High-Pressure Flux-Conserving Tokamak Equilibria

Abstract

An analytic theory is developed to calculate poloidal beta ${\ensuremath{\beta}}_{I}$ and the diamagnetic parameter ${\ensuremath{\mu}}_{I}$ for axisymmetric toroidal magnetohydrodynamic equilibria confining high-pressure plasmas [$\ensuremath{\beta}\ensuremath{\sim}O(\frac{a}{R})$] under the constraint of flux conservation. To satisfy the equilibrium equations, the plasma current increases with pressure as ${p}^{\frac{1}{3}}$. Previously calculated equilibrium limits on poloidal $\ensuremath{\beta}$ are avoided.