Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry

Abstract

Analytical solutions to the three-dimensional ideal magnetohydrodynamic equilibrium equations $(\nabla \times \vec{B}) \times \vec{B} = \nabla p$ and $\nabla \cdot \vec{B} = 0$ provide benchmarks for stellarator equilibrium codes. Two families of non-axisymmetric solutions were recently discovered by Landreman [arXiv:2609.26742] as counterexamples to Grad's conjecture, but both satisfy stellarator symmetry. Here, we generalize both families by introducing a symmetry-breaking parameter into each of the solutions, resulting in new non-axisymmetric solutions that break stellarator symmetry and reduce to the stellarator symmetric solutions when the newly introduced parameter is set to zero.