Numerical study of $$\delta$$-function current sheets arising from resonant magnetic perturbations
Abstract
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.
- Authors:
-
[1];
[2];
[3];
[4];
[1]
- 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)
- Publication Date:
- Research Org.:
- Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
- Sponsoring Org.:
- USDOE; Simons Foundation; Euratom; Shanghai Pujiang
- OSTI Identifier:
- 1887975
- Alternate Identifier(s):
- OSTI ID: 1856543
- Grant/Contract Number:
- AC02-09CH11466; 560651; 633053; 21PJ1408600
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Plasmas
- Additional Journal Information:
- Journal Volume: 29; Journal Issue: 3; Journal ID: ISSN 1070-664X
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Huang, Yi-Min, Hudson, Stuart R., Loizu, Joaquim, Zhou, Yao, and Bhattacharjee, Amitava. Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations. United States: N. p., 2022.
Web. doi:10.1063/5.0067898.
Huang, Yi-Min, Hudson, Stuart R., Loizu, Joaquim, Zhou, Yao, & Bhattacharjee, Amitava. Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations. United States. https://doi.org/10.1063/5.0067898
Huang, Yi-Min, Hudson, Stuart R., Loizu, Joaquim, Zhou, Yao, and Bhattacharjee, Amitava. Thu .
"Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations". United States. https://doi.org/10.1063/5.0067898. https://www.osti.gov/servlets/purl/1887975.
@article{osti_1887975,
title = {Numerical study of $\delta$-function current sheets arising from resonant magnetic perturbations},
author = {Huang, Yi-Min and Hudson, Stuart R. and Loizu, Joaquim and Zhou, Yao and Bhattacharjee, Amitava},
abstractNote = {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.},
doi = {10.1063/5.0067898},
journal = {Physics of Plasmas},
number = 3,
volume = 29,
place = {United States},
year = {Thu Mar 24 00:00:00 EDT 2022},
month = {Thu Mar 24 00:00:00 EDT 2022}
}
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