Relaxed plasma-vacuum states in cylinders

Abstract

The variational principle for relaxed toroidal plasma-vacuum systems with pressure is applied to axially periodic circular cylinders. More precisely, equilibria with cylindrical symmetry are investigated for their potential to be a relaxed state. Such equilibria are characterized by their pinch ratio μ, the jump δ of the pitch angle of the magnetic field across the plasma-vacuum interface, a constant plasma pressure β, and the ratio l of wall radius over interface radius. In the limit of an infinitely long cylinder, the necessary and sufficient condition for the equilibrium to be a relaxed state defines one or two intervals of allowed values of the pinch ratio μ, which depend still on the other parameters. These intervals are contained in the interval known from Taylor's theory, but are generally smaller. They shrink with increasing plasma pressure β or increasing radius ratio l. In particular, in the field-free limit case β = 1, for I exceeding the critical value l c 4.983, or for a vanishing δ, these intervals are zero.