Advancing novel group theoretical algorithms for the evaluation of MHD stability in complex 3D geometry

We present recent progress in the exploration of symmetry adapted Lanczos (SAL) methods employing group theory to analyze the discrete eigenvalues and continuous spectra of the ideal MHD force operator in conjunction with a new code for evaluating linear (global) ideal MHD stability in stellarator geometry utilizing Julia’s high performance mathematical libraries. SAL methods reduce the global eigenvalue problem into independent sub-problems partitioned by the geometric symmetries of stellarator configurations, allowing for (i) elimination of spectral pollution (numerical error caused by the continuous spectra) and (ii) adept exploitation of high performance computing (HPC) resources. 

Efficient and accurate evaluation of linear ideal MHD stability along with a thorough analysis of the ideal MHD eigenspectrum for complex 3D geometries is crucial to the design and optimization of next-generation stellarators for fusion energy. The development of mathematically rigorous SAL methods is key for precise, detailed, and computationally feasible (via modern HPC capabilities) stability evaluations and eigenspectrum analyses of stellarator configurations.