Numerical Studies of Magnetohydrostatic Finite-Beta Stellarator Equilibria

Properties of finite-beta stellarator equilibria are investigated which are obtained as fully three-dimensional finite-beta solutions of the magnetohydrostatic boundary value problem with the help of the code by Bauer, Betancourt, and Garabedian based on the energy method. In the case of slender 1 — 2 stellarator equilibria the displacement of the magnetic axis as well as its helical deformation as functions of beta are found to be close to the known theoretical predictions which were derived for slender low beta I — 2 configurations of large aspect ratio. In the case of I = 2 stellarators with moderate aspect ratio the shear has a weak effect on the displacement in contradiction to results from asymptotic theories. A class of I = 0,1, 2, 3 configurations with reduced secondary currents could be found showing axis displacements which are at least a factor of three smaller than those in pure I = 2 stellarators. A critical equilibrium beta value of ße(0) = 0.045 has been estimated in the W VII-AS stellarator for a bell-shaped pressure profile. Extensive numerical convergence studies are presented.