Equilibrium of a Magnetically Confined Plasma in a Toroid

Abstract

A variety of properties are derived satisfied by any static equilibrium of a plasma governed by the well-known magnetostatic equations. Some of these are local and quite trivial. Others involve integrals over surfaces of constant pressure, which are shown to be topologically toroidal under fairly general assumptions. A variational principle for such equilibria is derived. One of its consequences is to provide a characterization of equilibria by their values of certain invariants. Finally, conditions are obtained additional to the magnetostatic equations appropriate to the steady state of a plasma slowly diffusing across a magnetic field out of a topologically toroidal region.