# New Variational Principle for the Vlasov-Maxwell Equations

## Abstract

A new Eulerian variational principle is presented for the Vlasov-Maxwell equations. This principle uses constrained variations for the Vlasov distribution in eight-dimensional extended phase space. The standard energy-momentum conservation law is then derived explicitly by the Noether method. This new variational principle can be applied to various reduced Vlasov-Maxwell equations in which fast time scales have been asymptotically eliminated (e.g., low-frequency gyrokinetic theory). (c) 2000 The American Physical Society.

- Authors:

- Publication Date:

- OSTI Identifier:
- 20216893

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 25; Other Information: PBD: 19 Jun 2000; Journal ID: ISSN 0031-9007

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOLTZMANN-VLASOV EQUATION; MAXWELL EQUATIONS; VARIATIONAL METHODS; KINETIC EQUATIONS; CONSERVATION LAWS; THEORETICAL DATA

### Citation Formats

```
Brizard, Alain J.
```*New Variational Principle for the Vlasov-Maxwell Equations*. United States: N. p., 2000.
Web. doi:10.1103/PhysRevLett.84.5768.

```
Brizard, Alain J.
```*New Variational Principle for the Vlasov-Maxwell Equations*. United States. doi:10.1103/PhysRevLett.84.5768.

```
Brizard, Alain J. Mon .
"New Variational Principle for the Vlasov-Maxwell Equations". United States. doi:10.1103/PhysRevLett.84.5768.
```

```
@article{osti_20216893,
```

title = {New Variational Principle for the Vlasov-Maxwell Equations},

author = {Brizard, Alain J},

abstractNote = {A new Eulerian variational principle is presented for the Vlasov-Maxwell equations. This principle uses constrained variations for the Vlasov distribution in eight-dimensional extended phase space. The standard energy-momentum conservation law is then derived explicitly by the Noether method. This new variational principle can be applied to various reduced Vlasov-Maxwell equations in which fast time scales have been asymptotically eliminated (e.g., low-frequency gyrokinetic theory). (c) 2000 The American Physical Society.},

doi = {10.1103/PhysRevLett.84.5768},

journal = {Physical Review Letters},

issn = {0031-9007},

number = 25,

volume = 84,

place = {United States},

year = {2000},

month = {6}

}

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