On quasisymmetric plasma equilibria sustained by small force

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 $ξ$, to change the smooth structure on space so that the vector field $ξ$ is Killing for the new metric and construct $ξ$--symmetric solutions of the magnetohydrostatic equations on that background by solving a generalized Grad-Shafranov equation. If $ξ$ is close to a symmetry of Euclidean space, then these are solutions on flat space up to a small forcing.

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