# Fluid theory of magnetized plasma dynamics at low collisionality

## Abstract

Finite Larmor radius (FLR) fluid equations for magnetized plasmas evolving on either sonic or diamagnetic drift time scales are derived consistent with a broad low-collisionality hypothesis. The fundamental expansion parameter is the ratio {delta} between the ion Larmor radius and the shortest macroscopic length scale (including fluctuation wavelengths in the absence of small scale turbulence). The low-collisionality regime of interest is specified by assuming that the other two basic small parameters--namely, the ratio between the electron and ion masses and the ratio between the ion collision and cyclotron frequencies--are comparable to or smaller than {delta}{sup 2}. First significant order FLR equations for the stress tensors and the heat fluxes are given, including a detailed discussion of the collisional terms that need be retained under the assumed orderings and of the closure terms that need be determined kinetically. This analysis is valid for any magnetic geometry and for fully electromagnetic nonlinear dynamics with arbitrarily large fluctuation amplitudes. It is also valid for strong anisotropies and does not require the distribution functions to be close to Maxwellians. With a subsidiary small-parallel-gradient ordering for large-aspect-ratio toroidal plasmas in a strong but weakly inhomogeneous magnetic field, a new system of reduced two-fluid equations ismore »

- Authors:

- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States)

- Publication Date:

- OSTI Identifier:
- 20974987

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 5; Other Information: DOI: 10.1063/1.2717595; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ASPECT RATIO; CYCLOTRON FREQUENCY; DISTRIBUTION FUNCTIONS; ELECTRON TEMPERATURE; ELECTRONS; FLUCTUATIONS; HEAT FLUX; ION COLLISIONS; ION TEMPERATURE; IONS; LARMOR RADIUS; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NONLINEAR PROBLEMS; PLASMA; PLASMA DENSITY; PLASMA DIAMAGNETISM; PLASMA FLUID EQUATIONS

### Citation Formats

```
Ramos, J. J.
```*Fluid theory of magnetized plasma dynamics at low collisionality*. United States: N. p., 2007.
Web. doi:10.1063/1.2717595.

```
Ramos, J. J.
```*Fluid theory of magnetized plasma dynamics at low collisionality*. United States. doi:10.1063/1.2717595.

```
Ramos, J. J. Tue .
"Fluid theory of magnetized plasma dynamics at low collisionality". United States.
doi:10.1063/1.2717595.
```

```
@article{osti_20974987,
```

title = {Fluid theory of magnetized plasma dynamics at low collisionality},

author = {Ramos, J. J.},

abstractNote = {Finite Larmor radius (FLR) fluid equations for magnetized plasmas evolving on either sonic or diamagnetic drift time scales are derived consistent with a broad low-collisionality hypothesis. The fundamental expansion parameter is the ratio {delta} between the ion Larmor radius and the shortest macroscopic length scale (including fluctuation wavelengths in the absence of small scale turbulence). The low-collisionality regime of interest is specified by assuming that the other two basic small parameters--namely, the ratio between the electron and ion masses and the ratio between the ion collision and cyclotron frequencies--are comparable to or smaller than {delta}{sup 2}. First significant order FLR equations for the stress tensors and the heat fluxes are given, including a detailed discussion of the collisional terms that need be retained under the assumed orderings and of the closure terms that need be determined kinetically. This analysis is valid for any magnetic geometry and for fully electromagnetic nonlinear dynamics with arbitrarily large fluctuation amplitudes. It is also valid for strong anisotropies and does not require the distribution functions to be close to Maxwellians. With a subsidiary small-parallel-gradient ordering for large-aspect-ratio toroidal plasmas in a strong but weakly inhomogeneous magnetic field, a new system of reduced two-fluid equations is derived, rigorously taking into account all the diamagnetic effects associated with arbitrary density and anisotropic temperature gradients.},

doi = {10.1063/1.2717595},

journal = {Physics of Plasmas},

number = 5,

volume = 14,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}