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Title: On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory
Authors: Kumar, A.
Loizu, J.
Hole, M. J.
Qu, Zhisong
Hudson, S. R.
Dewar, R. L.
Keywords: Science::Physics
Issue Date: 2023
Source: Kumar, A., Loizu, J., Hole, M. J., Qu, Z., Hudson, S. R. & Dewar, R. L. (2023). On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory. Plasma Physics and Controlled Fusion, 65(7), 075004-.
Journal: Plasma Physics and Controlled Fusion 
Abstract: We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by ‘ideal interfaces’, and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient ∇ p = 0 . The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the ∇ p = 0 in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion 6 101; Glasser et al 1975 Phys. Fluids 18 875-88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.
ISSN: 0741-3335
DOI: 10.1088/1361-6587/acc96e
Schools: School of Physical and Mathematical Sciences 
Rights: © 2023 The Author(s). Published by IOP Publishing Ltd. Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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