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On quasisymmetric plasma equilibria sustained by small force

Published online by Cambridge University Press:  11 February 2021

Peter Constantin ,
Theodore D. Drivas  and
Daniel Ginsberg Open the ORCID record for Daniel Ginsberg [Opens in a new window]
Peter Constantin
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ08544, USA
Theodore D. Drivas
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ08544, USA
Daniel Ginsberg*
Affiliation:
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ08544, USA
*
†Email address for correspondence: dg42@math.princeton.edu
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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.

Keywords

fusion plasma
Type
Research Article
Information
Journal of Plasma Physics , Volume 87 , Issue 1 , February 2021 , 905870111
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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References

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