Numerical approach to delta-function current sheets arising from resonant magnetic perturbations

Apr 15, 2021, 8:00 am9:00 am


Event Description

A virtual Simons' Hour Talk by Yi-Min Huang

Note the time: 8:00am EDT / 12:00 UTC.  Zoom link will be sent via email.

General three-dimensional toroidal ideal magnetohydrodynamic equilibria with nested flux surfaces are susceptible to the formation of singular current sheets at surfaces resonant with externally imposed perturbations. The presence of singular current sheets indicates that magnetic reconnection will ensue, forming magnetic islands or regions of stochastic field lines. Numerically resolving singular current sheets has been a significant challenge. In this talk, I will present recent progress on the numerical solution of the Hahm-Kulsrud-Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad-Shafranov (GS) solver and the SPEC code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MrxMHD), where the solution relaxes to a Taylor state in each region. As the number of regions increases, the SPEC solution approaches ideal MHD and agrees with the high-resolution GS solution. This result is the first to show that SPEC can tackle current sheets induced by resonant magnetic perturbation even when the rotational transform is continuous.