Developing novel group theoretical algorithms for evaluating MHD stability in complex geometry*

We present recent progress on the development of a new code for evaluating linear (global) ideal MHD stability in stellarator geometry, using Julia’s high performance mathematical libraries. Here, we focus on the exploration of novel algorithms, based on representation theory of finite groups, that serve the dual purpose of (i) reducing the complex, global problem to simpler eigenvalue problems over the invariant subspaces of symmetry groups in stellarators and; (ii) minimize the impact of spectral pollution, allowing accurate location of continuous spectra and discrete eigenvalues for scalable, high-performance calculations. 

Efficient and accurate evaluation of linear ideal MHD stability is a crucial step in the design and analysis of next-generation stellarators for fusion energy. In ideal MHD, spectral pollution is an error that occurs in numerical eigenvalue calculations, which grows with increasing wavenumber and is compounded by the presence of the Alfvén continuum. This makes the development of mathematically rigorous algorithms key in developing modern tools for high performance evaluation of MHD stability in complex 3D geometry.