A general theory of simultaneous feedback stabilization of multimode oscillations in collisionless magnetized plasma is developed for reactive and dissipative instabilities. The gain and phase requirements of the feedback circuit are obtained using familiar stabilization techniques. From causality and stability considerations further requirements on phase and gain are determined for a physically realizable feedback system. It is shown that unstable modes can be suppressed without driving new instabilities or causing stable modes to become unstable. Although this method of stabilization provides marginal stability for instabilities of the reactive type by correctly choosing the frequency dependence of the feedback gain, this problem can be overcome, and the stability properties of the feedback loop can be improved. Applications to some known reactive instabilities are included as examples.
Circuit equation formulation of resistive wall mode feedback stabilization schemes