Feedback stabilization of tokamaks against slow axisymmetric MHD instabilities

Abstract

Single axis tokamaks as well as doublets may be unstable toward axisymmetric MHD instabilities. Such instabilities may, for the case of a single-axis tokamak, be slow when the plasma is surrounded by a relatively close fitting conducting wall, such as a vacuum chamber; the growth rate may be proportional to the resistivity of the wall material. For the case of doublets, slowly growing instabilities with growth rates proportional to the plasma resistivity exist. Such slow instabilities can be stabilized by feedback control of the currents through coils surrounding the plasma; since it is only required that the amplifiers used in the circuits respond fast compared with the growth time of the slow instabilities, this feedback stabilization is not technologically demanding. This paper describes a formalism for the stability analysis of such a system consisting of the plasma, surrounded by a conducting wall or vacuum chamber and coils with their control system.