Extension of Shafranov’s Equilibrium Theory to the Description of Current Quenches Affected by Resistive Wall Dissipation in Tokamaks

Abstract

An equation for the plasma column position in a tokamak is derived with account of the resistive wall reaction on the changes in the plasma. A similar problem was considered by V.D. Shafranov [J. Nucl. Energy C 5, 521 (1963)] but for a fixed plasma current. Here, this current is treated as time-dependent, which allows to cover the current quenches and expand the study to the analysis of disruptions. It is shown that the net toroidal current induced in the wall during the current quench (which is not accounted for in the mentioned and related existing analytical models) can strongly affect the plasma equilibrium. A general algorithm applicable to arbitrary tokamaks is presented. For a large-aspect-ratio “circular” tokamak a full cycle of the step-by-step reduction of a problem is carried out down to the equation for the plasma shift evolution. The technique and results are ready for use with standard equilibrium solvers and models.