Exact analytic anisotropic three-dimensional equilibria with nested magnetic surfaces, confined drift orbits and without spatial symmetry
Abstract
Exact toroidal fluid and kinetic equilibria with nested magnetic surfaces and no continuous symmetry are of great interest in laboratory, astrophysical and space plasmas. Their existence and stability have been open in physics and mathematics for decades. We construct such anisotropic-pressure equilibria by applying the Clemente transformation to exact vacuum fields. They connect smoothly to these fields on a fixed regular domain and preserve a regular magnetic axis, perfectly nested surfaces and spatially varying rotational transform. To our knowledge, the sheared configurations are the first exact anisotropic equilibria combining these properties with positive pressures and a positive firehose margin. The fixed-boundary Chew--Goldberger--Low (CGL) quadratic energy splits into a nonnegative vacuum-field term and a local pressure term, nonnegative for p_perp/p_parallel <= (3+\sqrt{21})/2 ~ 3.79. For p_parallel >= p_perp each configuration minimizes the finite-amplitude CGL energy over smooth boundary-fixed ideal material deformations. For the current-free configurations, physical guiding-center distributions produce these pressures within the same bound, with no free energy for magnetic-moment-conserving electrostatic perturbations. Trapped particles inherit the vacuum field's second adiabatic invariant at a rescaled magnetic moment, so local closed action contours carry over. The equilibrium code DESC reproduces them from the exact solution. Kinetic stability for surface-dependent rescalings and against general nonlinear electromagnetic perturbations remains open.
Related
- Analytic toroidal 3D MHD equilibria and steady Euler flows with invariant surfaces
- Geometrical Confinement of Magnetic Domains and Domain Walls on Two-Dimensional Cylindrical-Shaped Ferromagnetic Surfaces
- Analytic non-axisymmetric 3D MHD equilibria without stellarator symmetry
- A Variational Framework for Guiding-Center Kinetics, Anisotropic Equilibria, and Quasisymmetry in Stellarators
- Phase equilibria in MnSb2Te4 – GeSb2Te4 system and magnetic properties of Mn1-xGexSb2Te4 solid solutions
BibTeX
@misc{bhattacharjee2026exact,
title = {{Exact analytic anisotropic three-dimensional equilibria with nested magnetic surfaces, confined drift orbits and without spatial symmetry}},
author = {A. Bhattacharjee and W. Sengupta and V. N. Duarte and L. Fu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10786},
eprint = {2611.10786},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10786},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact analytic anisotropic three-dimensional equilibria with nested magnetic surfaces, confined drift orbits and without spatial symmetry
AU - A. Bhattacharjee
AU - W. Sengupta
AU - V. N. Duarte
AU - L. Fu
PY - 2026
DA - 2026/11/07
PB - arXiv
DO - 10.48550/arxiv.2611.10786
UR - https://arxiv.org/abs/2611.10786
AB - Exact toroidal fluid and kinetic equilibria with nested magnetic surfaces and no continuous symmetry are of great interest in laboratory, astrophysical and space plasmas. Their existence and stability have been open in physics and mathematics for decades. We construct such anisotropic-pressure equilibria by applying the Clemente transformation to exact vacuum fields. They connect smoothly to these fields on a fixed regular domain and preserve a regular magnetic axis, perfectly nested surfaces and spatially varying rotational transform. To our knowledge, the sheared configurations are the first exact anisotropic equilibria combining these properties with positive pressures and a positive firehose margin. The fixed-boundary Chew--Goldberger--Low (CGL) quadratic energy splits into a nonnegative vacuum-field term and a local pressure term, nonnegative for p_perp/p_parallel <= (3+\sqrt{21})/2 ~ 3.79. For p_parallel >= p_perp each configuration minimizes the finite-amplitude CGL energy over smooth boundary-fixed ideal material deformations. For the current-free configurations, physical guiding-center distributions produce these pressures within the same bound, with no free energy for magnetic-moment-conserving electrostatic perturbations. Trapped particles inherit the vacuum field's second adiabatic invariant at a rescaled magnetic moment, so local closed action contours carry over. The equilibrium code DESC reproduces them from the exact solution. Kinetic stability for surface-dependent rescalings and against general nonlinear electromagnetic perturbations remains open.
ER -