Comparison of Analytic and Numerical Unity-$\beta$ Equilibria

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 qualitatively and quantitatively compared across a spectrum of mutually relevant parameters. 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. These tools are intended to facilitate the study of transitions from low to high $\beta$ that avoid MHD instabilities.