Analytically and numerically computed tokamak equilibria at unity beta

The characteristics of near unity-$\beta$ equilibria are investigated with two codes. CUBE is a multigrid Grad-Shafranov solver, and ACUBE was written to compute solutions using analytic unity-$\beta$ equilibria [S.C. Cowley {\em et. al.}, 1991]. Results from each method are quantitatively compared in several distinct equilibrium conditions. These comparisons corroborate the theoretical results and provide benchmarks for high-resolution numerical results available from CUBE. These tools facilitate exploration of many properties of high-$\beta$ equilibria, such as a highly diamagnetic plasma and its ramifications for stability and transport as $\beta$ approaches unity.