Straight and toroidal plasma equilibria with an intense relativistic electron current component

Abstract

The equilibrium of an axisymmetric, large aspect-ratio, finite temperature toroidal plasma enclosed by a perfectly conducting toroidal container is studied analytically. The new feature of the analysis is the presence of a relativistic electron beam which circulates around the torus thus producing a poloidal magnetic field in addition to the external field and the field created by currents in the plasma. This problem may be of interest in connection with recent toroidal beam injection experiments at Cornell University and in tokamaks. The equilibria are obtained from the relativistic virial theorem. Specific examples are given wherein the plasma pressure is characterized by its dependence on the magnetic flux function and the relativistic electron beam is characterized by an electron distribution function which is a delta function in energy and canonical momentum in the toroidal direction.