Equilibrium of a Magnetically Confined Plasma in a Toroid

A static equilibrium of plasma (or of conducting fluid) with scalar pressure p and magnetic field B is often described by the so-called ''magnetostatic equations'', ∇p = j x B, (1) ∇ x B = j, (2) ∇ * B = 0, (3) where j is the electric current density. In particular, these equations apply to many proposed controlled thermonuclear reactors and their prototypes, especially the stellarator and the recently much discussed stabilized pinch effect. In sections B, C, and D are derived a variety of properties possessed by solutions of Eq. (1-3)