# Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations

## Abstract

A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated.

- Authors:

- Publication Date:

- Sponsoring Org.:
- (US)

- OSTI Identifier:
- 40205954

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 7; Journal Issue: 12; Other Information: DOI: 10.1063/1.1322063; Othernumber: PHPAEN000007000012004816000001; 044012PHP; PBD: Dec 2000; Journal ID: ISSN 1070-664X

- Publisher:
- The American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DISTRIBUTION; ENERGY CONSERVATION; LAGRANGIAN FUNCTION; PHASE SPACE; PHYSICS

### Citation Formats

```
Brizard, Alain J.
```*Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations*. United States: N. p., 2000.
Web. doi:10.1063/1.1322063.

```
Brizard, Alain J.
```*Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations*. United States. doi:10.1063/1.1322063.

```
Brizard, Alain J. Fri .
"Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations". United States. doi:10.1063/1.1322063.
```

```
@article{osti_40205954,
```

title = {Variational principle for nonlinear gyrokinetic Vlasov--Maxwell equations},

author = {Brizard, Alain J},

abstractNote = {A new variational principle for the nonlinear gyrokinetic Vlasov--Maxwell equations is presented. This Eulerian variational principle uses constrained variations for the gyrocenter Vlasov distribution in eight-dimensional extended phase space and turns out to be simpler than the Lagrangian variational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive self-consistent, nonlinear, low-frequency Vlasov--Maxwell bounce-gyrokinetic equations, in which the fast gyromotion and bounce-motion time scales have been eliminated.},

doi = {10.1063/1.1322063},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 12,

volume = 7,

place = {United States},

year = {2000},

month = {12}

}

DOI: 10.1063/1.1322063

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