Action principles for the Vlasov equation
Five action principles for the Vlasov–Poisson and Vlasov–Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov–Maxwell equations are altered so as to produce the V...
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| Veröffentlicht in: | Physics of fluids. B, Plasma physics Plasma physics, 1992-04, Vol.4 (4), p.771-777 |
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| container_title | Physics of fluids. B, Plasma physics |
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| creator | Ye, Huanchun Morrison, P. J. |
| description | Five action principles for the Vlasov–Poisson and Vlasov–Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov–Maxwell equations are altered so as to produce the Vlasov–Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov–Poisson equation is altered to produce the Vlasov–Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables. |
| doi_str_mv | 10.1063/1.860231 |
| format | Article |
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The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables.</description><identifier>ISSN: 0899-8221</identifier><identifier>EISSN: 2163-503X</identifier><identifier>DOI: 10.1063/1.860231</identifier><identifier>CODEN: PFBPEI</identifier><language>eng</language><publisher>New York, NY: American Institute of Physics</publisher><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY ; 700330 - Plasma Kinetics, Transport, & Impurities- (1992-) ; ACTION INTEGRAL ; CANONICAL TRANSFORMATIONS ; COLLISIONLESS PLASMA ; CONSTRAINTS ; DIFFERENTIAL EQUATIONS ; DISTRIBUTION FUNCTIONS ; EQUATIONS ; Exact sciences and technology ; FUNCTIONALS ; FUNCTIONS ; HAMILTON-JACOBI EQUATIONS ; HAMILTONIAN FUNCTION ; INTEGRALS ; KINETIC EQUATIONS ; MATHEMATICAL SPACE ; MAXWELL EQUATIONS ; PARTIAL DIFFERENTIAL EQUATIONS ; PHASE SPACE ; Physics ; Physics of gases, plasmas and electric discharges ; Physics of plasmas and electric discharges ; PLASMA ; Plasma kinetic equations ; Plasma properties ; POISSON EQUATION ; SPACE ; TRANSFORMATIONS ; VARIATIONAL METHODS</subject><ispartof>Physics of fluids. 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J.</creatorcontrib><title>Action principles for the Vlasov equation</title><title>Physics of fluids. B, Plasma physics</title><description>Five action principles for the Vlasov–Poisson and Vlasov–Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov–Maxwell equations are altered so as to produce the Vlasov–Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov–Poisson equation is altered to produce the Vlasov–Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables.</description><subject>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</subject><subject>700330 - Plasma Kinetics, Transport, & Impurities- (1992-)</subject><subject>ACTION INTEGRAL</subject><subject>CANONICAL TRANSFORMATIONS</subject><subject>COLLISIONLESS PLASMA</subject><subject>CONSTRAINTS</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>DISTRIBUTION FUNCTIONS</subject><subject>EQUATIONS</subject><subject>Exact sciences and technology</subject><subject>FUNCTIONALS</subject><subject>FUNCTIONS</subject><subject>HAMILTON-JACOBI EQUATIONS</subject><subject>HAMILTONIAN FUNCTION</subject><subject>INTEGRALS</subject><subject>KINETIC EQUATIONS</subject><subject>MATHEMATICAL SPACE</subject><subject>MAXWELL EQUATIONS</subject><subject>PARTIAL DIFFERENTIAL EQUATIONS</subject><subject>PHASE SPACE</subject><subject>Physics</subject><subject>Physics of gases, plasmas and electric discharges</subject><subject>Physics of plasmas and electric discharges</subject><subject>PLASMA</subject><subject>Plasma kinetic equations</subject><subject>Plasma properties</subject><subject>POISSON EQUATION</subject><subject>SPACE</subject><subject>TRANSFORMATIONS</subject><subject>VARIATIONAL METHODS</subject><issn>0899-8221</issn><issn>2163-503X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNp90EtLxDAUBeAgCo6j4E8o4sJZdMy7yXIYfMGAGxV3Ic2DqdSmJnHAf29rZXa6upuPczkHgHMElwhyco2WgkNM0AGYYcRJySB5PQQzKKQsBcboGJyk9AYhpoiyGVisTG5CV_Sx6UzTty4VPsQib13x0uoUdoX7-NQjOQVHXrfJnf3eOXi-vXla35ebx7uH9WpTGkJlLjGhlknNEaWV89a6ylkjvYQ18ZZDRDSWjFEjqpozbagQ0lbcEeulqzGXZA4uptyQcqOSabIzWxO6zpmsKgwZ59WAriZkYkgpOq-GAu86fikE1biDQmraYaCXE-11Mrr1UQ9F094TwSCldGCLiY0ffwr_F_mn3YW4d6q3nnwDdoV2gg</recordid><startdate>19920401</startdate><enddate>19920401</enddate><creator>Ye, Huanchun</creator><creator>Morrison, P. 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J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c349t-234d59a61447efdde7edc9f90b3fd6013a29554c87b65ac4889d76e3df9eb2693</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>70 PLASMA PHYSICS AND FUSION TECHNOLOGY</topic><topic>700330 - Plasma Kinetics, Transport, & Impurities- (1992-)</topic><topic>ACTION INTEGRAL</topic><topic>CANONICAL TRANSFORMATIONS</topic><topic>COLLISIONLESS PLASMA</topic><topic>CONSTRAINTS</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>DISTRIBUTION FUNCTIONS</topic><topic>EQUATIONS</topic><topic>Exact sciences and technology</topic><topic>FUNCTIONALS</topic><topic>FUNCTIONS</topic><topic>HAMILTON-JACOBI EQUATIONS</topic><topic>HAMILTONIAN FUNCTION</topic><topic>INTEGRALS</topic><topic>KINETIC EQUATIONS</topic><topic>MATHEMATICAL SPACE</topic><topic>MAXWELL EQUATIONS</topic><topic>PARTIAL DIFFERENTIAL EQUATIONS</topic><topic>PHASE SPACE</topic><topic>Physics</topic><topic>Physics of gases, plasmas and electric discharges</topic><topic>Physics of plasmas and electric discharges</topic><topic>PLASMA</topic><topic>Plasma kinetic equations</topic><topic>Plasma properties</topic><topic>POISSON EQUATION</topic><topic>SPACE</topic><topic>TRANSFORMATIONS</topic><topic>VARIATIONAL METHODS</topic><toplevel>online_resources</toplevel><creatorcontrib>Ye, Huanchun</creatorcontrib><creatorcontrib>Morrison, P. J.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Physics of fluids. B, Plasma physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ye, Huanchun</au><au>Morrison, P. J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Action principles for the Vlasov equation</atitle><jtitle>Physics of fluids. B, Plasma physics</jtitle><date>1992-04-01</date><risdate>1992</risdate><volume>4</volume><issue>4</issue><spage>771</spage><epage>777</epage><pages>771-777</pages><issn>0899-8221</issn><eissn>2163-503X</eissn><coden>PFBPEI</coden><abstract>Five action principles for the Vlasov–Poisson and Vlasov–Maxwell equations, which differ by the variables incorporated to describe the distribution of particles in phase space, are presented. Three action principles previously known for the Vlasov–Maxwell equations are altered so as to produce the Vlasov–Poisson equation upon variation with respect to only the particle variables, and one action principle previously known for the Vlasov–Poisson equation is altered to produce the Vlasov–Maxwell equations upon variations with respect to particle and field variables independently. Also, a new action principle for both systems, which is called the leaf action, is presented. This new action has the desirable features of using only a single generating function as the dynamical variable for describing the particle distribution, and manifestly preserving invariants of the system known as Casimir invariants. The relationships between the various actions are described, and it is shown that the leaf action is a link between actions written in terms of Lagrangian and Eulerian variables.</abstract><cop>New York, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.860231</doi><tpages>7</tpages></addata></record> |
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| ispartof | Physics of fluids. B, Plasma physics, 1992-04, Vol.4 (4), p.771-777 |
| issn | 0899-8221 2163-503X |
| language | eng |
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| source | AIP Digital Archive |
| subjects | 70 PLASMA PHYSICS AND FUSION TECHNOLOGY 700330 - Plasma Kinetics, Transport, & Impurities- (1992-) ACTION INTEGRAL CANONICAL TRANSFORMATIONS COLLISIONLESS PLASMA CONSTRAINTS DIFFERENTIAL EQUATIONS DISTRIBUTION FUNCTIONS EQUATIONS Exact sciences and technology FUNCTIONALS FUNCTIONS HAMILTON-JACOBI EQUATIONS HAMILTONIAN FUNCTION INTEGRALS KINETIC EQUATIONS MATHEMATICAL SPACE MAXWELL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS PHASE SPACE Physics Physics of gases, plasmas and electric discharges Physics of plasmas and electric discharges PLASMA Plasma kinetic equations Plasma properties POISSON EQUATION SPACE TRANSFORMATIONS VARIATIONAL METHODS |
| title | Action principles for the Vlasov equation |
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