Active control of resistive wall mode via modification of external tearing index

Abstract

Modification of the external tearing index, Δext′, by magnetic feedback is analytically investigated for the purpose of controlling the resistive plasma resistive wall mode (RP-RWM). The matching method is pursued by deriving expressions for the close-loop Δext′ and by linking it to the counterpart from the inner layer. Various feedback coil configurations are found to generally reduce Δext′ and stabilize the RWM, with either proportional or derivative control. Feedback modification of Δext′ is found to be generally independent of the inner layer resistive interchange index DR, confirming that feedback action primarily modifies the solution in the outer ideal region for the RP-RWM. Exception occurs when either the inner layer favorable curvature effect becomes sufficiently large or the feedback action is sufficiently strong to introduce a rotating RP-RWM in the static plasma, leading to complex-valued close-loop Δext′. The perturbed magnetic energy dissipation in the outer region, associated with the eddy current in the resistive wall, is identified as the key physics reason for feedback induced complex Δext′. Similar results are also obtained for active control of the external kink instability, whose open-loop growth rate is significantly reduced by inclusion of the plasma resistivity. Within the single poloidal harmonic approximation, which is most suitable for the matching approach, external active coils combined with poloidal sensors are often found to be more efficient for feedback stabilization of the mode at large proportional gain values. This counter-intuitive result is explained as the lack of (non-resonant) poloidal harmonics for proper description of the feedback coil geometry.