Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. II. Control analysis

Active feedback of nonaxisymmetric resistive wall modes in tokamaks is investigated using control theory. Control systems are designed to stabilize the resistive wall mode of toroidal mode number n=1 and meet certain performance specifications for a set of test equilibria. The response of the plasma and resistive wall is described by low order rational functions from an electromagnetic model [Y. Q. Liu , Phys. Plasmas 7, 3681 (2000)]. Simple coil arrangements are assumed, both for the sensor and feedback coil arrays, and the sensors detect the perturbed poloidal field. The active coils are modeled both as broad strips and as thin wires, and several different controllers: P (proportional), PD (proportional plus derivative) and H-infinity are investigated. An important parameter is the ratio, tau, of control system response time to the resistive wall time, and the analysis shows the restrictions on this ratio for acceptable performance. For an equilibrium that exceeds the no-wall beta limit by 63%, good control with broad strips and a PD controller is possible for tau less than or similar to 5.4, while thin-wire coils require tau less than or similar to 2.1. H-infinity controllers give some improvement for thin wires and about a factor of 2 increase in tau for broad strips. The upper limit in tau decreases with increasing pressure. A control system designed to stabilize a certain pressure generally works well at lower pressures. (C) 2000 American Institute of Physics. [S1070-664X(00)04110-0].