First realization of LHW–plasma coupling feedback control for long-pulse operation in EAST

To sustain good lower hybrid wave (LHW)–plasma coupling for long-pulse plasma operation, for the first time, coupling feedback control is designed and realized in EAST using a proportion integration differentiation method by choosing the reflection coefficient (RC) of LHW power as the reference for gas-puffing feedback, and including one pulse test and multi-pulse experiments. Experiments show that such feedback control can work correctly and maintains good LHW–plasma coupling effectively for a long time, suggesting the possibility of feedback control application on LHW–plasma coupling in long-pulse plasma. Furthermore, during the feedback control process of multi-pulse supersonic molecular beam injection (SMBI), the stored energy changes from 29 kJ to 58 kJ, and the energy confinement factor (H 89) increases from 0.98 to 1.45, implying a positive effect of coupling feedback on plasma performance. Experiments between SMBI puffing and the gas puffing system, fed by a piezoelectric valve near the antenna, are further investigated, showing that the response time of the RC with SMBI is faster than that by the piezoelectric valve. In addition, SMBI puffing on the electron-drift side of the LHW antenna is a little quicker than that on the ion-drift side. Studies suggest that such feedback control is effective for long-pulse LHW–plasma coupling, and the gas puffing by SMBI on the electron-drift side of the LHW antenna could offer an effective way to sustain good LHW coupling in steady-state operation in the future. Further optimization will be continued at a later date.

Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Introduction
Lower hybrid current drive (LHCD) [1] has proven to be one of the most efficient methods of non-inductive current drive, off-axis current profile control, and long-pulse plasma operation sustainment in tokamak experiments [2].Good waveplasma coupling, mainly determined by the plasma density at the grill mouth (n e,grill ) and its gradient, is the first necessary condition for LHCD, requiring the density value to be above a cut-off density expressed by n e,co = (ω 2 m e )/(4πe 2 ), where ω is the wave frequency, m e is the electron mass, and e is the electron charge.Theory studies [3,4] indicate that the plasma density at the grill mouth and its gradient are two key factors that determine wave-plasma coupling.As is known, the grill density is mainly related to the distance d between the last closed flux surface (LCFS) and the grill mouth, and the decay length of electron density in the scrape-off layer (λ SOL ), i.e. n e,grill = n e,LCFS • exp (−d/λ SOL ) [5], where n e,LCFS is the density at the LCFS.To avoid heavy heat load to the lower hybrid wave (LHW) antenna from the plasma in a fusion device, it is necessary to increase the distance between the antenna and the plasma.In addition, in high-confinement (Hmode) plasma, the edge density will decrease rapidly due to the large density gradient.Therefore, it is natural that the density will be below the cut-off density in high-performance plasma.As a result, the LHW power will not be effectively coupled to the plasma when the plasma density at the grill is relatively low.These are inevitable problems in the coming ITER (International Thermonuclear Experimental Reactor) [6] and China Engineering Fusion Test Reactor [7] operation.
To solve the above problem, local gas puffing (LGP) technology near the LHW antenna has been developed and put into use in JET, Tore-supra, HT-7, and EAST, demonstrating that such technology can effectively improve LHW-plasma coupling [8][9][10][11][12][13].Also, experimental results [13] in EAST show that the effect of gas puffing from the electron-drift side of LHW antenna on LHW-plasma coupling is better than that from the ion-drift side.
However, until now, the gas puffing described above was usually pre-set before the discharge in previous experiments; in fact, the density in front of the grill is under constantly changing conditions during the discharge.Such pre-set gas puffing programs do not achieve optimal coupling as the plasma evolves over the course of a long pulse in ways that are difficult or impossible to fully predict.When faced with transients or unforeseen changes in the plasma, pre-set gas programs can fail to improve LHW coupling, harm plasma performance, or even extinguish the plasma.Therefore, gas flows must be calculated in real time and be feedback controlled via gas fueling for best LHW coupling in long-pulse operation.With the aim to achieve steady-state LHCD plasma, LHW-plasma coupling feedback control by gas fueling was designed and studied experimentally for the first time in EAST, to modify the grill density that matches the LHW-plasma coupling effectively during the discharge.
The paper is arranged as follows.In section 2, the experimental setup of the gas fueling system is described, followed by the design of the wave-plasma coupling feedback control in section 3.In section 4, experiments of coupling feedback control are performed and analyzed.Finally, a summary and discussion are presented in section 4.

Experimental setup of the gas fueling system
In EAST [14], there are five fueling systems, including two LGP systems (LGP-1 and LGP-2) near the LHW antenna and three supersonic molecular beam injection (SMBI) systems (SMBI-1, SMBI-2, and SMBI-3) that could be used to enhance the electron density in front of the LHW antenna.The layout of the gas fueling system in EAST is shown in figure 1, where the positions of the LHCD antenna (2.45 GHz and 4.6 GHz) are also marked.By considering the plasma current is in the counter-clockwise direction and taking 4.6 GHz LHW antenna as the reference, LGP-2, SMBI-1, and SMBI-2 locate at the electron-drift side, whereas LGP-1 and SMBI-3 locate at the ion-drift side.
Usually, to improve the grill density effectively, a fueling system close to the LHW antenna is preferred.In addition, a short fueling delay is another issue to be considered, otherwise the density increases too much before switching off the fueling system.
The LGP [13] in EAST is equipped with a piezoelectric valve and the response time is about 50-300 ms, mainly contributed from the gas flow time in the fueling pipe located inside the vacuum chamber.The SMBI [15] device consists of a high-pressure gas source (1-2 MPa), a solenoid valve, a Laval nozzle, and magnetic shielding, etc.The key characteristic is that the beam is ejected freely to the vacuum chamber without any guiding pipe.Compared to LGP, the molecular supersonic beam has a higher speed, which is also demonstrated by the experimental response of central line-averaged density on LGP and SMBI [15].

Design of wave-plasma coupling feedback control
As is known, wave-plasma coupling strongly depends on the electron density in front of the lower hybrid (LH) grill, which can be effectively modified by local gas fueling in the edge region.Usually, a suitable range of n e,grill , based on the coupling characteristics, is preferred for good coupling.In principle, gas fueling can be controlled by the feedback of the measured n e,grill due to the directive relevance between coupling and the grill density.However, n e,grill is usually obtained via off-line processing of the measurement by Langmuir probes, as it is unavailable in real time feedback.Since the coupling is directly indicated by the reflection coefficient (RC) of LHW power, which is calculated using RC = P re /P in (P in and P re are the injected and the reflected power measured by a directional coupler with a frequency of 1 kHz, respectively), the RC is chosen as the reference signal for the feedback control of gas fueling.As there is some fluctuation in the power measurement, for reliability, the RC for the feedback is averaged on a time width of a cycle (T cycle ), which is regarded as the response time (e.g. 5 ms) of the feedback control, and the corresponding average is called RC.
The gas fueling is realized by controlling the pulse width of the valve opened for gas injection.The feedback loop is based on the comparison between RC and the threshold of the RC, and the flow of the feedback control is shown in figure 2, where n is the flag of the gas fueling status (0 means OFF and 1 means ON), t start and t end are the time slice of the start and end for the control, while R th-up and R th-down are the upper and the lower threshold of the RC set in advance, respectively.In general, the gas valve for the gas injection will be opened, if two necessary conditions (RC > R th-up and T pulse > T min ) are satisfied.Here, T pulse is the effective pulse width controlling the gas injection and is calculated via proportion integration differentiation (PID) according to the difference between RC and R th-up .Meanwhile, T min , determined by the characteristic of the valve, is the minimum time width required to open the valve.Therefore, the gas valve will not be opened when T pulse ⩽ T min .Also, the gas injection will be closed or does not work if RC < R th-down .

Experiments of coupling feedback control
As the current drive efficiency of 4.6 GHz LHW is higher than that of 2.45 GHz LHW, coupling experiments of feedback control were performed with 4.6 GHz LHW, whose cut-off density for coupling is about 2.62 × 10 17 m −3 and the density for optimized coupling is about 1.05 × 10 18 m −3 .These experiments included the test of a single SMBI pulse, multi-pulse injection of SMBI, and experimental comparison between different gas fuelings with SMBI and LGP.

Test of a single SMBI pulse
The gas flow rate is key when determining the density in front of the LH grill and affects the wave-plasma coupling.To avoid plasma disruption due to too much fueling, for the first step, an experiment of one pulse of SMBI fed by SMBI-3 is performed to test its effect on the feedback control, in which R th-up and R th-down are set as 7% and 4%, respectively.The typical waveforms are shown in figure 3, where the period (4.78-4.88ms) of gas injection is enlarged.In the experiments, the distance between the LCFS and the antenna (Gap out ) was scanned from a small value (∼1.8 cm) to a larger value (∼4.0 cm), and then back to a small value (∼1.8 cm), to change the LHW-plasma coupling actively.It is seen that with the increase in Gap out , the density at the grill measured by the Langmuir probe near the antenna decreases gradually to 2.5 × 10 17 m −3 , accompanying the increase in the RC.When the RC reaches the upper threshold (∼7%), SMBI is switched on; consequently, the density at the grill increases and the RC decreases quickly.When the RC decreases to the lower threshold (4%), SMBI is switched off, being consistent with the increased edge density of 7.5 × 10 17 m −3 , which satisfies wave-plasma coupling conditions.
Experiments indicate that the feedback control progress of one pulse injection works correctly and is valid for LHWplasma coupling improvement.Note that due to the gas fueling pulse, the central line-averaged density (n e,avg ), measured by a POlarimeter-INTerferometer (POINT) diagnostic [16], also increases to a high value (∼2.35 × 10 19 m −3 ), and it returns to the normal value after about 100 ms, suggesting the effects of local gas fueling on core plasma.Such effects could be reduced somewhat by optimizing the amount of gas injection.

Experiments with multi-pulse SMBI
For long-pulse plasma operation, the feedback of multi-pulse SMBI is necessary and performed with SMBI-3.In the experiments, the upper and the lower thresholds of the RC are set to 6% and 4%, respectively, and the feedback control is applied from 3 s to 6 s.The typical waveforms are displayed in figure 4, where part of the time period is enlarged.Seen from the enlarged plot, the SMBI is switched on when the RC is above the threshold (6%), and continues with a certain pulse width, which is calculated by PID according to the RC, indicating the reliability of the multi-pulse feedback control.
It is seen that the RC is about 20% and the edge density is about 1.1 × 10 17 m −3 before the feedback application.When the feedback is applied, the edge density increases quickly to 3.0 × 10 17 m −3 , and the RC decreases sharply to a value around 6%.During the process of multi-pulse SMBI, the edge density remains at about 3.0 × 10 17 m −3 , though there is a little fluctuation on the amplitude.Consequently, the RC between 3% and 6% is almost maintained.As a result, the plasma loop voltage decreases from ∼0.6 V to ∼0.4 V, suggesting that with the feedback application, the current fraction driven by the LHW is enhanced due to more coupled LHW power, even if with a higher plasma density.In addition, the gas flow shown in figure 4(c) increases quickly and then slowly, meaning that the gas required for good coupling decreases with the time evolution.Furthermore, during the feedback process, the stored energy (W mhd ), obtained from equilibrium reconstruction using an EFIT code [17] constrained by the measurements with the external magnetic coils, increases from 29 kJ to 50 kJ quickly with the application of SMBI, and then to about 58 kJ with the evolution of feedback.Also, the energy confinement factor of H 89 (=τ E /τ E ITER89-P ) behaves with similar characteristics (from 0.9 to 1.5) to the stored energy, where τ E is the experimental energy confinement time and τ E ITER89-P = 0.048M 0.5 I p 0.85 R 1.2 a 0.3 k 0.5 n 0.1 B 0.2 P −0.5 [18], implying a certain improvement in the plasma performance.
As seen in figure 4(a), this could be mainly ascribed to the improved coupling power of LHW since other sources, including the plasma current, are fixed during the process.
The results indicate that such an improvement in LHW power due to coupling feedback is helpful for current drive capability, stored energy, and plasma performance.
Similar to the one-pulse injection, the gas injection has an effect on the core plasma.It is seen that the central lineaveraged density increases from 1.75 × 10 19 m −3 to about 2.0 × 10 19 m −3 , and then decreases to the initial value gradually.The density increment (∼0.25 × 10 19 m −3 ) is much smaller than that with single-pulse SMBI and is acceptable.This is mainly due to the smaller gas flow rate in the multipulse SMBI, suggesting the effect of gas injection on core plasma can be reduced further by optimization of the gas flow.

Comparison of response between LGP and SMBI
Usually, gas fueling contributes to the enhancement of edge density as follows: (1) the gas is firstly ionized locally near the gas pipe and then moves to the LHW antenna region; and (2) the gas firstly diffuses to the antenna region and then is ionized by the LH electric field.Studies [13] show that the effect of puffing from the electron side is a little more effective in improving the density in the SOL region, implying that the local gas ionization near the gas pipe is more dominant.
The above experiments indicate that SMBI is effective for the feedback control of LH coupling.Although it is reported [15] that the response of central line-averaged density to SMBI is faster than that to LGP, experiments of wave-plasma coupling response to fueling by LGP-2 SMBI-2 and SMBI-3 are performed with the same order of edge electron density.In the experiments, LGP-2, SMBI-2, and SMBI-3 working with deuterium (D 2 ) are utilized to enhance the edge density to get a reduced RC of LHW power.Due to the uncertainty of Langmuir probe measurement, the RC is used to investigate the fueling response, although its response to gas fueling should be a little later than that of edge electron density; the typical waveforms are plotted in figure 5.It is seen that the RC decreases with the three methods, but with different time delays as follows, suggesting the differences in response.
Firstly, LGP-2 and SMBI-2, both located in the electrondrift side of the LHW antenna, are chosen for the comparison.As seen in figure 5(c), by comparing the time slice of gas injection and the RC decrease, the time delay of the RC decrease with LGP-2 (t LGP-2 ) and SMBI-2 (t SMBI-2 ) is 140 ms and 14 ms, respectively, suggesting the response of SMBI-2 is much faster than that of LGP-2, even if the magnetic field line length between the gas fueling position and the LHW antenna is shorter in LGP-2.As mentioned in section 2, this is mainly due to the guiding pipe in the LGP-2.
Secondly, by considering the local gas ionization near the gas valve and the movement of ionized electrons along the magnetic field line, the gas fueling experiments by SMBI-2 and SMBI-3, located at the electron-drift side and the ion-drift side of the LHW antenna, respectively, are further investigated.As shown in figure 5, it is seen that the response time of the RC with SMBI-3 (t SMBI-3 ) is about 30 ms, nearly double the value in SMBI-2 (t SMBI-2 ∼ 14 ms).Compared to the gas fueling on the electron-drift side, the electrons ionized on the ion-drift side will pass a long route before reaching the LHW antenna.Estimated from figure 1, the magnetic connection length between the LHW antenna and the position of the gas fueling system is about L J-E = 4.72 m and L A-E = 11 m for SMBI-2 and SMBI-3 injection, respectively.The ratio of the response time (t SMBI-3 /t SMBI-2 ) is close to that of the magnetic connection length between SMBI-2 and SMBI-3 (L J-E /L A-E ).Since the LHW antenna is just located at the center between SMBI-2 and SMBI-3, and, consequently, the gas diffusion time to the LHW antenna should be similar, the discrepancy in response time is mainly ascribed to the difference in the magnetic connection length between the LHW antenna and the gas fueling position in the toroidal direction.Therefore, it is inferred that the local gas ionization in the gas fueling region is dominant for the enhancement of LH coupling, and the position at the electron-drift side is preferred for the gas fueling, as reported in [13].
In general, studies show that the fastest feedback response time is SMBI fed on the electron-drift side and the slowest response is LGP, between which is SMBI fed on the ion-drift side.The difference between SMBI and LGP is mainly ascribed to the characteristics of the gas fueling system, whereas the difference between the ion-and electrondrift sides is mainly due to the different lengths of the magnetic field lines from the gas valve to the LHW antenna.Considering that, compared to the perturbation on core plasma, which could be reduced by optimizing the gas flow rate, the response time of the RC is more important to the feedback, the gas fueling of SMBI at the electron-drift side of the LHW antenna is preferred for the feedback control.Note that shot 87564 is far apart from shots 93265 and 93266, and the initial conditions for the plasma are different.Although, it possibly leads to different plasma performances, as indicated by the initial plasma density and the perturbation on the core plasma, as shown in figure 5(a), this may not change the achieved conclusion since we mainly focus on the coupling response, which is barely affected by the plasma performance.

Conclusion
This is the first time that LHW-plasma coupling feedback control has been designed and realized in EAST via the PID method by choosing the RC LHW power as the reference for gas puffing feedback.Based on the successful experimental test of one-pulse SMBI, experiments with multi-pulse SMBI show that such feedback control can work correctly and maintains good LHW-plasma coupling effectively for a long time, suggesting the possibility of feedback control application in LHW-plasma coupling.Furthermore, the results indicate that the improvement in LHW power due to coupling feedback is helpful for current drive capability, stored energy, and plasma performance.Experiments between SMBI puffing and LGP fed by a piezoelectric valve near the antenna are further investigated, showing that the response time of the RC with SMBI is faster than that by the piezoelectric valve and that SMBI puffing on the electron-drift side of the LHW antenna is preferred for the control.These studies offer an effective way to sustain good LHW coupling in steady-state operation in the future.Further optimization will be continued at a later date.Q.P. Yuan  https://orcid.org/0000-0003-4292-1302M.H. Li  https://orcid.org/0000-0002-3658-8243

Figure 1 .
Figure 1.The layout of the gas fueling system for LH coupling in EAST.

Figure 2 .
Figure 2. The flow of the feedback control.

Figure 3 .
Figure 3.Typical waveforms of a single SMBI pulse: (a) the central line-averaged electron density (ne,avg); (b) the distance between the LCFS and the antenna (Gapout), and electron density at the grill (n e,grill ); (c) the RC of LHW power and the SMBI signal (SMBI-3); (d) local enlargement of plot (b); and (e) local enlargement of plot (c).

Figure 4 .
Figure 4. Typical waveforms of the multi-pulse of SMBI: (a) the plasma current (Ip) and input LHW power (P in ); (b) the stored energy (W mhd ) and energy confinement factor (H 89 ), (c) the central line-averaged electron density (ne,avg), electron density at the grill (n e,grill ), and plasma loop voltage (V loop ); (d) the RC of LHW power, SMBI signal (SMBI-3), and SMBI-3 gas flow; and (e) local enlargement of plot (d).