Design and operation of a load-tolerant ICRH system in Experimental Advanced Superconducting Tokamak

Ion Cyclotron Resonance Heating (ICRH) has been a dependable tool for sturdy plasma heating with high RF power of several megawatts. However, a sudden increase in the reflected power during ICRH heating experiments is a problem that should be solved for future fusion experimental devices. To solve this issue, a load tolerant matching network has been designed for the ICRH system in EAST. The matching network includes a 3-stub tuner impedance matching system with conjugate-T structure, 30 Ω to 50 Ω transmission line and center grounded antenna strap. By maintaining a low reflection ratio in the network for a wide range of resistance, this matching network can allow sturdy high-power operations without fast impedance matching in EAST. In our matching network, the two arms of a conjugate-T are designed to have a λ/2 length difference which could mitigate current imbalance and antenna poloidal phasing outside of the control problem. The T-point corresponds to the maximum point of the standing wave voltage, which could greatly improve the input impedance of the antenna.


Introduction
Ion Cyclotron Resonance Heating (ICRH) is a significant heating method in tokamak devices, and it is one of the most important heating systems on ITER to heat ions [1][2][3].However, ICRF waves need to tunnel through the evanescent layer before reaching the plasma core, where the waves can transmit energy to ions by resonance heating [4,5].According to the wave dispersion relationship, we know that the evanescent layer normally exists because the plasma density is relatively low compared to the ICRH wave cutoff density in front of the ICRH antenna [6,7].Even if the antenna has good coupling, the coupling impedance is still relatively low compared to the characteristic impedance of the transmission line.This impedance difference will result in a large reflection and a high standing voltage in the transmission line, which will reduce the transmitter's efficiency and the stability of the ICRH system [8].To avoid this undesirable condition, an impedance matching network needs to be designed and installed in the ICRH system to separate the transmitter and antenna [2,[9][10][11][12][13][14].Another complication of impedance matching arises from the rapid change of antenna load during discharges.The confine mode transition between L and H modes and edge localized mode activity are the sources of sudden increase and decrease in antenna load, related to the rapid evolution of plasma density in edge regions [15][16][17].Many ideas to improve the load-tolerance in the ICRH system have been proposed, including employing a 3 dB 90 • hybrid junction [18][19][20], complex conjugate antenna system [3,11,21,22] and traveling wave antenna [23][24][25] etc.In this report, we discuss a 3-stub tuner impedance matching system accompanied by a conjugate-T antenna system and 30 Ω-50 Ω transmission line.The schematic diagram for one antenna strap of the ICRH system in EAST is shown in figure 1.From the left side to the right, there is a transmitter, directional coupler, 3-stub tuner impedance matching system, voltagecurrent (V−I) probe pairs, pre-matching part and center grounded antenna strap.The V-I probe pairs are used to detect the input impedance near the 3-stub tuner impedance matching system, and the directional coupler is used to detect the transmitter power.The pre-matching part includes 30 Ω to 50 Ω transmission line and a conjugate-T configuration.The operation frequency of the ICRH antenna in EAST is 37 MHz and H minority heating is chosen as the main ICRH scheme.With an operation frequency of 37 MHz, the electrical length of the center grounded antenna strap is about λ/4.
According to previous research, by using the conjugate-T configuration, the reflected RF power fraction can be reduced in a wide range of plasma resistance which occurs in the ELMs and H-L mode transition [21][22][23][24][25][26].However, poloidal phasing is expected to be affected, as more current might be present on the upper strap than on the lower, or the opposite.The heating efficiency may be reduced in this case, and it is not excluded that loading variations could result from this as well.As a result, the two arms of a conjugate-T were designed to have λ/2 length difference in EAST tokamak.The rest of the paper is organized as follows: in section 2, the characteristics of the 3-stub tuner impedance matching system are introduced, then the pre-matching part has been analyzed in sections 3 and 4 corresponding to the 30-50 Ω transmission line and conjugate-T structures, respectively.After that, the load-tolerant characteristics of the ICRH system are investigated in section 5 and conclusions are presented in the last part.

The 3-stub tuner impedance matching system
A schematic view of the 3-stub tuner impedance matching system is shown in figure 2. The symbol A 23 is the normalized electrical length between stub2 and stub3, A 12 is the normalized electrical length between stub1 and stub2, A A1 is the normalized electrical length between stub1 and the V−I probes.A 1 , A 2 , A 3 are the normalized electrical length of stub1, stub2 and stub3 respectively.Based on those parameters, the RF voltage and current V l , I l at the top of stub3 can be expressed by RF voltage and current at the location of V−I probes V A , I A as shown in equation (1) [13,14].Then, the impedance after matching at the top of stub3 can be calculated as: Z l = V l I l .Impedance matching can be achieved when the real and imaginary parts of Z 1 are 50 Ω and 0 Ω, respectively.The values of 50 Ω are the characteristic impedance of the coaxial transmission line.Normally, for 3-stub tuner impedance matching system, the value of A A1 ,A 12 , A 23 are constant, A 1 , A 2 , A 3 are variable.So, we can make the ICRF antenna impedance matching by take appropriate value of A 1 , A 2 , A 3 , Here, It is known that the 3-stub tuner impedance matching system can only match a fixed impedance if the normalized electrical length of the stubs is kept constant.However, when the antenna impedance varies, the matching state will shift and the reflected power will increase.The reflected power fraction R ref can be expressed by the impedance at the top of stub3 (Z 1 ) as shown in equation (3), The dependence of the reflected power fraction on variable resistance R is shown in figure 3. The abscissa and the ordinate of figure 3 are the resistance R and the reflected power fraction R ref . Here, The impedance matching is obtained at different resistance (R) including 1 Ω, 5 Ω, 10 Ω and 14 Ω, respectively.It is clear that the load-tolerance characteristic appeared with larger resistance, as the reflected power fraction R ref is less than 3% in the range of 10-20 Ω with the impedance matching at 14 Ω.It is known that a change in the reactive part of the antenna loading is correlated with the increase in the resistive part; and the electrical length of the antenna is usually reduced in the presence of plasma.In order to simulate the real experimental environment, the equivalent length perturbation of the loading resistance is introduced while with resistance perturbation.The simulated results are shown in figure 4, even the resistance R is in the range of 10-20 Ω, and the equivalent length perturbation of the loading resistance is up to 200 mm with the operation frequency of 37 MHz, the reflected power fraction R ref is still less than 5 %.If we can increase the input impedance of the 3-stub tuner impedance matching system, we can improve the loadinsensitive ability of the ICRH system.In the next two parts, the pre-matching part including conjugate-T structure and 30-50 Ω transmission line will be described comprehensively, and they play a significant role in the raising of antenna input impedance.

The 30-50 Ω transmission line
A schematic view of the 30-50 Ω transmission line is shown in figure 5.The antenna impedance is represented by Z L , followed by a 30 Ω transmission line with a length of L. The 30-50 Ω transmission line is installed after 30 Ω transmission lines with a length of L T .L 1 is the sum length from the end of 30 Ω transmission line to the end of 50 Ω transmission line.Based on these parameters, the RF voltage and current V in , I in can be expressed by the RF voltage and current at antenna V L , I L as shown in equation ( 5), (5) Here, A L ,A L1−LT stands for the electrical length of 30,50 Ω transmission line.For the input impedance Z in calculation, we divided a 30-50 Ω transmission line into n sections with the length of d, d ≪ L T , L T = n * d, n = 1, 2, 3 . . ., A d is the electrical length of each section, in each section we assumed that the characteristic impedance (labeled as Z n , n = 1, 2, 3 . ..) of the transmission line remained constant.The input impedance at the minimum voltage distribution node (R min ) could be expressed as: Here, Z in = V in I in .Then, R min could be expressed as a function of L, L T and Z L .Now, we assume that the normalized antenna impedance is Z L = 0.02 + 0 * j Ω, and the length of the 30-50 Ω transmission line is L T = 0 m, 0.1 m and 0.354 m.Then, R min could be expressed as a function of L. The relationship between R min and L with difference L T is shown in figure 6.It can be seen that R min and L are closely related, and there is no obvious relationship between R min and L T .From the case of L T = 0 m shown in the red curve of figure 6, it is clear that the value of R min will go from 0.6 at 0 and λ/2-1.67 at λ/4.In the EAST tokamak, for engineering feasibility and input impedance Z in maximizing, the length of the 30-50 Ω transmission line was chosen to be L T = 0.354 m, and the installation position of the 30-50 Ω transmission line is around 0.25 λ shown in figure 6.In this case, the impedance can be increased by ∼ 1.6 times.The blue dot line corresponding to the structure without 30-50 Ω transmission line, the ICRH antenna is directly connected to the 50 Ω transmission line.

The conjugate-T structure
The schematic diagram of transmission lines near T-connector is shown in figure 7. Z 1 and Z 2 are the input impedance of the antenna, L 1 is the distance from Z 1 to T point, L 2 is the distance from Z 2 to T point, Z T is the input impedance at T-point.Then, Z T could express as a function of L 1 and L 2 if Z 1 and Z 2 are fixed as shown in equation (7).
Here, A L1 and A L2 is the electrical length of L 1 and L 2 .Based on the input impedance at T-point Z T , Voltage Standing Wave Ratio (VSWR) could be expressed as a function of Z T : As shown in the left side of figure 8, contours of VSWR are calculated for the case of Z 1 = Z 2 = 5 + j * 0 Ω (corresponding to the minimum standing wave voltage), the dashed red line corresponds to conjugate-T structure, the black dot shown in the middle of the figure corresponds to the maximum standing wave voltage as the distance from the black dot to Z 1 and Z 2 is 0.25 λ.The input impedance in minimum voltage distribution node R min corresponding to the dashed red line in counters of VSWR is shown in the right side of figure 8.In EAST, the location of the black dot was chosen as the location of the T-point.There are three reasons for choosing this point as the T-point.The first reason is that the changing rate of VSWR is lower around this point, which means that our ICRH system could be more load-tolerant to the equivalent length perturbation of the loading resistance caused by the plasma disturbance.The second reason is that this kind of design could mitigate antenna strap current imbalance and antenna poloidal phasing out of control problem as the length difference between two arms of the T-branches is n × λ/2.The third reason is that the input impedance can be doubled as the input impedance in the minimum voltage distribution node R min after T point is 10 and the antenna resistance of Z 1 , Z 2 equals to 5, which could decrease the voltage in the transmission line.

Analyzation based on experimental results in EAST tokamak
The system resilience to ICRH antenna coupling impedance perturbations was studied during discharges with strong plasma instability in shot 116 125 as shown in figure 9.The plasma density and D α signal are shown in figure 9(b).The stored energy of the plasma and input impedance at the location of V-I probes is shown in figure 9(c).The input and reflected ICRH power are shown in figure 9(d).It is clear that all those parameters have strong fluctuations during discharges.Even with strong plasma parameter fluctuations the reflected power is always kept low which results in better waveform control and increased average levels of power generated by the RF amplifier involved.The relationship between the antenna resistance R detected by V-I probes and the power reflection ratio is shown in figure 10.The blue circle is the measurement result which is calculated by the measured reflect and input power.The red circle is the calculation results which are calculated by equation ( 5) described in part II.It can be seen that the reflected power ratio is less than 7% even with impedance variation from 8 Ω to 16 Ω.These results prove that this system does have good load-tolerance.
Based on V-I probes shown in figure 1, the variations of the input impedance with different plasma parameters have been studied in 2021 in EAST.Typical Smith Chart loadings at V-I probes location is shown in the left side of figure 11.It is clear that the variation of the input impedance of the antenna is restricted to a small area of the Smith Chart.The antenna resistance R calculated based on V-I probes as shown in figure 1 varies from 8 Ω to 22 Ω, and the voltage distribution of the standing wave is shifted within 330 mm in the operating frequency of 37 MHz (phase varies within 30 • ).Only with the pre-matching part, the input impedance of the antenna is still low compared to the characteristic impedance of 50 Ω transmission lines, which could introduce large reflection and high VSWR.From part II, it is known that the 3-stub tuner impedance matching system can match any fixed impedance.Here, we choose to match the impedance at the position of the red dot Z = 16.7 + j * 7.5 Ω in Smith Chart of figure 11(a).In our 3-stub tuner impedance matching system, shown in figure 2, the electrical length of A A1 , A 12 , A 23 is 0.5, 0.29, 0.19 and A 1 , A 2 , A 3 is adjusted to 0.896, 1.197 and 1.130 respectively with the frequency of 37 MHz to match the impedance with Z = 16.7 + j * 7.5 Ω.Then, the reflection coefficient after 3-stub impedance matching system can be calculated, which is shown in the right side of figure 11, it is clear that the simulated results are almost in the black dot circle which means that the power reflection ratio is less than 8 %.It is safe for the RF amplifier operation in EAST.The statistical results show that the system has good load-tolerance.

Conclusions
In the EAST tokamak, an improved system with a 3-stub tuner impedance matching system, a conjugate-T structure, 30-50 Ω transmission line and a center grounded antenna strap for ICRH have been discussed in this paper.This system can achieve and maintain antenna matching with power reflection ratio below 5% for many kinds of operating conditions, which means that this matching network could allow robust high power operations without fast impedance matching in EAST tokamak.In our matching network, the two arms of conjugate-T were designed to have λ/2 length difference which could mitigate current imbalance and antenna poloidal phasing out of control problem.

Figure 1 .
Figure 1.The schematic diagram for one antenna strap of the ICRH system in EAST.There include the transmitter, directional coupler, 3-stub impedance matching system, V-I probe pairs, pre-matching part and antenna strap.The pre-matching part include conjugate-T structure and 30-50 Ω transmission line.

Figure 3 .
Figure 3.Comparison of reflected RF power fraction after 3-stub tuner impedance matching system (shown in figure 1) with R. The impedance matching is obtained at different resistance R including 1 Ω, 5 Ω, 10 Ω and 14 Ω respectively.

Figure 4 .
Figure 4.The resistance R is in the range of 10-20 Ω and the equivalent length perturbation on the loading resistance is shifted under 200 mm with the ICRH operation frequency of 37 MHz.It is clear that the reflected RF power fraction after 3-stub impedance matching system is less than 5%.

Figure 5 .
Figure 5.The detail structure and installed location of 30-50 Ω transmission line.The length of 30-50 Ω transmission line is L T = 354 mm, the inner conductor radius (r) is a constant, r = 50 mm.The distance from 30 Ω to 50 Ω transmission line to the antenna is L.

Figure 6 .
Figure 6.R min stands for input impedance at minimum voltage of standing wave, L is the length of 30 Ω transmission line, the normalized antenna impedance is assumed to be Z L = 0.02 + 0 * j Ω.

Figure 7 .
Figure 7.The schematic diagram of transmission lines near T-connector.Z 1 , Z 2 is the input impedance to antenna, Z T is the input impedance at T-point.

Figure 8 .
Figure 8. Left side: the VSWR contours in case of symmetric resistive loading Z 1 = Z 2 = 5 Ω, accompanied by transmission lines (L 1 and L 2 ) length changing, n 1 and n 2 represent integers.The dashed red line corresponding to conjugate-T configuration.Right side: the relationship between L 1 and the impedance at minimum voltage distribution node R min corresponding to the dashed red line in the left side figure.The black dot shown in the figures corresponding to maximum standing wave voltage in transmission line L 1 and L 2 .

Figure 9 .
Figure 9. Load-tolerance of the antenna system in shot 116 125.(a) Plasma current and loop voltage, (b) plasma density and Dα emission intensity, (c) plasma stored energy and coupling resistance in V-I probes and (d) ICRH input and reflect powers.

Figure 10 .
Figure10.The relationship between the antenna resistance R detected by V-I probes shown in figure1and the power reflection ratio.The blue circles corresponding to the measurement results and the red circles corresponding to the calculation results.

Figure 11 .
Figure 11.Left side: Smith Chart plot of input impedance at V-I probe pairs in EAST tokamak during the 2021 campaign; right side: Smith Chart plot of calculated reflection coefficient after 3-stub impedance matching.