Figure
1.
CSMC superconducting magnet test system.
| Citation: |
Pengcheng ZHAO, Zhongyu LIU, Rui WANG, Panpan SHU, Lixin GUO, Xiangxin CAO. Effect of desorbed gas on microwave breakdown on vacuum side of dielectric window[J]. Plasma Science and Technology, 2024, 26(4): 045401. DOI: 10.1088/2058-6272/ad0d58
|
The gas desorbed from the dielectric surface has a great influence on the characteristics of microwave breakdown on the vacuum side of the dielectric window. In this paper, the dielectric surface breakdown is described by using the electromagnetic particle-in-cell-Monte Carlo collision (PIC-MCC) model. The process of desorption of gas and its influence on the breakdown characteristics are studied. The simulation results show that, due to the accumulation of desorbed gas, the pressure near the dielectric surface increases in time, and the breakdown mechanism transitions from secondary electron multipactor to collision ionization. More and more electrons generated by collision ionization drift to the dielectric surface, so that the amplitude of self-organized normal electric field increases in time and sometimes points to the dielectric surface. Nevertheless, the number of secondary electrons emitted in each microwave cycle is approximately equal to the number of primary electrons. In the early and middle stages of breakdown, the attenuation of the microwave electric field near the dielectric surface is very small. However, the collision ionization causes a sharp increase in the number density of electrons, and the microwave electric field decays rapidly in the later stage of breakdown. Compared with the electromagnetic PIC-MCC simulation results, the mean energy and number of electrons obtained by the electrostatic PIC-MCC model are overestimated in the later stage of breakdown because it does not take into account the attenuation of microwave electric field. The pressure of the desorbed gas predicted by the electromagnetic PIC-MCC model is close to the measured value, when the number of gas atoms desorbed by an incident electron is taken as 0.4.
CSMC superconducting magnet is a main component in the CRAFT project, used to confine and stabilize the plasma for fusion. During the operation of a tokamak device, plasma disruptions may occur, at which point the CSMC magnet contains a huge amount of energy [1, 2]. To maintain the safety of the CSMC superconducting magnet and ensure the steady operation of the fusion device, it is necessary to design a grounding fault protection system for the superconducting magnet.
A grounding fault refers to abnormal grounding resistance of electrical equipment or circuits, or leakage faults in electrical equipment or circuits, which may lead to damage to electrical equipment, short circuits in the power system, and even serious accidents such as fires [3–5]. Many scholars have conducted research on the grounding protection design of superconducting magnets in fusion devices. EAST, as the first domestically developed tokamak experimental device, detects grounding faults by collecting neutral point short-circuit current through current sensors in the poloidal field coils, achieving grounding protection [6, 7]; the NSTX coil grounding protection system of the US TFTR fusion device measures differential currents between power supplies and circuits to detect grounding faults [8]; the international thermonuclear fusion device ITER uses a combination of 10 kΩ resistors and parallel switches to connect 18 toroidal field coils to ground, issuing instructions to protective switches by measuring and comparing grounding currents [9, 10]. Additionally, an isolation circuit needs to be built to achieve isolation of current signals [11].
Compared with the current detection scheme, the peripheral circuit of the voltage detection scheme is simpler, and in some cases, it has higher measurement and detection accuracy [12]. Based on these advantages, the CRAFT CSMC magnet ground protection scheme based on neutral point voltage acquisition is proposed. Firstly, the CRAFT superconducting magnet testing system is introduced, and the theoretical calculation of grounding resistance protection parameters is performed. Secondly, the types of magnet grounding faults are analyzed, and loss calculations are performed during faults. Finally, the feasibility of the superconducting magnet grounding protection scheme is verified through MATLAB simulation and experimental testing platform.
The CSMC superconducting magnet testing system mainly consists of magnet power supply, bypass switch BS, fast discharge unit FDU, CSMC magnet, and grounding protection unit, as shown in figure 1 [13]. When the circuit is operating normally, the PMS switch is open, the FDU switch is closed, the ideal current flowing through detection point DP is zero, but there are a lot of ground networks in the superconducting magnet system, so when the loop is running normally, there is a small current flowing through DP, and when the ground fault current is small, the current sensor may cause protection misoperation due to insufficient accuracy. Therefore, a method of ground fault detection based on central point voltage is proposed, when a grounding fault occurs in the circuit, the PMS switch is closed and the FDU switch is opened, and the fault energy is dissipated through the FDU resistor. In addition, due to the appearance of the grounding fault circuit, the neutral detection point DP generates a fault voltage, which can be sampled and identified to detect magnet ground faults. The parameters of the CSMC magnet testing platform are shown in table 1 [14].
| Parameters | Values |
| Rated current (kA) | 48 |
| Inductance (H) | 0.359 |
| Discharge resistor (mΩ) | 51 |
| FDU Rated voltage (kV) | 2.5 |
| Converter no-load voltage (V) | 1420 |
DownLoad:
CSV
The grounding protection system of the CSMC superconducting magnet consists of two grounding resistors Rtn with the same resistance value and a neutral point grounding resistor Rng, as shown in figure 1.
The purpose of resistor Rtn connected between the coil terminal and the neutral bus is to fix the coil terminal potential to ground and reduce the transient voltage value of the coil during the opening period of the DC circuit breaker in fast discharge. According to previous research on DC circuit breakers, the value range of grounding resistor Rtn is 50–500 Ω. Due to the large dissipated energy during fast discharge and the dissipated power during the rise and fall of coil current for small resistances, the value of Rtn is chosen as 500 Ω in the study.
In the CSMC superconducting magnet circuit, the conductivity of the bus to ground is approximately 5 × 10–7 S, and the total length of the bus for natural cooling of the coil is about 200 m [15]. Without considering the influence of inlet and outlet pipeline connections, the total conductivity of the bus to ground in the coil should be greater than 10–4 S, so the total resistance of the bus to ground should be less than 104 Ω. The role of resistor Rng is to fix the neutral point potential to ground, so the resistance value of Rng should be less than ten times the total grounding resistance of the system, and Rng should be less than 1000 Ω. In this study, the value of Rng is 1000 Ω.
Considering the maximum voltage of the rectification, when the magnet circuit is operating normally, the rated power of the Rtn resistor can be calculated by equation (1). During periods of rapid discharge, the voltage discharge waveform is approximately triangular, so the rated energy consumption of Rtn during fast discharge can be calculated according to equation (2). Since the current of the magnet loop does not pass through Rng during normal operation, its parameters are difficult to determine. Therefore, it is assumed that the magnet loop has a single-end grounding fault, and the Rtn resistance and Rng resistance form the grounding circuit. According to the principle of voltage division, the rated power of Rng and the energy loss during discharge can be calculated by equations (3) and (4).
| PRtn=Umax | (1) |
| W_{R_{\mathrm{tn}}}\ =\frac{T\times U_{\text{FDU}}^{\text{2}}}{8\times R_{\text{tn}}}, | (2) |
| P_{R\mathrm{_{ng}}_{ }}=\frac{\left(U_{\text{FDU}}\times R_{\text{ng}}\right)^2}{\left(2R_{\text{ng}}+R_{\text{tn}}\right)^2\times R_{\text{ng}}}, | (3) |
| W_{R_{\text{ng}}}=\frac{\left(U_{\text{FDU}}\times R_{\text{ng}}\right)^2\times T}{\left(2R_{\text{ng}}+R_{\text{tn}}\right)^2\times R_{\text{ng}}\times2}, | (4) |
where Rtn is the resistance from the coil end to the neutral point, Rng is the neutral grounding resistance, Umax is the rectifier no-load voltage, T is the equivalent discharge time constant, UFDU is the overload protection rated voltage, PRtn is the rated power of Rtn, WRtn is the maximum energy loss during the rapid discharge of Rtn, PRng is the rated power of Rng and WRng is the maximum energy loss during the rapid discharge of Rng.
According to the above four equations, the energy loss and rated power of the grounding protection resistors Rtn and Rng can be calculated as shown in table 2.
| Parameters | Resistance values | Energy loss | Rated power |
| Rtn | 500 Ω | 4.38 kJ | 1.25 kW |
| Rng | 1000 Ω | 3.5 kJ | 1 kW |
DownLoad:
CSV
When there is insulation issue between the superconducting magnet and the coil housing or connecting pipes, a single grounding fault may occur at any position of the magnet. According to Kirchhoff’s law, at different grounding points, the neutral fault detection point voltage shows different amplitudes. In this study, considering the worst-case scenario where the grounding fault occurs at both ends of the superconducting magnet, the grounding fault current and voltage are at their maxima. The single-end grounding fault scenarios are shown in figure 2.
The minimum breakdown voltage of helium in the Paschen curve in fusion devices is 160 V [16, 17]. According to the electrical design handbook (EDH) requirements, to prevent Paschen breakdown in the cryostat and maintain a certain safety margin, all surface voltages of the cryostat should be less than 100 V. Therefore, in the case of single and double grounding faults, the fault-to-ground voltage should be less than 50 V. Thus, in the design process of the grounding resistor Rcg, the fault grounding voltage should be limited to less than 50 V.
When the magnet is single-end grounding fault, the magnet enters a state of fast discharge, according to the Kirchhoff’s current law, the peak current Ig and peak voltage Vg of a single-end grounding fault can be calculated as shown in equations (5) and (6):
| {I_{\text{g}}}{\text{ = }}\frac{{{U_{{\text{FDU}}}}}}{{{R_{{\text{tn}}}} + 2{R_{{\text{cg}}}} + 2{R_{{\text{ng}}}}}} , | (5) |
| {V_{\text{g}}} = \frac{{{U_{{\text{FDU}}}} \times {R_{{\text{cg}}}}}}{{{R_{{\text{tn}}}} + 2{R_{{\text{cg}}}} + 2{R_{{\text{ng}}}}}} . | (6) |
Peak current Ig and peak voltage Vg are related to the equivalent grounding resistance Rcg, as shown in figure 3. From figure 3, it can be seen that when the resistance Rcg is less than 52 Ω, the fault point voltage is less than 50 V. The Rcg is the equivalent resistance of the metal connection between the coil housing and the cryostat. Depending on the length of the connected metal, the resistance value generally ranges from a few ohms to tens of milliohms. When a single-end grounding fault occurs in the magnet, the resistance value of Rcg meets the design requirements of the EDH, ensuring that the grounding fault voltage is less than 50 V.
According to Kirchhoff’s current law, when a single-end grounding fault occurs, the voltage Vn at point ③ should satisfy equation (7)
| {V_{\text{n}}} = - \frac{{{V_{\text{g}}} \times {R_{{\text{ng}}}}}}{{{R_{{\text{cg}}}}}}. | (7) |
The voltage Vn under different single grounding conditions can be calculated theoretically. When a grounding fault occurs, the detection point voltage is approximately −1 kV, and in another scenario, it is approximately 1 kV.
Considering the worst-case scenario of a single grounding fault with a fault voltage of 50 V and a fault current of approximately 1 A, as shown in figure 3, the energy dissipated during the entire discharge process can be calculated as 0.17 kJ using equations (8) and (9). This amount of heat can only melt 0.13 g of steel, resulting in minimal damage to the equipment. Therefore, the CSMC superconducting magnet can withstand the harm caused by a single grounding fault.
| W_{\mathrm{g}}\text{ = }\int_{\text{0}}^{5\tau}\left(u_{\mathrm{g}}\times i_{\mathrm{g}}\right)\text{d}t, | (8) |
| i_{\text{g}}=I_{\text{g}}\times\text{e}^{-\frac{t}{\tau}},\ \ u_{\text{g}}=U_{\text{g}}\times\text{e}^{-\frac{t}{\tau}}, | (9) |
where Wg is the energy loss caused by rapid discharge, τ is the discharge time constant, ug is the grounding fault voltage waveform, ig is the grounding fault current waveform, Ig is the fault peak current and Vg is the fault peak voltage.
The CSMC magnet actually consists of five superconducting coils, and the metal air-cooled pipes connecting the housing of each magnet coil to the ground cryostat act as the grounding resistance Rcg. If a single ground fault in one part of the CSMC magnet coils is not addressed promptly and another single-end grounding fault occurs in another part of the magnet, the single-end grounding fault will develop into double-end grounding fault. When a portion of the magnet coil is short-circuited, the effective inductance value decreases, and the total charge-discharge duration of the circuit shortens. The more parts of the coil are short-circuited, the larger the peak fault voltage and fault current. This study considers the worst-case scenario of a double-end grounding fault, where all CSMC coils are short circuited, as shown in figure 4.
When the magnet is grounded, the resistances Rcg1 and Rcg2 are connected in series at both ends of the CSMC. The ground fault current Icg and voltage Vcg when both ends of the magnet are grounded are given by equations (10) and (11).
| {I_{\text{g}}} = \frac{{{U_{{\text{FDU}}}}}}{{{R_{{\text{cg1}}}} + {R_{{\text{cg2}}}} + {R_{{\text{FDU}}}}}}, | (10) |
| {V_{\text{g}}} = \frac{{({R_{{\text{cg1}}}} + {R_{{\text{cg2}}}}) \times {U_{{\text{FDU}}}}}}{{{R_{{\text{cg1}}}} + {R_{{\text{cg2}}}} + {R_{{\text{FDU}}}}}}. | (11) |
The relationship between the equivalent grounding resistance and the grounding fault current and voltage can be shown in figure 5. To prevent electrical breakdown, the grounding fault voltage should be less than 50 V. From the red curve Vg in the figure, it can be seen that the resistance value of Rcg1 + Rcg2 should be less than 1 mΩ.
To assess the maximum harm of a double-end grounding fault, assuming a grounding fault voltage of 50 V and a grounding fault current of 48 kA, the energy released during the entire discharge process when a double-end grounding fault occurs is calculated to be approximately 6.2 MJ using equations (8) and (9). This would result in significant damage to the equipment. Therefore, to prevent the relatively minor harm of a single-end grounding fault from escalating into a significantly damaging double-end grounding fault, timely diagnosis and maintenance should be carried out for single-end ground faults in the CSMC superconducting magnet coils.
The CRAFT magnet power supply consists of four rectifier units, each capable of outputting 30 kA of current [18]. Operating two rectifier units in parallel can meet the testing requirements of the CSMC superconducting magnet.
To meet the design requirements of EDH, the resistance values of Rcg are set to 0.02 Ω and 2 Ω for simulating single-end grounding faults. Considering the worst-case scenario where the peak current reaches 48 kA, an accidental grounding short circuit occurs at point ① or ② in the simulation. The waveform of single ground fault current and voltage is shown in figure 6, where Vc represents the high voltage generated at the coil ends during a ground fault, Vn is the neutral point-to-ground voltage, Vg is the ground fault voltage, and Ig represents the fault ground short-circuit current. The waveforms at each point follow the RL exponential discharge law [19, 20]. The simulation results show that when Rcg = 0.02 Ω or Rcg = 2 Ω, Vc is approximately −2.5 kV. When point ① experiences a ground fault, the detected current Vn at the neutral point is around 1 kV, as shown in figure 6(a). Due to the small resistance value of Rcg, its influence can be neglected, and the single-end ground fault cur-rent is mainly determined by Rng and Rtn, approximately −1 A, as shown in figure 6(b). When point ② experiences a ground fault, the waveforms at various points are similar to point ①, but Vn becomes around −1 kV, and the grounding fault current becomes 1 A. The simulation results are in good agreement with theoretical calculations. The neutral point voltage during a single-end grounding fault is 1 kV, which is 40% of the voltage at the two ends of the magnet, and the grounding fault current is small, causing negligible damage to the equipment. By sampling and comparing the neutral point voltage, single end ground fault detection can be achieved.
To meet the design requirements of EDH, Rcg1 = Rcg2 = 0.5 mΩ and Rcg1 = 0.8 mΩ, Rcg2 = 0.2 mΩ are set for the simulation analysis of double-end grounding faults. Since it is rare for both ends of the superconducting magnet to be grounded simultaneously, a grounding fault is simulated at point ① when the current reaches 48 kA, followed by a ground fault at point ② 0.5 s later. The specific waveforms of Vg and Vn are shown in figure 7. When both ends are grounded, the equivalent grounding resistances Rcg1 and Rcg2 of the coil casing are in parallel with the rapid discharge resistances RFDU at both ends of the CSMC magnet. Since RFDU \gg Rcg1 + Rcg2, the current mainly flows through Rcg1 and Rcg2. When both ends are grounded simultaneously, the potential at Vn is zero. The coil voltage Vc at both ends drops to 50 V, which is the potential difference between fault points ① and ②, as shown in figure 7(b). As per equation (7), when the sum of the resistances Rcg1 and Rcg2 remains constant, the ground currents are equal, with the peak value of the grounding short-circuit current being approximately 43.5 kA, slightly lower than the normal operating current, as shown in figure 8.
The simulation results indicate that due to the changes in the discharge circuit, the equivalent discharge time of the CSMC magnet coil is 51 times that of single-end grounding discharge time. With a 0.5 s interval between faults at both ends of the magnet, the detection voltage at the neutral point Vn appears as a pulsed waveform every 0.5 s. By identifying the pulsed waveform at Vn, detection of double-end grounding faults can be achieved.
Grounding short circuits in superconducting magnets are accidental faults with significant damage. Therefore, a small-scale test platform was constructed to simulate different types of grounding faults in superconducting magnets and validate the feasibility of the grounding protection system. The test platform mainly consists of switch units, oscilloscope, power supply, load inductor, resistors, and ground protection device, as shown in figure 9. The parameters of each unit are listed in table 3.
| Devices | Parameters |
| JZ-AC220SDC50V8kW | 50 V / 8 kW |
| ZX9-4 | 4 Ω / 39 A |
| AGW R2050 | 5.2 mH / 30 A |
| FF200R12KS4 | 200 A |
| V23086-C1001-A403 | 12 V / 30 A / 3 ms |
| VF4-15F13 | 12 V/ 40 A / 7 ms |
| INFINIVISIONDS0X4034A | 350 MHz / 5 GS/s |
DownLoad:
CSV
In the experiment, at time 0 s, the bypass switch was closed, the rapid discharge switch was turned off, and 0.003 s later, a single-end grounding fault occurred in the load. The deep blue curves in figures 10 and 11 represent the switch trigger signal. When the coil is grounded at one end, the main circuit current Ic starts discharging from 30 A, the voltage Vc at both ends of the coil becomes 24 V, the ground current Ig approaches 0 A, the potential Vn at the neutral point is 5.8 V, the fault state sampling voltage Vs is 0.058 V, and the fault state light response can be achieved by adjusting the detection device’s fault threshold. Additionally, an output voltage Vf of 0.038 V is sent to the main control end to control the protection switch and provide a protective loop.
After setting a single-end grounding fault on one end of the load coil, another grounding fault occurred on the other end after 0.004 s, turning the single grounding fault into a double-end grounding fault. The deep blue curve in figures 12 and 13 represent the switch trigger signal. The single-end grounding fault occurs between 0.003 s and 0.007 s, with waveforms at various points consistent with figures 10 and 11. At 0.007 s, a double-end grounding fault occurs, short-circuiting the ground protection resistors Rtn and Rng, causing the current Ic and voltage Vc at both ends of the magnet to drop to 0, and the magnet’s grounding short-circuit current Ig increases from 0 A to 14 A, indicating a significant current. The neutral point fault detection voltage Vn, fault state sampling voltage Vs, and output control end voltage Vf have amplitudes consistent with the single-end grounding fault, displaying a pulse-like waveform characteristic. Transmitting these waveform characteristics to the central controller enables magnet circuit protection.
In the experiment, waveforms of inductive loads experiencing single-end and double-end grounding faults were measured, and the experimental waveform characteristics matched the simulated waveforms. In practical operation, the maximum fault voltage at the neutral point of the CSMC superconducting magnet is 1000 V. The sampling ratio set in the ground protection device is 1:100. By comparing the fault threshold of the grounding protection device with the fault sampling voltage Vs, the fault indication light can be controlled to indicate the magnet’s operating status. Upon receiving the fault voltage Vf at the main control end, instructions can be sent to the switch unit to implement grounding fault protection.
This study designed a central point voltage acquisition grounding protection scheme for the CRAFT CSMC superconducting magnet. Theoretical analyses of single-end grounding fault protection and double-end grounding fault protection were conducted to prevent electrical breakdown within the device. The grounding wind cooling pipe Rcg between the magnet coil casing and the cryostat should be less than 1 mΩ. The built magnet ground protection model’s simulation results were consistent with the theoretical calculations. The neutral point voltage Vn during a ground fault is 1000 V, 0.4 times the voltage of the superconducting magnet coil. The fault current for a single-end grounding fault is 1 A, while for a double-end grounding fault, it is approximately 43.5 kA. Timely detection and treatment of single-end faults are necessary to prevent them from developing into potentially hazardous double-end faults. Functional verification of the ground protection system through a testing platform showed that comparing the neutral point fault sampling voltage with a 1:100 sampling ratio and the fault protection threshold can detect different types of grounding faults. This grounding protection scheme can be applied in various scenarios by setting different sampling ratios and protection voltage thresholds, providing valuable reference for future designs of grounding protection for superconducting magnet systems in fusion devices.
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Supported by: Beijing Renhe Information Technology Co., Ltd. 
| Parameters | Values |
| Rated current (kA) | 48 |
| Inductance (H) | 0.359 |
| Discharge resistor (mΩ) | 51 |
| FDU Rated voltage (kV) | 2.5 |
| Converter no-load voltage (V) | 1420 |
DownLoad:
CSV
| Parameters | Resistance values | Energy loss | Rated power |
| Rtn | 500 Ω | 4.38 kJ | 1.25 kW |
| Rng | 1000 Ω | 3.5 kJ | 1 kW |
DownLoad:
CSV
| Devices | Parameters |
| JZ-AC220SDC50V8kW | 50 V / 8 kW |
| ZX9-4 | 4 Ω / 39 A |
| AGW R2050 | 5.2 mH / 30 A |
| FF200R12KS4 | 200 A |
| V23086-C1001-A403 | 12 V / 30 A / 3 ms |
| VF4-15F13 | 12 V/ 40 A / 7 ms |
| INFINIVISIONDS0X4034A | 350 MHz / 5 GS/s |
DownLoad:
CSV
