# On push-forward representations in the standard gyrokinetic model

## Abstract

Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.

- Authors:

- Japan Atomic Energy Agency, 2-116 Omotedate, Obuchi, Rokkasho, Aomori 039-3212 (Japan)
- Max-Planck-Institut für Plasmaphysik, D-85748 Garching (Germany)

- Publication Date:

- OSTI Identifier:
- 22407981

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 22; Journal Issue: 1; Other Information: (c) 2015 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; DISTRIBUTION FUNCTIONS; FLUCTUATIONS; GYROMAGNETIC RATIO; LARMOR RADIUS; MATHEMATICAL SOLUTIONS; POISSON EQUATION; POLARIZATION; POTENTIALS; SCALARS; TRANSFORMATIONS

### Citation Formats

```
Miyato, N., E-mail: miyato.naoaki@jaea.go.jp, Yagi, M., and Scott, B. D..
```*On push-forward representations in the standard gyrokinetic model*. United States: N. p., 2015.
Web. doi:10.1063/1.4905705.

```
Miyato, N., E-mail: miyato.naoaki@jaea.go.jp, Yagi, M., & Scott, B. D..
```*On push-forward representations in the standard gyrokinetic model*. United States. doi:10.1063/1.4905705.

```
Miyato, N., E-mail: miyato.naoaki@jaea.go.jp, Yagi, M., and Scott, B. D.. Thu .
"On push-forward representations in the standard gyrokinetic model". United States.
doi:10.1063/1.4905705.
```

```
@article{osti_22407981,
```

title = {On push-forward representations in the standard gyrokinetic model},

author = {Miyato, N., E-mail: miyato.naoaki@jaea.go.jp and Yagi, M. and Scott, B. D.},

abstractNote = {Two representations of fluid moments in terms of a gyro-center distribution function and gyro-center coordinates, which are called push-forward representations, are compared in the standard electrostatic gyrokinetic model. In the representation conventionally used to derive the gyrokinetic Poisson equation, the pull-back transformation of the gyro-center distribution function contains effects of the gyro-center transformation and therefore electrostatic potential fluctuations, which is described by the Poisson brackets between the distribution function and scalar functions generating the gyro-center transformation. Usually, only the lowest order solution of the generating function at first order is considered to explicitly derive the gyrokinetic Poisson equation. This is true in explicitly deriving representations of scalar fluid moments with polarization terms. One also recovers the particle diamagnetic flux at this order because it is associated with the guiding-center transformation. However, higher-order solutions are needed to derive finite Larmor radius terms of particle flux including the polarization drift flux from the conventional representation. On the other hand, the lowest order solution is sufficient for the other representation, in which the gyro-center transformation part is combined with the guiding-center one and the pull-back transformation of the distribution function does not appear.},

doi = {10.1063/1.4905705},

journal = {Physics of Plasmas},

number = 1,

volume = 22,

place = {United States},

year = {Thu Jan 15 00:00:00 EST 2015},

month = {Thu Jan 15 00:00:00 EST 2015}

}