(DEMO) to follow ITER by 2050 demands high frequency. (>230 GHz), high power (in the range from 1 MW to 2 MW) gyrotrons as RF sources for electron ...
Interaction Circuit Design and RF Behavior of a 236 GHz Gyrotron for DEMO P. Kalaria1, K. A. Avramidis1, J. Franck1, G. Gantenbein1, S. Illy1, I. Gr. Pagonakis1, M. Thumm1,2 and J. Jelonnek1,2 1
Institute for Pulsed Power and Microwave Technology (IHM), Institute of High Frequency Techniques and Electronics (IHE) Karlsruhe Institute of Technology (KIT) Karlsruhe, Germany
2
Abstract— The Demonstration Fusion Power Reactor (DEMO) to follow ITER by 2050 demands high frequency (>230 GHz), high power (in the range from 1 MW to 2 MW) gyrotrons as RF sources for electron cyclotron resonance heating and current drive (ECRH&CD). In the frame of the EUROfusion programme at KIT, the designs of conventional-cavity type and coaxial-cavity type DEMO-compatible gyrotrons are under investigation. In this presentation, the physical design of the interaction circuit of a 236 GHz conventional cavity gyrotron and its RF behavior are presented. The simulation results show a stable single mode RF output power without serious mode competition. Keywords—gyrotron; DEMO; tokamak; plasma heating; cavity design; RF behavior; multi-mode calculations
ECRH systems in the development of the various tokamaks and stellarators because they are the only known sources which can produce the required continuous wave (CW) output power. For the W7-X stellarator, conventional-cavity gyrotrons with an operating frequency of 140 GHz are being installed, while in ITER, 170 GHz gyrotrons will be used. DEMO is the prototype of a fusion power plant which will follow ITER. The detailed goals and design parameters of the DEMO gyrotron according to the 2012 baseline of DEMO (aspect ratio of 4.0) are listed in Table 1 [7,8]. Along with these specifications, it is also preferred to use a quasi-optical mode converter for the axial output and a single disk CVD-diamond RF window [9]. TABLE I.
DESIGN GOALS AND PARAMETERS FOR DEMO GYROTRONS. Goal
I. INTRODUCTION Gyrotron oscillators (gyrotrons) are fast-wave devices which can produce megawatts of RF power at millimeter/submillimeter frequencies. High-frequency, high-power gyrotrons are widely used or planned as RF sources in Electron Cyclotron Resonance Heating and Current Drive (ECRH&CD) systems in plasma experiments related to thermonuclear fusion [1]. The stellarator Wendelstein 7-X (W7-X) in Greifswald, Germany [2] and the international tokamak ITER in Cadarache, France [3] are two main fusion plasma devices under development in Europe. Both devices are relying on ECRH for steady-state operation. Other than plasma heating and control, gyrotrons are also used for many other applications like materials processing, high resolution radars, deep space and specialized satellite communication systems [4-6] etc.
Frequency
In gyrotrons, an annular electron beam, generated by the magnetron injection gun (MIG), is focused towards the interaction cavity with the help of a very high magnetic field produced by superconducting magnets. In the cavity, the electron beam interacts with and transfers a part of its kinetic energy to a transverse electric wave (TE mode). Using quasioptical converters, the electromagnetic field is separated from the electron beam and the spent electron beam is absorbed by a collector.
Emitter radius
Conventional (hollow cavity) gyrotrons are employed in This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
Value
230 – 240 GHz
Output power
~ 1 – 2 MW
Efficiency (with multi-stage depressed collector)
> 60%
Interaction efficiency
> 35%
Frequency step for fast tunability
2 – 3 GHz
Frequency step (slow) for multi-frequency operation
30 – 40 GHz
Peak ohmic wall loading at cavity
≤ 2 kW/cm2
Cathode emitter current density
< 4 A/cm2
Electric field at cathode
7 kW/mm
Spread of electron guiding centers Parameter Magnetic field (cavity)
~ ≤ λ/5 Value ~ 9 – 10 T ~ 50 – 70 mm
The basic principles of mode selection for a highfrequency high-power gyrotron operating at very high-order modes have been explained in [10,11]. In there, it has been shown, that primary criterion for mode selection can be the possible multi-frequency operation of the gyrotron, rather than the selection of specific spectral properties for the operating modes and its main competitors. Bases on that, a higher order mode TE43,15 has been selected for the 236 GHz conventional cavity gyrotron design which allows multi-frequency operation with TE31,11, TE37,13 and TE49,17 modes at the additional frequencies of 170 GHz, 203 GHz and 269 GHz, respectively, employing variation of the magnet field and a
simple single-disk output window [12]. After the selection of the operating mode, the investigations toward an optimized conventional cavity design for the DEMO gyrotron have been started. The finalized cavity design is discussed in section II and its RF behavior is described in section III. II. INTERACTION SECTION DESIGN The proposed cavity geometry for the 236 GHz, TE43,15 mode gyrotron and its normalized field profile are shown in Fig. 1. Main parts of the cavity are an input down-taper section, a straight interaction section and an up-taper section. The gyrotron operates near the cut–off frequency of the desired TE mode. The input and the output tapers of the cavity provide enough reflection to ensure a sufficiently high Q-factor and field profile in the interaction section. Parabolic smoothing of the input and output tapers is carried out to reduce unwanted mode conversion at sharp transitions. All other geometrical parameters are not fixed and can be optimized for best performance of the gyrotron. With consideration of a maximum 2 kW/cm2 cavity wall loading, an extensive parametric analysis has been carried out. Herein, the length of the interaction section determines the final performance of the cavity. To achieve high output power with optimum efficiency, the results of the analysis suggest an interaction length (L2) of 12 mm and lengths of 16 mm for both the input and output taper sections (L1 and L3). In the proposed design, the values of the input taper angle θ1 and output taper angle θ3 are 2.5º and 2º, respectively. Using the TE43,15 mode, electron beam radius and cavity radius are 9.06 mm and 20.88 mm, respectively. The diffraction quality factor (Q) of the cavity is 1443 at the desired operating mode and frequency.
Fig. 1. Conventional cavity design for DEMO gyrotron with normalized field profile.
mode for the DEMO gyrotron is compared with the mode pattern of the TE32,9 mode of the EU 1 MW conventional cavity gyrotron for ITER. Compared to the ITER gyrotron the DEMO gyrotron operates at a significant higher order mode. Therefore a large number of modes with the smaller eigenvalues, i.e. above cut-off exist in the cavity and might be excited during gyrotron operation. The proper start-up scenario and the most appropriate operating point for stable RF output have been investigated. Initially, multiple single mode calculations were carried out to finalize the operating parameters of the cavity. The optimum performance of the cavity is achieved with a magnetic field (B0) of 9.13 T at the cavity center. The corresponding values of the steady-state beam voltage (Vb) and beam current (Ib) are 58 keV and 39 A, respectively, with a ratio between axial and transversal velocity (pitch factor α) of 1.25.
TE32,9
(a)
TE43,15 TE43,15
(b)
Fig. 2. Mode pattern of the (a) TE32,9 mode of the EU conventional cavity ITER gyrotron and (b) TE43,15 mode of the conventional cavity DEMO gyrotron
Fig. 3: Mode spectrum of the selected neighboring for multi-mode start-up simulations from -5% to +10% of the 236 GHz.
III. IV. RF BEHAVIOR OF THE CAVITY The RF behavior of the conventional cavity has been simulated using the code packages “EURIDICE” [13] and “CAVITY” [14]. In Fig. 2, the mode pattern of the TE43,15
Multi-mode, self-consistent, time dependent calculations (full start-up scenario) were carried out in order to verify the effects of competing neighboring modes on the performance of the gyrotron. All neighboring modes within the range
Fig. 4: Result of multi-mode, time dependent calculations with consideration of 99 neighboring modes. The co-rotating mode TE43,15, which is excited at the desired parameters of the gyrotron, is the desired operating mode. (TE43,15 main mode, 99 neighboring modes)
of -5 % to +10 % of the center frequency at 236 GHz and having a coupling coefficient greater than 35 % of the main mode were selected for the calculations. Fig. 3 shows the corresponding coupling spectrum, consisting of the main mode and its most severe competitors. Using this methodology, the possible effects of the vast majority of the neighboring modes which could affect the main mode operation are considered. Considering 99 neighboring modes the result is presented in Fig. 4. In the start-up phase, the beam voltage is raised linearly from 20 keV to 58 keV, while beam current and pitch factor vary adiabatically. A stable output power of 830 kW is achieved with an electronic efficiency of 38 % (with ideal beam properties and without depressed collector operation). The neighboring modes with high relative coupling (see Fig. 3) are excited during the start-up. At steady state condition, the power of all neighboring modes is less than 0.1 % of the main mode power which implies stable, single frequency operation of the gyrotron. The short pulse situation (without space charge neutralization) is considered for these start-up simulations.
Fig. 5: Start-up scenario for the conventional cavity gyrotron assuming 6 % velocity spread. (TE43,15 main mode, 99 neighbouring modes)
process. The output power and the gyrotron operating parameters with the higher cavity wall loading are listed in Table. II. Results support an output power of more than 1 MW with improved cavity cooling technologies. As a rule-ofthumb, with given cavity design, the output power is proportional to the permitted ohmic loading, especially at constant beam voltage. TABLE II. OUTPUT POWER AND OPERATING PARAMETERS OF CONVENTIONAL CAVITY GYROTRON WITH THE HIGHER WALL LOADING. Maximum wall loading (kW/cm2)
Output power (kW)
Beam voltage (keV)
Beam current (A)
2.00
830
58.00
39.00
2.30
965
60.00
42.00
2.48
1050
60.00
47.00
The interaction performance of the gyrotron cavity is also verified by considering a realistic electron beam with a perpendicular velocity spread and a linear guiding center spread. The start-up scenario with the electron beam having a 6 % (rms) perpendicular velocity spread (Gaussian distribution) is shown in Fig. 5. Stable output is achieved with the reduced output power of 778 kW. Due to influence of the velocity spread, a different mode series is excited before the steady-state operation. The effects of the realistic electron beam on the operation of the DEMO gyrotron are discussed in [15] with the multi-frequency behavior of the cavity. Considering the current technological limits, a maximum wall loading of 2 kW/cm2 is fixed during the cavity design
Fig. 6: Output power, efficiency and wall loading of the cavity as a function of velocity ratio (α) with: Vb = 58 keV, Ib = 39 A, B0 = 9.130 T.
[2]
The self-consistent calculations have been carried out to verify further relationships of the gyrotron output power, efficiency and wall loading with the gyrotron’s external parameters. In Figs. 6 and 7, the gyrotron output power, efficiency and wall loading are plotted as functions of velocity ratio and beam current, respectively. This is a very effective method to identify the gyrotron behavior during small deviations from the stable operating point. Output power, efficiency and cavity wall loading increase with increasing velocity ratio. However, it is also very challenging to design a Magnetron Injection Gun (MIG) producing an electron beam with high pitch factor. In the case of increasing beam current, output power and wall loading increase rapidly with the slight variation of gyrotron efficiency.
[3] [4]
[5]
[6]
[7]
[8]
[9]
[10]
[11] Fig. 7: Output power, efficiency and wall loading of the cavity as a function of beam current (Ib) with: Vb = 58 keV, α = 1.25, B0 = 9.130 T.
[12]
CONCLUSIONS
[13]
In this paper, a systematic approach to the design of a conventional (hollow) cavity for a 236 GHz DEMO gyrotron has been presented. Despite considering a large number of neighboring modes in simulations, the RF behavior of the cavity supports stable output in the TE43,15 mode, which validates the proposed cavity design and operating parameters. The design of other components (MIG, quasi-optical output coupler, depressed collector) for the hollow-cavity 236 GHz DEMO gyrotron are progressing at KIT. REFERENCES [1]
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