Tokamak plasma equilibrium with relativistic runaway electrons

Abstract

We consider axisymmetric equilibrium of a tokamak plasma that includes current carried by relativistic runaway electrons (REs). Using a guiding center approach, a qualitative picture of the equilibrium of a pure RE beam is elucidated. In a hot thermal plasma, none of the classical drifts of charged particles contribute to the net field-perpendicular current density, which is purely due to magnetization current. In the case of a runaway beam, however, the curvature drift of REs provides the Lorentz force needed to maintain the centripetal acceleration associated with the relativistic toroidal motion. Two different equilibrium formulations are derived for the general case consisting of a mix of thermal and RE current. At higher RE energies, the shift between flux-surfaces and surfaces of constant generalized angular momentum of REs in such equilibria can exceed the radial extent of a typical magnetohydrodynamic mode such that its stability properties could be altered. Simplified one-dimensional governing equations are derived for the absolute and relative orbit shifts in the case of a circular tokamak, enabling quick estimates of parameter dependencies.