# Differential formulation of the gyrokinetic Landau operator

## Abstract

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

- Authors:

- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Saint Michael's College, Colchester, VT (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Saint Michael's College, Colchester, VT (United States)

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

- OSTI Identifier:
- 1351535

- Report Number(s):
- PPPL-5340

Journal ID: ISSN 0022-3778; PII: S0022377816001203

- Grant/Contract Number:
- AC02-09CH11466; SC0014032

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Plasma Physics

- Additional Journal Information:
- Journal Volume: 83; Journal Issue: 1; Journal ID: ISSN 0022-3778

- Publisher:
- Cambridge University Press

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; fusion plasma; plasma nonlinear phenomena; plasma simulation

### Citation Formats

```
Hirvijoki, Eero, Brizard, Alain J., and Pfefferlé, David.
```*Differential formulation of the gyrokinetic Landau operator*. United States: N. p., 2017.
Web. doi:10.1017/s0022377816001203.

```
Hirvijoki, Eero, Brizard, Alain J., & Pfefferlé, David.
```*Differential formulation of the gyrokinetic Landau operator*. United States. doi:10.1017/s0022377816001203.

```
Hirvijoki, Eero, Brizard, Alain J., and Pfefferlé, David. Thu .
"Differential formulation of the gyrokinetic Landau operator". United States.
doi:10.1017/s0022377816001203. https://www.osti.gov/servlets/purl/1351535.
```

```
@article{osti_1351535,
```

title = {Differential formulation of the gyrokinetic Landau operator},

author = {Hirvijoki, Eero and Brizard, Alain J. and Pfefferlé, David},

abstractNote = {Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this work investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Finally, based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.},

doi = {10.1017/s0022377816001203},

journal = {Journal of Plasma Physics},

number = 1,

volume = 83,

place = {United States},

year = {Thu Jan 05 00:00:00 EST 2017},

month = {Thu Jan 05 00:00:00 EST 2017}

}

Free Publicly Available Full Text

Publisher's Version of Record

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.