Nature of ideal MHD instabilities as described by multi-region relaxed MHD

A. Kumar; C. Nührenberg; Z. Qu; M. J. Hole; J. Doak; R. L. Dewar; S. R. Hudson; J. Loizu; K. Aleynikova; A. Baillod; H. Hezaveh

doi:10.1088/1361-6587/ac53ee

Nature of ideal MHD instabilities as described by multi-region relaxed MHD

A. Kumar^*, C. Nührenberg, Z. Qu, M. J. Hole, J. Doak, R. L. Dewar, S. R. Hudson, J. Loizu, K. Aleynikova, A. Baillod, H. Hezaveh

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.

Original language	English
Article number	065001
Journal	Plasma Physics and Controlled Fusion
Volume	64
Issue number	6
DOIs	https://doi.org/10.1088/1361-6587/ac53ee
Publication status	Published - Jun 2022

Access to Document

10.1088/1361-6587/ac53ee

Cite this

@article{2c43c126b6af4353bd0f5ef8cd865fac,

title = "Nature of ideal MHD instabilities as described by multi-region relaxed MHD",

abstract = "In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.",

keywords = "linear MHD instability, multi-region relaxed (MRx) MHD, relaxed MHD, stepped pressure equilibria",

author = "A. Kumar and C. N{\"u}hrenberg and Z. Qu and Hole, {M. J.} and J. Doak and Dewar, {R. L.} and Hudson, {S. R.} and J. Loizu and K. Aleynikova and A. Baillod and H. Hezaveh",

note = "Publisher Copyright: {\textcopyright} 2022 IOP Publishing Ltd.",

year = "2022",

month = jun,

doi = "10.1088/1361-6587/ac53ee",

language = "English",

volume = "64",

journal = "Plasma Physics and Controlled Fusion",

issn = "0741-3335",

publisher = "IOP Publishing Ltd.",

number = "6",

}

TY - JOUR

T1 - Nature of ideal MHD instabilities as described by multi-region relaxed MHD

AU - Kumar, A.

AU - Nührenberg, C.

AU - Qu, Z.

AU - Hole, M. J.

AU - Doak, J.

AU - Dewar, R. L.

AU - Hudson, S. R.

AU - Loizu, J.

AU - Aleynikova, K.

AU - Baillod, A.

AU - Hezaveh, H.

PY - 2022/6

Y1 - 2022/6

N2 - In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.

AB - In this work, the stepped pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502), which computes the equilibria of the multi-region relaxed magnetohydrodynamic energy principle (MRxMHD), has been upgraded to determine the MRxMHD stability in toroidal geometry. A theoretical formalism for SPEC is obtained by relating the second variation of the MRxMHD energy functional to the Hessian matrix, enabling the prediction of magnetohydrodynamic (MHD) linear instabilities. Negative eigenvalues of this matrix imply instability. Further, we demonstrate our method on simplified test scenarios in both tokamak and stellarator magnetic topologies, with a systematic comparison study between the marginal stability prediction of the SPEC with the ideal MHD stability code packages CAS3D and MISHKA-1.

KW - linear MHD instability

KW - multi-region relaxed (MRx) MHD

KW - relaxed MHD

KW - stepped pressure equilibria

UR - http://www.scopus.com/inward/record.url?scp=85129584884&partnerID=8YFLogxK

U2 - 10.1088/1361-6587/ac53ee

DO - 10.1088/1361-6587/ac53ee

M3 - Article

SN - 0741-3335

VL - 64

JO - Plasma Physics and Controlled Fusion

JF - Plasma Physics and Controlled Fusion

IS - 6

M1 - 065001

ER -

Nature of ideal MHD instabilities as described by multi-region relaxed MHD

Abstract

Access to Document

Other files and links

Fingerprint

Cite this