On toroidal equilibrium of non-neutral plasma

The equilibrium of a non-neutral cloud in a toroidal magnetic field is analyzed. In the zero mass limit it is shown that, because of plasma diamagnetism and electrostatic hoop force, there is a net force on the cloud along the major radius. In a large-aspect-ratio conducting vessel, this force is balanced by image charges that produce a compensating force toward the major axis. As a result, shift of potential minimum (or maximum) from the geometric center of the vessel (in the poloidal plane) is toward the major axis. A partial differential equation governing the two-dimensional axisymmetric equilibrium is obtained and solved in the large-aspect-ratio limit. Further, it is shown that modification of this equilibrium owing to first-order guiding center drifts is small, i.e., drift surfaces are still closed, however, they are further displaced toward the major axis from the potential surfaces by a small distance. Finally, a brief comparison of the properties of the equilibrium of neutral and non-neutral plasma is given.