High-Pressure Flux-Conserving Tokamak Equilibria

An analytic theory is developed to calculate poloidal beta ${\beta }_I$ and the diamagnetic parameter ${\mu }_I$ for axisymmetric toroidal magnetohydrodynamic equilibria confining high-pressure plasmas [$\beta \sim O\left(\frac{a}{R}\right)$] 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 $\beta$ are avoided.