Figure
1.
The general view and photo of the gyrotron.
| Citation: |
Weikang TANG, Qibin LUAN, Hongen SUN, Lai WEI, Shuangshuang LU, Shuai JIANG, Jian XU, Zhengxiong WANG. Screening effect of plasma flow on the resonant magnetic perturbation penetration in tokamaks based on two-fluid model[J]. Plasma Science and Technology, 2023, 25(4): 045103. DOI: 10.1088/2058-6272/aca372
|
Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC (MHD@Dalian Code). Based on a set of two-fluid four-field equations, the bootstrap current, parallel, and perpendicular transport effects are included appropriately. Taking into account the bootstrap current, a mode penetration-like phenomenon is found, which is essentially different from the classical tearing mode model. To reveal the influence of the plasma flow on the mode penetration process, E × B drift flow and diamagnetic drift flow are separately applied to compare their effects. Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode. Furthermore, an oscillation phenomenon of island width is discovered. By analyzing it in depth, it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island. This physical mechanism is verified again by key parameter scanning.
For the generation of high power at millimeter and sub-millimeter waves, conventional slow-wave devices, such as magnetrons, travelling-wave tubes and klystrons, have an inherent limitation: the decrease in the dimensions of the interaction structure with increasing frequency. Gyrotrons can break through the limitation because they are fast-wave devices based on the electron cyclotron maser (ECM) mechanism [1, 2]. The ECM mechanism was independently proposed by R Q Twiss [3], J Schneider [4] and A V Gaponov [5] in late 1960s, and it was first confirmed experimentally by J L Hirshfield and J M Wachtel in 1964 [1]. Gyrotrons have the unparalleled ability to produce continuous waves (CW) at millimeter to sub-millimeter wavelengths at hundreds of kilowatts or even higher power. Nowadays, gyrotrons have already become irreplaceable sources for high-power applications at high frequencies. They have been presented in detail in several review papers [6–12] and the references therein describe electron cyclotron resonance heating (ECRH), industrial material processing, advanced spectroscopic techniques, etc.
Most notably, gyrotrons are currently the only candidates for ECRH experiments. The ECRH method offered easy access of millimeter-wave power to the plasma center. Since the power and pulse duration have reached a sufficient level over wide frequency ranges (14‒300 GHz, 0.1‒1.0 MW) [13, 14], gyrotrons have been widely used in magnetically confined fusion research all over the world.
Among these large-scale scientific facilities, some require gyrotrons at high frequencies [9], such as the International Thermonuclear Experimental Reactor (ITER) [15], the stellarator W7-X [16], DEMO [17], DIII-D [18], EAST [19, 20] and HL-2A [9, 21].
Currently, ECRH experiments in some plasma devices require gyrotrons with relatively low frequencies (14–35 GHz) [13, 14]. For example, the Q-shu University Experiments with Steady State Spherical Tokamak (QUEST), requires a 28 GHz, 0.4 MW CW gyrotron. A Tsukuba's 28 GHz, 1 MW gyrotron has been used with the QUEST system to demonstrate plasma heating and current drive effects. The gyrotron achieved a short pulse output power of 1.38 MW and stable operation at 0.6 MW for 2 s. Furthermore, a new 28 and 35 GHz dual-frequency gyrotron is being developed.
In China, a medium-scale spherical tokamak XL-50 has been built at the ENN Energy Research Institute. This spherical tokamak also requires 28 GHz gyrotrons for ECRH experiments. In 2019, a 28 GHz, 50 kW, long-pulse (30 s) gyrotron [22], developed by the Institute of Applied Electronics, China Academy of Engineering Physics (IAE-CAEP), was delivered and successfully used in the ECRH experiments, and it is planned to use six high-power long-pulse (400 kW, 5 s) 28 GHz gyrotrons to increase the total injected microwave power to more than 2 MW. In 2021, the high-power 28 GHz gyrotron successfully delivered an output power of 400 kW with a pulse duration of 5 s [23]. This was the first time that a long-pulse gyrotron with over 100 kW had been developed in China and it is currently being used in the ECRH experiments. In this paper, the design considerations and experimental results of the high-power 28 GHz gyrotron are presented.
The schematic diagram and a photo of the 28 GHz gyrotron are shown in figure 1. A diode-type magnetron injection gun (MIG) is used to generate the gyrating electron beam. A simple cylindrical cavity and an internal quasi-optical mode converter are carefully optimized to generate and propagate the millimeter-wave power, and a single-stage depressed collector with a sweeping coil is designed to enhance the overall efficiency. No gun coils are used. It should be pointed out that the diode MIG looks like a triode one because the same ready-made ceramic parts of a triode MIG are used in this 28 GHz gyrotron, and we added an electrode at ground potential between the cathode and anode to ensure the insulation, as shown in the figure.
Figure 2 shows the MIG geometry which was carefully optimized. The emitter has a diameter of 96 mm and slant length of 2.6 mm. The tilt angle of the cathode surface is 40 degrees. The magnetic compression ratio is about 10. The emitter current density is 2 A cm-2 with a current of 16 A. For a beam voltage of 70 kV, the maximum electric field on the cathode surface is less than 8 kV mm-1, and less than 5 kV mm-1 on the emitter surface.
According to PIC (particle-in-cell) simulation results, the velocity ratio is about 1.2 when the accelerating voltage is 70 kV, as shown in figure 3, and the perpendicular and axial velocity spread is 1.7% and 2.4%, respectively. The perpendicular velocity spread decreases while the axial velocity spread increases as the accelerating voltage increases. As shown in figure 4, the velocity ratio remains nearly constant as the beam current increases. Both the perpendicular velocity spread and axial velocity spread increase as the beam current increases. But they are still less than 4% even when the current is 34 A. That is partially because the emitter current density is relatively low for a thermionic cathode. However, a higher emitter current density was not expected for the 28 GHz gyrotron because it is difficult to make a narrower emitter ring with a diameter of 96 mm.
A simple cylindrical cavity was designed for the gyrotron and the chosen operating mode is TE8, 3. The cavity size and normalized field profile are shown in figure 5. The radius and length of the straight section are 30.3 mm and 64 mm, respectively. The diffraction and ohmic quality factor are, respectively, 610 and 3.1 × 103, according to the cold cavity theory. The ohmic loss is about 1.9% on the cavity wall. Obviously, the power density of wall losses is rather low and there is no problem cooling the oxygen-free copper cavity.
For a 28 GHz gyrotron operating in TE8, 3 mode, mode competition is not yet a severe problem. A code based on the single-mode, self-consistent theory [24] was used to calculate the beam–wave interaction in the cavity. Figure 6 shows the output power of the TE8, 3 mode as a function of magnetic field for various beam currents and velocity ratios. A power of about 440 kW can be extracted from a 70 kV, 16 A electron beam with a velocity ratio of 1.3. The power can be more than 500 kW when the velocity ratio is 1.4.
Furthermore, a time-domain multimode code developed by our lab [25] was used to analyze mode competitions in the cavity. As shown in figure 7, although the competitor TE9, 3 appears during the rising stage of the accelerating voltage, single-mode operation in the cavity can be realized, and the power of the TE8, 3 mode is almost the same as the single-mode calculation.
An internal quasi-optical mode converter was designed for the gyrotron, in order to separate the microwave power from the spent electron beam and convert the TE8, 3 mode into a Gaussian beam, following the method developed in [26]. The converter is composed of four parts: a pre-bunch dimpled-wall launcher, a quasi-parabolic mirror and two phase-correcting mirrors, as shown in figure 8. The converter was optimized by using a code based on the scalar diffraction theory and the K-S algorithm [27]. The conversion efficiency of the converter is 96% and the Gaussian purity is 98% at the window plane [28], according to the simulation results.
A single-disk, edge-cooled window was designed for the gyrotron. The material of the window disk is boron nitride (BN). The disk has a diameter of 100 mm and thickness of 2.4 mm, respectively. The relative dielectric constant of the BN ceramic is 4.9, and the loss tangent is 2 × 10-4. The window disk temperature will rise by 220 °C for CW operation with an output power of 400 kW (see figure 13). For BN ceramic, this temperature rise will not cause damage. Therefore, it is possible to realize CW operation of a 28 GHz, 400 kW gyrotron with a BN window.
A single-stage depressed collector was designed for enhancing the overall efficiency. To decrease heat power density on the inner surface of the collector, an additional sweeping coil was used. The coil is driven by a triangle wave, with a peak current of 10 A, and a repetition frequency 5 Hz. The radius of the collector is 135 mm. When the dissipated power is 500 kW, the maximum power density on the collector surface is less than 0.25 kW cm-2, as shown in figure 9.
Taking the ohmic loss and diffraction loss into consideration, the 28 GHz gyrotron can deliver about 400 kW power with an electron beam of 70 kV, 16 A. When the retarding voltage of the depressed collector is 20 kV, the overall efficiency is about 50%. The design parameters of the gyrotron are shown in table 1.
| Parameters | Values |
| Frequency | 28 GHz |
| Cavity mode | TE8, 3 |
| Output mode | Gaussian-like |
| MIG type | Diode |
| Accelerating voltage | 70 kV |
| Beam current | 16 A |
| Output power | 400 kW |
| Pulse width | 5 s |
| Efficiency | 50% (with depressed collector) |
| Window | BN, single disk |
| Collector | Single-stage depressed collector with a sweeping coil |
| Height | 2.4 m |
| Weight | 400 kg (with sweeping coil) |
DownLoad:
CSV
Figure 1 shows the photo of the 28 GHz gyrotron. The height is 2.4 m, and its weight with a sweeping coil is about 400 kg. The gyrotron body, including the mirrors of the quasi-optical mode converter, was cooled by water. The magnetic field required for the gyrotron is generated by a liquid helium-free superconducting magnet with a hot bore diameter of 300 mm. The uniform area has a length of 70 mm and a diameter of 40 mm (uniformity ±0.3%). The superconductor material is niobium–titanium alloy. When the operating current is 48 A, the maximum magnetic field in the uniform area is 1.2 T.
During the short-pulse test, the cathode voltage is -50 kV and the body voltage is 21 kV. The output frequency of the gyrotron was measured by using a heterodyne receiver system. Figure 10 shows the measurement results with a beam current of 16 A. The gyrotron operational frequency is 28.1 GHz with the mode TE8, 3. When the magnetic field was lower than 1.085 T, the TE5, 4 mode at 27.0 GHz could be observed. When the magnetic field was 1.085 T, the gyrotron operated at a tipping point. More specifically, both the operating mode TE8, 3 and its competitor TE5, 4 could be observed in one single pulse, and the competitor often dominated. The gyrotron was prone to breakdown problems when the magnetic field was less than 1.08 T, so no more data were collected. Single-mode operation of the gyrotron was realized when the magnetic field ranged from 1.088 to 1.15 T. However, the output signals with magnetic fields higher than 1.13 T were rather weak, and when the magnetic field was higher than 1.15 T, the neighboring TE6, 4 mode at 29.4 GHz could be observed. Figure 11 shows patterns on thermal papers heated by the output Gaussian-like beam.
A calorimeter with Teflon tubes inside was used to measure the output power. When the cathode voltage was -50 kV and the body voltage 21 kV, the output power of the gyrotron was 200 kW with a current of 9 A, 300 kW with a current of 12 A, and 400 kW with a current of 16 A, respectively [17]. For the 400 kW output power, the electronic efficiency was about 35% ignoring power loss in the tube. The output efficiency was improved to 50% with a retarding voltage of 21 kV (the body voltage). The body current was about 15 mA, when the cooling liquid for the gyrotron is deionized water. However, higher efficiency was limited because there were some high voltage breakdown problems at the ceramic insulator (see figure 1). The measured output power of the gyrotron as a function of magnetic field is shown in figure 6. The maximum pulse duration is 5 s due to the limitation of power supply in our lab. It is worth noting that there are no arcing problems inside the water load during the long-pulse test. Figure 12 shows oscilloscope traces of the 400 kW, 5 s pulse operation.
During the test, an infrared camera was used to monitor the temperature of the window disk surface. Figure 13 shows the maximum temperature rise with various pulse widths for output powers of 200 kW and 400 kW. For the 400 kW, 5 s pulse operation, the maximum temperature variation observed on the disk surface was 84 °C. Based on the measurement and calculation results, CW operation of a 28 GHz, 400 kW gyrotron with a BN window can be expected.
The temperature of the insulating ceramic (shown in figure 1) was also observed by the infrared camera. For the 400 kW, 5 s pulse operation, maximum temperature rise was about 40 °C. The insulating ceramic part will not be damaged even without cooling.
The 28 GHz, 400 kW gyrotron has been delivered to the ENN Energy Research Institute and installed on the spherical tokamak XL-50, as shown in figure 14. The gyrotron system has been successfully used in the ECRH experiments.
A high-power 28 GHz gyrotron was successfully developed by IAE-CAEP in China. A 400 kW output power with a duration of 5 s was delivered by this gyrotron. Up to now, four tubes have been manufactured and delivered to the ENN Energy Research Institute and successfully used in the ECRH experiments. All four tubes have realized 400 kW, 5 s operation with almost the same efficiency of about 50%. Limited by the test conditions, higher power and longer pulse tests have not been carried out yet. However, it is expected that higher power and longer pulse operation can be realized.
We acknowledge the Super Computer Center of Dalian University of Technology for providing computer resources. This work is supported by the National Key R & D Program of China (No. 2022YFE03040001), National Natural Science Foundation of China (Nos. 11925501 and 12075048), Chinese Academy of Sciences, Key Laboratory of Geospace Environment, University of Science & Technology of China (No. GE2019-01) and Fundamental Research Funds for the Central Universities (No. DUT21GJ204).
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Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Parameters | Values |
| Frequency | 28 GHz |
| Cavity mode | TE8, 3 |
| Output mode | Gaussian-like |
| MIG type | Diode |
| Accelerating voltage | 70 kV |
| Beam current | 16 A |
| Output power | 400 kW |
| Pulse width | 5 s |
| Efficiency | 50% (with depressed collector) |
| Window | BN, single disk |
| Collector | Single-stage depressed collector with a sweeping coil |
| Height | 2.4 m |
| Weight | 400 kg (with sweeping coil) |
DownLoad:
CSV
