Comparison of stability characteristics of different smoothness classes of MHD equilibria

We present a comparison of the stability properties of magnetohydrodynamic (MHD) equilibria characterized by different smoothness i.e., C^0, C^1, C^{\infty}, to examine whether there exist fundamental differences in the physical features of these states. Specifically, we use the Energy Principle to analyze how physical properties associated with contributions arising from smooth and non-smooth terms lead to stabilizing and/or destabilizing effects on steady state, magnetically confined fusion plasmas.

Understanding the properties of 3D MHD equilibria is essential for both stellarators and tokamaks. In the absence of axisymmetry, magnetic fields admit a variety of rich topological structures that can profoundly impact transport and confinement properties in fusion plasmas. Over the years, numerous classes of smooth and non-smooth MHD equilibria have been proposed, particularly for 3D equilibria. Non-smooth equilibria can admit structures including discontinuous pressure profiles and current densities, for which the physical interpretation and implications remain to be fully understood.