Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations

Huang, Yi-Min; Hudson, Stuart R.; Loizu, Joaquim; Zhou, Yao; Bhattacharjee, Amitava

doi:10.1063/5.0067898

Numerical study of $$\delta$$-function current sheets arising from resonant magnetic perturbations

Journal Article · Thu Mar 24 00:00:00 EDT 2022 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0067898· OSTI ID:1887975

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Princeton University, NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Ecole Polytechnique Federale Lausanne (EPFL Switzerland)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Shanghai Jiao Tong University (China)

We report 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 magnetohydrodynamics (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 Stepped Pressure Equilibrium Code (SPEC) code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), whereby 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 appears to approach the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate agreement between the numerical solutions obtained from the two codes through a convergence study.

View Accepted Manuscript (DOE)

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: Euratom; Shanghai Pujiang; Simons Foundation; USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1887975

Alternate ID(s):: OSTI ID: 1856543

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 3 Vol. 29; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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