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Title: Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code

The VMEC nonlinear ideal MHD equilibrium code [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] is compared against analytic linear ideal MHD theory in a screw-pinch-like configuration. The focus of such analysis is to verify the ideal MHD response at magnetic surfaces which possess magnetic transform (ι) which is resonant with spectral values of the perturbed boundary harmonics. 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 suggestmore » that 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 profile indicate that for experimentally relevant levels of transform shear the response becomes increasing localised. Furthermore, careful examination of a large experimental tokamak equilibrium, with applied resonant fields, indicates that this shielding response is present, suggesting the phenomena is not limited to this verification exercise.« less
ORCiD logo [1] ;  [2] ;  [3] ; ORCiD logo [1]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Max-Planck-Institut fur Plasmaphysik, Greifswald (Germany)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Report Number(s):
Journal ID: ISSN 1070-664X; PHPAEN
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 23; Journal Issue: 1; Related Information: A publisher's note has been published for this content:Publisher's Note: “Verification of the ideal magnetohydrodynamic response at rational surfaces in the VMEC code” [Phys. Plasmas 23, 012507 (2016)]; Journal ID: ISSN 1070-664X
American Institute of Physics (AIP)
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
Country of Publication:
United States
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; equilibrium; MHD - toridal; pinch; magnetohydrodynamics; toroidal plasma confinement; discontinues; current density; magnetic resonance
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1234781