Verification of the ideal MHD response at rational surfaces in VMEC

Authors:   Samuel A. Lazerson, Princeton Plasma Physics Laboratory
, Joaquim Loizu, Max-Plank Intitute-fur-Plamaphysik,
 Steven Hirshman, Oak Ridge National Laboratory
, Stuart R. Hudson, Princeton Plasma Physics Lab

Abstract:  The VMEC nonlinear ideal MHD equilibrium code [1] is verified against analytic linear ideal MHD theory in a screw-pinch-like
configuration, in order to verify the code response at rational surfaces. A large aspect ratio circular cross section zero-beta equilibrium is considered. This equilibrium possess a rational surface with safety factor q = 2 at a normalized flux value of 0.5. A small resonant boundary perturbation is introduced, exciting a response at the resonant rational surface. The code is found to capture the plasma response as predicted by a newly developed analytic theory that ensures the existence of nested flux surfaces by allowing for a jump in rotational transform (ι = 1=q). The VMEC code satisfactorily reproduces these theoretical results without the necessity of an explicit transform discontinuity (Δι
) at the rational surface. It is found that the response across the rational surfaces depends upon both radial grid resolution and local shear (dι / dΦ), where ι is the rotational transform and Φ the enclosed toroidal flux). Calculations of an implicit
 Δι
 suggest it does not arise due to numerical artifacts (attributed to radial finite differences in VMEC) or existence conditions for flux surfaces as predicted by linear theory (minimum values of Δι

). Scans of the rotational transform profile indicate that for experimentally relevant levels of transform shear, the response becomes increasing localised. Careful examination of a DIII-D equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.
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Submitted to:  Physics of Plasmas
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Download PPPL-5205 (pdf 2.5 MB 11 pp)
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