Feedback stabilization of resistive shell modes in a reversed field pinch

Abstract

A reactor relevant reversed field pinch (RFP) must be capable of operating successfully when surrounded by a close-fitting resistive shell whose L/R time is much shorter than the pulse length. Resonant modes are largely unaffected by the shell resistivity, provided that the plasma rotation is maintained against the breaking effect of nonaxisymmetric eddy currents induced in the shell. This may require an auxiliary momentum source, such as a neutral beam injector. Nonresonant modes are largely unaffected by plasma rotation, and are expected to manifest themselves as nonrotating resistive shell modes growing on the L/R time of the shell. A general RFP equilibrium is subject to many simultaneously unstable resistive shell modes; the only viable control mechanism for such modes in a RFP reactor is active feedback. It is demonstrated than an N-fold toroidally symmetric arrangement of feedback coils, combined with a strictly linear feedback algorithm, is capable of simultaneously stabilizing all intrinsically unstable resistive shell modes over a wide range of different RFP equilibria. The number of coils in the toroidal direction N, at any given poloidal angle, must be greater than, or equal to, the range of toroidal mode numbers of the unstable resistive shell modes. However, this range is largely determined by the aspect-ratio of the device. The optimum coil configuration corresponds to one in which each feedback coil slightly overlaps its immediate neighbors in the toroidal direction. The critical current which must be driven around each feedback coils is, at most, a few percent of the equilibrium toroidal plasma current. The feedback scheme is robust to small deviations from pure N-fold toroidal symmetry or a pure linear response of the feedback circuits.