# Non-axisymmetric MHD equilibria with an arbitrary number of field periods

“Non-axisymmetric MHD equilibria with an arbitrary number of field periods” (2026), by Opal Issan et al. Physics and Astronomy research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Opal Issan, Lucas José, Matt Landreman, J. Citrin, Brendan Tracey
- Published: November 5, 2026
- Field: Physics and Astronomy
- DOI: https://doi.org/10.48550/arxiv.2611.07672
- Free PDF: https://arxiv.org/pdf/2611.07672

## 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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