Computation of stable equilibria in minimum- B mirror devices

Abstract

We present a three-dimensional code that solves for plasma equilibria in open-field geometries, which allows analysis of most minimum- B mirror systems. Open confinement with p = p( B) only requires the hydromagnetic equilibrium equation to reduce to one elliptic, scalar partial differential equation involving a tensor pressure. The finite difference form of the equation is solved by an implicit iterative algorithm similar to the ADI (alternating direction implicit) method. Cylindrical grid coordinates are employed, and the mesh spacing is variable to allow representation of far boundary conditions. We have time-optimized the program, so the memory requirements are large. It is found that, when the threshold for hydromagnetic instability is passed, the hydromagnetic equilibrium equation becomes hyperbolic, which leads to an ill-posed problem as predicted by Grad. Equilibria are found for an increasing sequence of pressures until the instability threshold is reached. The present code utilized planes of inversion symmetry common to many minimum- B devices, to allow a reduction in the domain to be studied; Ioffe bar devices, Baseball II, 2 X-II, and the proposed mirror fusion experiment are representable. We present sample results for Baseball II and the Ioffe bar device, including cases near the high beta instability threshold.