Circuit equation formulation of resistive wall mode feedback stabilization schemes

Recently, various schemes for controlling the resistive wall mode have been proposed. Here, the problem of resistive wall mode feedback control is formulated utilizing concepts from electrical circuit theory. Each of the coupled elements (the perturbed plasma current, the poloidal passive shell system and the active coil system) is considered as lumped parameter electrical circuits obeying the usual laws of linear circuit theory. A dispersion relation is derived using different schemes for the feedback logic. The various schemes differ in the choice of sensor signal, which is determined by some combination of the three independent circuit currents. Feedback schemes are discussed which can, ideally, completely stabilize the kink mode. These schemes depend, for their success, on a suitable choice for the location of the sensors. A feedback scheme based on sensing the passive shell eddy current is discussed which seeks to drive the feedback system response to a point of marginal stability. For realizable feedback gain factors, this feedback system can suppress the kink mode amplitude for times that are very long compared with the L/R time-scale of the passive shell system. The circuit equation approach discussed provides a useful means for comparing various control strategies for n greater than or equal to 1 kink mode control, and allows useful analogies to be drawn between kink mode control and the control of n = 0 vertical position instabilities.