Non-axisymmetric MHD equilibria with an arbitrary number of field periods
Abstract
Several closed-form non-axisymmetric magnetic fields with nested toroidal flux surfaces have recently been discovered as exact benchmarks for verifying three-dimensional magnetohydrodynamic equilibrium codes. However, all of these solutions have at most two field periods (N ≤ 2), i.e., identical segments that repeat toroidally. Here, we derive closed-form non-axisymmetric magnetohydrodynamic equilibria for an arbitrary integer number of field periods N ≥ 1. The equilibria have non-constant pressure and closed magnetic field lines with either zero rotational transform (ι= 0) for N ≥ 1 or integer rotational transform (ι= ± N) for N ≥ 3. For the reflection-symmetric ι= 0 equilibria, we also construct a matched exterior vacuum field with continuous magnetic field across the plasma boundary, providing a benchmark for free-boundary equilibrium codes.
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BibTeX
@misc{issan2026nonaxisymmetric,
title = {{Non-axisymmetric MHD equilibria with an arbitrary number of field periods}},
author = {Opal Issan and Lucas José and Matt Landreman and Jonathan Citrin and Brendan Tracey},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07672},
eprint = {2611.07672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07672},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Non-axisymmetric MHD equilibria with an arbitrary number of field periods
AU - Opal Issan
AU - Lucas José
AU - Matt Landreman
AU - Jonathan Citrin
AU - Brendan Tracey
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07672
UR - https://arxiv.org/abs/2611.07672
AB - Several closed-form non-axisymmetric magnetic fields with nested toroidal flux surfaces have recently been discovered as exact benchmarks for verifying three-dimensional magnetohydrodynamic equilibrium codes. However, all of these solutions have at most two field periods (N ≤ 2), i.e., identical segments that repeat toroidally. Here, we derive closed-form non-axisymmetric magnetohydrodynamic equilibria for an arbitrary integer number of field periods N ≥ 1. The equilibria have non-constant pressure and closed magnetic field lines with either zero rotational transform (ι= 0) for N ≥ 1 or integer rotational transform (ι= ± N) for N ≥ 3. For the reflection-symmetric ι= 0 equilibria, we also construct a matched exterior vacuum field with continuous magnetic field across the plasma boundary, providing a benchmark for free-boundary equilibrium codes.
ER -