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.