Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Kumar, A.; Qu, Z.; Hole, M. J.; Wright, A. M.; Loizu, J.; Hudson, S. R.; Baillod, A.; Dewar, R. L.; Ferraro, N. M.

doi:10.1088/1361-6587/abdbd0

Title: Computation of linear MHD instabilities with the multi-region relaxed MHD energy principle

Journal Article · 10 February 2021 · Plasma Physics and Controlled Fusion

DOI: https://doi.org/10.1088/1361-6587/abdbd0 · OSTI ID:1817209

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Australian National Univ., Canberra, ACT (Australia). Mathematical Sciences Inst.
Australian National Univ., Canberra, ACT (Australia). Mathematical Sciences Inst.; Australian Nuclear Science and Technology Organisation (ANSTO), Kirrawee, NSW (Australia)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Ecole Polytechnique Federale Lausanne (Switzerland). Swiss Plasma Center

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C¹ code and the tearing mode $$\Delta^{^{\prime}}$$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Overall, our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

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Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: Australian Research Council (ARC); EUROfusion Consortium; Simons Foundation; USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1817209

Journal Information:: Plasma Physics and Controlled Fusion, Journal Name: Plasma Physics and Controlled Fusion Journal Issue: 4 Vol. 63; ISSN 0741-3335

Publisher:: IOP ScienceCopyright Statement

Country of Publication:: United States

Language:: English

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