Experimental and theoretical studies of active control of resistive wall mode growth in the EXTRAP T2R reversed-field pinch

Abstract

Active feedback control of resistive wall modes (RWMs) has been demonstrated on the EXTRAP T2R reversed-field pinch experiment. The control system includes a sensor consisting of an array of magnetic coils (measuring mode harmonics) and an actuator consisting of a saddle coil array (producing control harmonics). Closed-loop (feedback) experiments using a digital controller based on a real time Fourier transform of sensor data have been studied for cases where the feedback gain was constant and real for all harmonics (intelligent-shell) and cases where the feedback gain could be set for selected harmonics, with both real or complex values (targeted-harmonics). The growth of the dominant RWMs can be suppressed by feedback for both the intelligent-shell and targeted-harmonic control systems. Because the number of toroidal positions of saddle coils in the array is half the number of sensors, it is predicted and observed experimentally that the control harmonic spectrum has sidebands. As a result, each control harmonic has to control simultaneously two mode harmonics. Real gains can stabilize non-rotating RWMs, while complex gains give better results for (slowly) rotating RWMs. In addition open loop experiments have been used to observe the effects of resonant field errors applied to unstable, marginally stable and robustly stable modes. The observed effects of field errors are consistent with the thin-wall model, where mode growth is proportional to the resonant field error amplitude and the wall penetration time for that mode harmonic.

Error field assessment from driven rotation of stable external kinks at EXTRAP-T2R reversed field pinch

“…The results are presented in Fig.9 and analyzed in Fig.10. The best correction is obtained for a rotating perturbation b 1 =0.11mT, corresponding to a static (unshielded) b 0 = 0.20 ± 0.02mT, in agreement with earlier estimates [12,13]. Fig.9b indicates that its toroidal phase is approximately φ=0.…”

“…Stable Resistive Wall Modes (RWMs) of toroidal mode number n=8 and 10 were generated and their rotation sustained by rotating magnetic perturbations. Due to finite EFs, and in spite of the applied perturbations rotating uniformly and having constant amplitude, the RWMs were observed to rotate non-uniformly and be modulated in amplitude (Figs.5,6,9,10,12,13,14,15,). This behavior was interpreted with a simple theoretical model (Eq.7) and used to characterize and correct intrinsic n=8 and 10 EFs, leading to longer discharges and more uniform mode rotation (Figs.7, 16).…”

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

“…Even without additional damping, a weakly unstable RWM can be relatively easily controlled by a magnetic feedback scheme. [44][45][46][47] On the other hand, depending on the plasma parameters (rotation, EPs pressure fraction, etc. ), there can be more than one branch of unstable modes.…”

Active control of the resistive wall mode with power saturation

“…Extensive theory [16][17][18][19][20][21][22] and experimental [23][24][25][26][27][28][29][30][31] work has been carried out to study the active control of the RWM, in both tokamak and RFP devices. Even though the power saturation of the feedback system is often the case in experiments, very few theoretical work has been performed addressing this issue.…”