## Exact linearized Coulomb collision operator in the moment expansion

## Abstract

In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collision operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.

- Authors:

- Utah State Univ., Logan, UT (United States). Department of Physics

- Publication Date:

- Research Org.:
- Utah State Univ., Logan, UT (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- OSTI Identifier:
- 1247320

- Grant/Contract Number:
- FC02-05ER54812; FG02-04ER54746; FC02-04ER54798

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 13; Journal Issue: 10; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; polynomials; plasma collisions; Boltzmann equations; fluid equations; Maxwell equations

### Citation Formats

```
Ji, Jeong -Young, and Held, Eric D. Exact linearized Coulomb collision operator in the moment expansion. United States: N. p., 2006.
Web. doi:10.1063/1.2356320.
```

```
Ji, Jeong -Young, & Held, Eric D. Exact linearized Coulomb collision operator in the moment expansion. United States. doi:10.1063/1.2356320.
```

```
Ji, Jeong -Young, and Held, Eric D. Thu .
"Exact linearized Coulomb collision operator in the moment expansion". United States. doi:10.1063/1.2356320. https://www.osti.gov/servlets/purl/1247320.
```

```
@article{osti_1247320,
```

title = {Exact linearized Coulomb collision operator in the moment expansion},

author = {Ji, Jeong -Young and Held, Eric D.},

abstractNote = {In the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integro-differential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collision operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Furthermore, useful forms involving the small mass-ratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.},

doi = {10.1063/1.2356320},

journal = {Physics of Plasmas},

number = 10,

volume = 13,

place = {United States},

year = {2006},

month = {10}

}

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