# Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics

## Abstract

A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.

- Authors:

- Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)
- 3311 Black Locust Dr., Sugar Land, Texas 77479 (United States)

- Publication Date:

- OSTI Identifier:
- 22303753

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 21; Journal Issue: 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; EQUILIBRIUM; HAMILTONIANS; MAGNETOHYDRODYNAMICS; TWO-DIMENSIONAL CALCULATIONS; VARIATIONAL METHODS

### Citation Formats

```
Morrison, P. J., E-mail: morrison@physics.utexas.edu, Lingam, M., E-mail: manasvi@physics.utexas.edu, and Acevedo, R., E-mail: raul-ace60@yahoo.com.
```*Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics*. United States: N. p., 2014.
Web. doi:10.1063/1.4891321.

```
Morrison, P. J., E-mail: morrison@physics.utexas.edu, Lingam, M., E-mail: manasvi@physics.utexas.edu, & Acevedo, R., E-mail: raul-ace60@yahoo.com.
```*Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics*. United States. doi:10.1063/1.4891321.

```
Morrison, P. J., E-mail: morrison@physics.utexas.edu, Lingam, M., E-mail: manasvi@physics.utexas.edu, and Acevedo, R., E-mail: raul-ace60@yahoo.com. Fri .
"Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics". United States.
doi:10.1063/1.4891321.
```

```
@article{osti_22303753,
```

title = {Hamiltonian and action formalisms for two-dimensional gyroviscous magnetohydrodynamics},

author = {Morrison, P. J., E-mail: morrison@physics.utexas.edu and Lingam, M., E-mail: manasvi@physics.utexas.edu and Acevedo, R., E-mail: raul-ace60@yahoo.com},

abstractNote = {A general procedure for constructing action principles for continuum models via a generalization of Hamilton's principle of mechanics is described. Through the procedure, an action principle for a gyroviscous magnetohydrodynamics model is constructed. The model is shown to agree with a reduced version of Braginskii's fluid equations. The construction reveals the origin of the gyromap, a device used to derive previous gyrofluid models. Also, a systematic reduction procedure is presented for obtaining the Hamiltonian structure in terms of the noncanonical Poisson bracket. The construction procedure yields a class of Casimir invariants, which are then used to construct variational principles for equilibrium equations with flow and gyroviscosity. The procedure for obtaining reduced fluid models with gyroviscosity is also described.},

doi = {10.1063/1.4891321},

journal = {Physics of Plasmas},

number = 8,

volume = 21,

place = {United States},

year = {Fri Aug 15 00:00:00 EDT 2014},

month = {Fri Aug 15 00:00:00 EDT 2014}

}