# Action principles for extended magnetohydrodynamic models

## Abstract

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.

- Authors:

- Institute for Fusion Studies and Department of Physics, The University of Texas at Austin, Austin, Texas 78712 (United States)
- Department of Physical and Biological Sciences, Western New England University, Springfield, Massachusetts 01119 (United States)

- Publication Date:

- OSTI Identifier:
- 22303430

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; ELECTRONS; EQUATIONS OF MOTION; FLUIDS; HAMILTONIANS; MAGNETOHYDRODYNAMICS; PLASMA; PLASMA EXPANSION; SYMMETRY; VARIATIONAL METHODS

### Citation Formats

```
Keramidas Charidakos, I., Lingam, M., Morrison, P. J., White, R. L., and Wurm, A.
```*Action principles for extended magnetohydrodynamic models*. United States: N. p., 2014.
Web. doi:10.1063/1.4896336.

```
Keramidas Charidakos, I., Lingam, M., Morrison, P. J., White, R. L., & Wurm, A.
```*Action principles for extended magnetohydrodynamic models*. United States. doi:10.1063/1.4896336.

```
Keramidas Charidakos, I., Lingam, M., Morrison, P. J., White, R. L., and Wurm, A. Mon .
"Action principles for extended magnetohydrodynamic models". United States. doi:10.1063/1.4896336.
```

```
@article{osti_22303430,
```

title = {Action principles for extended magnetohydrodynamic models},

author = {Keramidas Charidakos, I. and Lingam, M. and Morrison, P. J. and White, R. L. and Wurm, A.},

abstractNote = {The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.},

doi = {10.1063/1.4896336},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 21,

place = {United States},

year = {2014},

month = {9}

}