Magnetohydrodynamic equilibria and local stability of axisymmetric tokamak plasmas

Abstract

Axisymmetric magnetohydrodynamic equilibria are evaluated in terms of the Mercier Stability Criterion. The parameters of interest include poloidal beta (..beta../sub p/), current and pressure profile widths, D-shaped and doublet plasmas with elongation (sigma) and triangularity (delta), and the aspect ratio (A). For marginal local stability, the critical values of ..beta.., plasma current, and the safety factor q with fixed toroidal field at the geometric center of the plasma are obtained. It is shown that for a wide range of profiles in a D-shaped plasma with A = 3, the highest critical ..beta.. occurs at ..beta../sub p/ = 2.4, sigma = 1.65, and delta = 0.5. If the toroidal field at the coil surface is fixed, the highest critical pressure occurs near A approximately 3 to 4, given reasonable distance between the coils and the plasma edge. Calculations for a Doublet II-A plasma with sigma = 3 show that with similar pressure profile the highest critical ..beta.. occurs at ..beta../sub p/ = 1 and is 84 percent of the highest critical ..beta.. for the D-shaped plasmas. Critical values of ohmic heating power density are also found to be comparable for the two plasma shapes. A D-shaped plasma with the above parameters is suggested for use in future high-..beta.. tokamak devices.