On quasisymmetric plasma equilibria sustained by small force

Abstract

We construct smooth, non-symmetric plasma equilibria which possess closed, nested flux surfaces and solve the magnetohydrostatic (steady three-dimensional incompressible Euler) equations with a small force. The solutions are also `nearly' quasisymmetric. The primary idea is, given a desired quasisymmetry direction $\xi$, to change the smooth structure on space so that the vector field $\xi$ is Killing for the new metric and construct $\xi$--symmetric solutions of the magnetohydrostatic equations on that background by solving a generalized Grad-Shafranov equation. If $\xi$ is close to a symmetry of Euclidean space, then these are solutions on flat space up to a small forcing.

arXiv comment24 pages, 2 figures, accepted version

References in corpus (7)

• Computation of multi-region relaxed magnetohydrodynamic equilibria
• Necessary and Sufficient Conditions for Quasisymmetry
• Flexibility and rigidity in steady fluid motion
• Quasi-axisymmetric magnetic fields: weakly non-axisymmetric case in a vacuum
• Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis
• Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions
• Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria

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• Measures of quasisymmetry for stellarators
• Magnetic Relaxation of a Voigt-MHD System
• Generalized Boozer coordinates: a natural coordinate system for quasisymmetry
• Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface
• Islands and current singularities in quasisymmetric toroidal plasmas
• Flexibility and rigidity of free boundary MHD equilibria
• Relaxed Magnetohydrodynamics with Ideal Ohm's Law Constraint
• Existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains with non-tangential quasisymmetry
• Connection between quasi-symmetric magnetic fields and anisotropic pressure equilibria in fusion plasmas
• Quasisymmetric magnetic fields in asymmetric toroidal domains
• Rigidity of Beltrami fields with a non-constant proportionality factor
• Steady plasma flows in a periodic non-symmetric domain
• Weakly Quasisymmetric Near-Axis Solutions to all Orders