Inductive inhibition of cold-plasma stabilization of curvature-driven modes in finite-length plasmas

Abstract

A modified quasistatic theory that incorporates inductive effects in earlier electrostatic models connects the conventional electrostatic and magnetohydrodynamic (MHD) pictures of line tying by cold plasma. The modified theory predicts that curvature-driven flute modes in mirror-confined plasmas can be stabilized by moderate concentrations of cold plasma if the beta of the hot, mirror-confined plasma is less than a critical value. The maximum stable beta for an idealized stratified model of a hot-ion plasma, separated from conducting end walls by cold plasma, is given approximately by βcrit≂(4RpRc/LhLc) ×[ω2pe(cold)/ (k2⊥c2+ω2pe(cold))]. For ω2pe(cold) ≪k2⊥ c2, this result is identical with the predictions of electrostatic models. In the opposite limit, the result resembles the predictions of ideal MHD models, namely, that unstable curvature-driven modes can occur even in the presence of dense cold plasmas if the hot-plasma beta exceeds a limiting value estimated to be π2RpRc/L2.