Magnetohydrodynamic Equilibrium Calculation with Voigt-Regularization

Three-dimensional toroidal magnetohydrodynamic (MHD) equilibria with a continuum of nested magnetic flux surfaces often exhibit singular current density on surfaces where the rotational transforms are rational numbers. In actual plasma systems, non-ideal effects disrupt the flux surfaces that surround the singular current densities, resulting in the creation of magnetic islands or regions with chaotic field lines. This work explores Voigt-regularized MHD as a possible solution to the issue of singular current densities arising in ideal MHD models with nested flux surfaces. Voigt regularization modifies the MHD dynamics by introducing additional terms, which vanish as the solution asymptotically becomes time-independent in the infinite time limit. Therefore, Voigt regularization does not affect the force balance in MHD equilibria. On the other hand, the Voigt regularization of the induction equation is analogous to the electron inertia effect, thereby allowing magnetic reconnection and breaking of magnetic flux surfaces. The utility of the Voigt-MHD system in obtaining MHD equilibria without the assumption of nested flux surfaces is demonstrated by numerical solutions of simple test problems.