Feedback stabilization of nonaxisymmetric resistive wall modes in tokamaks. I. Electromagnetic model

Active feedback stabilization of pressure-driven modes in tokamaks is studied computationally in toroidal geometry. The stability problem is formulated in terms of open-loop transfer functions for fluxes in sensor coils resulting from currents in feedback coils. The transfer functions are computed by an extended version of the MARS stability code [A. Bondeson et al., Phys. Fluids B 4, 1889 (1992)] and can be accurately modeled by low order rational functions. In the present paper stability is analyzed for a system with an ideal amplifier (current control). It is shown that feedback with modest gain, and a single coil array poloidally, gives substantial stabilization for a range of coil shapes. Optimum design uses sensors for the poloidal field, located inside the resistive wall, in combination with rather wide feedback coils outside the wall. Typically, the feedback does not strongly modify the plasma-generated magnetic field perturbation. A future companion paper [C. M. Fransson et al., Phys. Plasmas (accepted for publication)] will apply control theory to study the limitations arising for finite time-constant of the amplifier-feedback coil circuit.