Testing a new differentiable MHD equilibrium solver

Many 3D MHD equilibria solvers exist, each with a set of benefits and drawbacks. However, many are missing a crucial feature: the ability to handle and model chaotic behavior and magnetic islands. The proposed MHD equilibria solver MRX attempts to rectify this problem. This work is grounded in differential geometry and structure-preserving finite element methods (FEM). The code is written in differentiable Python, allowing for faster computational times. In addition to testing the solver’s functionality, work has been done to translate the tools in differential geometry to several 1D and 2D examples, as well as to the ideal MHD Force operator. The eigenvalues of this operator provide insight into certain instabilities and physical phenomena, and the examples confirm the reliability and efficiency of the code. We have (1) implemented the terms of the force operator to construct the Hessian matrix and solve the corresponding eigenproblem, and (2) implemented and benchmarked lower-dimensional examples with high-levels of convergence. Future work includes benchmarking 3D examples in a wider variety of geometries.