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.

Flexibility and rigidity of free boundary MHD equilibria

“…In the special case of u = 0 (G = 0), we deduce that the self-supporting magnetic field must be radial. This result was obtained recently by Hamel and Nadirashvili [14] (Theorem 1.10 therein) and is meaningful in the context of Grad's conjecture concerning rigidity of magnetohydrostatic equilibria, see discussion in [3,4].…”

Relaxed magnetohydrodynamics with ideal Ohm's law constraint

“…Potential applications include reconnection events and the conjectured formation of equilibrium fractal magnetic and fluid flow patterns in 3-D systems. Other potential physical phenomena to investigate in 3-D systems include the linear normal mode spectrum, nonlinear saturation, bifurcations to oscillatory modes and the effect of quasisymmetry (Nührenberg & Zille 1988;Burby, Kallinikos & MacKay 2020;Rodriguez, Helander & Bhattacharjee 2020;Constantin, Drivas & Ginsberg 2021) on 3-D equilibria with flow (Vanneste & Wirosoetisno 2008).…”

Islands and current singularities in quasisymmetric toroidal plasmas

“…Throughout the present paper, we shall also adopt this simple form of equilibrium in order to make comparisons with existing literature clear. However, it is worth noting that recent research points towards force balance with more general forces (in particular anisotropic pressure) as a more natural framework in which to deal with quasisymmetric fields 3,[5][6][7] . An analysis of singularities in the context of more general forces of equilibrium is left for future work.…”