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

Active feedback of nonaxisymmetric resistive wall modes in tokamaks is inve stigated using control theory. Control systems are designed to stabilize th e resistive wall mode of toroidal mode number n=1 and meet certain performa nce specifications for a set of test equilibria. The response of the plasma and resistive wall is described by low order rational functions from an el ectromagnetic model [Y. Q. Liu , Phys. Plasmas 7, 3681 (2000)]. Simple coil arrangements are assumed, both for the sensor and feedback coil arrays, an d the sensors detect the perturbed poloidal field. The active coils are mod eled both as broad strips and as thin wires, and several different controll ers: 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 restri ctions on this ratio for acceptable performance. For an equilibrium that ex ceeds the no-wall beta limit by 63%, good control with broad strips and a P D controller is possible for tau less than or similar to 5.4, while thin-wi re coils require tau less than or similar to 2.1. H-infinity controllers gi ve 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. [S1070-66 4X(00)04110-0].