Equilibrium of a Magnetically Confined Plasma in a Toroid

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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.

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