 4. Handling procedures of the particle accelerator The design of the cyclotron per se does not preclude all of the safety issues involved.

For instance, the sucient shielding installations does not guarantee

against overdosage of ionising radiation by virtue of human error. A more detailed discussion of the procedures for the operation of the device is thereby necessary. 17.

Electrical hazards

Conventional procedures for handling electronics will be followed, but a further discussion of these is trivial.

However, it would be forseeable there are nontriv-

ial safety issues to take note of when handling electronics in vacuo. One concern cannot be addressed by design and must be noted while handling the cyclotron: inorganic salts are hygroscopic and tend to absorb moisture and consequently become conductive, incurring the possibility of high voltage discharges along insulator surfaces upon which these are deposited. After cleaning, it is necessary to rinse the surfaces of insulators with distilled water followed by ethanol, and dried with hot air to remove these salts. Gases adsorbed to the electrodes will be removed by running a high voltage direct current through the electrodes, which would eectuate the ionisation of these gases.

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

37

The gaseous ions can then be removed through ventilation or preferably, vacuum. The glow of plasma would indicate that adsorbed gas molecules are still present. It can be accepted that surfaces of the electrodes are free of

18.

Chemical hazards

There is an area regarding the handling of chemicals which requires further attention. The storage of hydrogen may present physical danger depending on the means by which it is obtained. A secure connection to the inlet has to be ensured. If the hydrogen gas is purchased in a pressurised tank, a regulator is required. If the gas is extracted through decomposition of zinc in hydrochloric acid medium or electrolysis of water, more thought has to be directed at its safe storage and eective separation methods and trapping. Lithium is ammable and easily tarnished in air, and hence must be stored under mineral oil.

19.

Radiation hazards

A very small amount of high energy electrons penetrate stainless steel or glass as the number passing through decays exponentially with increasing thickness and it is predicted that the count rate would be attributed mostly to gamma and x-ray radiation from the radiative stopping of charged particles. A secondary source of x-ray radiation arises as vacancies are produced in the inner shell of the atoms of the target medium as it is ionised by the passing beam. The atom becomes highly excited and the re-occupation of the vacancy by an electron from a higher shell results in either radiationless, Auger transition or uorescence.

Based on Niell's

report [2] of 20mRad integrated dosage throughout 3 months of experimentation without lead shielding, we would presume that the operation of the cyclotron does not pose signicant carcinogenic threat.

However, his report also warned of the

sensitivity of the corneas and skin to beta radiation and x-rays; vision can be impaired and burns may surface as a result of exposure, and this would be deemed the primary hazard of this project. His report mentions the detection of multi-MeV gamma radiation and hard x-rays. Only radioactive products encountered are extremely short-lived fusile products which are produced and contained in a 1/4" type-304 stainless steel vacuum vessel during their lifetimes. Hence, no special means of disposal will be employed.

Dosimetry.

A GeigerMüller tube is used dedicatedly to detect ionising radiation

escaping the walls of the vacuum chamber to ensure the safety of approaching the apparatus. It will be secured at 30.0cm distance from the vacuum chamber. A quartz ber dosimeter will be carried by each member of the team as a quick precaution for the immediate monitoring gamma and x-ray radiation exposure. A thermoluminescent dosimeter badge is also worn by each member of the team at all times while operating the cyclotron as a more accurate measure of monitoring personal exposure to gamma, beta and x-ray radiation. Most of the x-rays will be in the 'hard x-ray' range. Some radiation will be distinctly energetic (17.2 MeV gamma photons) from the decay of beryllium-8. Compton eect is predominant in high energy photons, and the best recommendation is to be behind high density concrete. The initial operation of the cyclotron will be

DESIGN OF A 3-MEV PARTICLE ACCELERATOR

38

carried out behind 12.901cm of concrete (averaged over 3 measurements) of a typical chemistry laboratory as a precaution. Based on radiation exposure readings, an improved course of action can be taken. The integrated dose is reduced by a factor of at least 4 at half-length of a lab away due to the inverse square law behaviour of the radiation. Photoelectric eect is predominant in low energy x-rays and gamma radiation (