Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria

The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stabil...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Physics of plasmas 2020-01, Vol.27 (1)
Hauptverfasser: Kaltsas, D. A., Throumoulopoulos, G. N., Morrison, P. J.
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 1
container_start_page
container_title Physics of plasmas
container_volume 27
creator Kaltsas, D. A.
Throumoulopoulos, G. N.
Morrison, P. J.
description The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.
format Article
fullrecord <record><control><sourceid>osti</sourceid><recordid>TN_cdi_osti_scitechconnect_1801010</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1801010</sourcerecordid><originalsourceid>FETCH-osti_scitechconnect_18010103</originalsourceid><addsrcrecordid>eNqNjMFqAjEQhoO0UNv6DkPPLmRxu7s9i9JDjx68yWwyrtNmJ5iJ0Ly9FnyA8h--7_Dxz8y8tv1H1bVd8_Dnna3attk_mWfVb2tt0773c_OzEUpjqdaoPHFagi-CEzsMoQA6R6o8BFoCiocvHBPKyCigGQcOnAvEI9BvJvHkYcJRKMdT8Snej4DOl1s4JMZX83jEoLS488W8bTe79WcVNfNBHWdyJxdFyOVD3dv6ttW_oit0wEtG</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria</title><source>AIP Journals Complete</source><source>Alma/SFX Local Collection</source><creator>Kaltsas, D. A. ; Throumoulopoulos, G. N. ; Morrison, P. J.</creator><creatorcontrib>Kaltsas, D. A. ; Throumoulopoulos, G. N. ; Morrison, P. J. ; Univ. of Texas, Austin, TX (United States)</creatorcontrib><description>The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.</description><identifier>ISSN: 1070-664X</identifier><identifier>EISSN: 1089-7674</identifier><language>eng</language><publisher>United States: American Institute of Physics (AIP)</publisher><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY ; Calculus of variations ; Hall effect ; Hamiltonian field theory ; Hamiltonian mechanics ; Lagrangian field theories ; Magnetic fields ; Magnetohydrodynamics ; Partial differential equations ; Physics ; Stability theory ; Tokamaks</subject><ispartof>Physics of plasmas, 2020-01, Vol.27 (1)</ispartof><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000000315875072 ; 000000033336687X ; 0000000300769015</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881</link.rule.ids><backlink>$$Uhttps://www.osti.gov/servlets/purl/1801010$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Kaltsas, D. A.</creatorcontrib><creatorcontrib>Throumoulopoulos, G. N.</creatorcontrib><creatorcontrib>Morrison, P. J.</creatorcontrib><creatorcontrib>Univ. of Texas, Austin, TX (United States)</creatorcontrib><title>Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria</title><title>Physics of plasmas</title><description>The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.</description><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</subject><subject>Calculus of variations</subject><subject>Hall effect</subject><subject>Hamiltonian field theory</subject><subject>Hamiltonian mechanics</subject><subject>Lagrangian field theories</subject><subject>Magnetic fields</subject><subject>Magnetohydrodynamics</subject><subject>Partial differential equations</subject><subject>Physics</subject><subject>Stability theory</subject><subject>Tokamaks</subject><issn>1070-664X</issn><issn>1089-7674</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNqNjMFqAjEQhoO0UNv6DkPPLmRxu7s9i9JDjx68yWwyrtNmJ5iJ0Ly9FnyA8h--7_Dxz8y8tv1H1bVd8_Dnna3attk_mWfVb2tt0773c_OzEUpjqdaoPHFagi-CEzsMoQA6R6o8BFoCiocvHBPKyCigGQcOnAvEI9BvJvHkYcJRKMdT8Snej4DOl1s4JMZX83jEoLS488W8bTe79WcVNfNBHWdyJxdFyOVD3dv6ttW_oit0wEtG</recordid><startdate>20200102</startdate><enddate>20200102</enddate><creator>Kaltsas, D. A.</creator><creator>Throumoulopoulos, G. N.</creator><creator>Morrison, P. J.</creator><general>American Institute of Physics (AIP)</general><scope>OIOZB</scope><scope>OTOTI</scope><orcidid>https://orcid.org/0000000315875072</orcidid><orcidid>https://orcid.org/000000033336687X</orcidid><orcidid>https://orcid.org/0000000300769015</orcidid></search><sort><creationdate>20200102</creationdate><title>Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria</title><author>Kaltsas, D. A. ; Throumoulopoulos, G. N. ; Morrison, P. J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-osti_scitechconnect_18010103</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</topic><topic>Calculus of variations</topic><topic>Hall effect</topic><topic>Hamiltonian field theory</topic><topic>Hamiltonian mechanics</topic><topic>Lagrangian field theories</topic><topic>Magnetic fields</topic><topic>Magnetohydrodynamics</topic><topic>Partial differential equations</topic><topic>Physics</topic><topic>Stability theory</topic><topic>Tokamaks</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kaltsas, D. A.</creatorcontrib><creatorcontrib>Throumoulopoulos, G. N.</creatorcontrib><creatorcontrib>Morrison, P. J.</creatorcontrib><creatorcontrib>Univ. of Texas, Austin, TX (United States)</creatorcontrib><collection>OSTI.GOV - Hybrid</collection><collection>OSTI.GOV</collection><jtitle>Physics of plasmas</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kaltsas, D. A.</au><au>Throumoulopoulos, G. N.</au><au>Morrison, P. J.</au><aucorp>Univ. of Texas, Austin, TX (United States)</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria</atitle><jtitle>Physics of plasmas</jtitle><date>2020-01-02</date><risdate>2020</risdate><volume>27</volume><issue>1</issue><issn>1070-664X</issn><eissn>1089-7674</eissn><abstract>The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible stability method. Specifically, we find explicit sufficient stability conditions for axisymmetric XMHD and Hall MHD (HMHD) equilibria with toroidal flow and for equilibria with arbitrary flow under constrained perturbations. The dynamically accessible, second-order variation of the Hamiltonian, which can potentially provide explicit stability criteria for generic equilibria, is also obtained. Moreover, we examine the Lagrangian stability of the general quasineutral two-fluid model written in terms of MHD-like variables, by finding the action and the Hamiltonian functionals of the linearized dynamics, working within a mixed Lagrangian-Eulerian framework. Upon neglecting electron mass, we derive a HMHD energy principle, and in addition, the perturbed induction equation arises from Hamilton's equations of motion in view of a consistency condition for the relation between the perturbed magnetic potential and the canonical variables.</abstract><cop>United States</cop><pub>American Institute of Physics (AIP)</pub><orcidid>https://orcid.org/0000000315875072</orcidid><orcidid>https://orcid.org/000000033336687X</orcidid><orcidid>https://orcid.org/0000000300769015</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1070-664X
ispartof Physics of plasmas, 2020-01, Vol.27 (1)
issn 1070-664X
1089-7674
language eng
recordid cdi_osti_scitechconnect_1801010
source AIP Journals Complete; Alma/SFX Local Collection
subjects 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Calculus of variations
Hall effect
Hamiltonian field theory
Hamiltonian mechanics
Lagrangian field theories
Magnetic fields
Magnetohydrodynamics
Partial differential equations
Physics
Stability theory
Tokamaks
title Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-16T09%3A50%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-osti&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Energy-Casimir,%20dynamically%20accessible,%20and%20Lagrangian%20stability%20of%20extended%20magnetohydrodynamic%20equilibria&rft.jtitle=Physics%20of%20plasmas&rft.au=Kaltsas,%20D.%20A.&rft.aucorp=Univ.%20of%20Texas,%20Austin,%20TX%20(United%20States)&rft.date=2020-01-02&rft.volume=27&rft.issue=1&rft.issn=1070-664X&rft.eissn=1089-7674&rft_id=info:doi/&rft_dat=%3Costi%3E1801010%3C/osti%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true