Numerical study of -function current sheets arising from resonant magnetic perturbations
arXiv:2108.09327 · doi:10.1063/5.0067898
Abstract
General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal MHD limit has been a significant challenge. This work presents numerical solutions 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 while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution approaches the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate excellent agreement between the numerical solutions obtained from the two codes through a thorough convergence study.
References in corpus (6)
- Variational integration for ideal magnetohydrodynamics with built-in advection equations
- Do Potential Fields Develop Current Sheets Under Simple Compression or Expansion?
- On the non-existence of stepped-pressure equilibria far from symmetry
- An adjoint method for determining the sensitivity of island size to magnetic field variations
- Islands and current singularities in quasisymmetric toroidal plasmas
- Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities