# Gyrokinetic Landau collision operator in conservative form

## Abstract

A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator’s conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present modelmore »

- Authors:

- Publication Date:

- DOE Contract Number:
- FC02-08ER54966

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center

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

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

- OSTI Identifier:
- 1881330

- DOI:
- https://doi.org/10.7910/DVN/H4TFRB

### Citation Formats

```
Pan, Qingjiang, and Ernst, Darin R.
```*Gyrokinetic Landau collision operator in conservative form*. United States: N. p., 2019.
Web. doi:10.7910/DVN/H4TFRB.

```
Pan, Qingjiang, & Ernst, Darin R.
```*Gyrokinetic Landau collision operator in conservative form*. United States. doi:https://doi.org/10.7910/DVN/H4TFRB

```
Pan, Qingjiang, and Ernst, Darin R. 2019.
"Gyrokinetic Landau collision operator in conservative form". United States. doi:https://doi.org/10.7910/DVN/H4TFRB. https://www.osti.gov/servlets/purl/1881330. Pub date:Tue Apr 09 00:00:00 EDT 2019
```

```
@article{osti_1881330,
```

title = {Gyrokinetic Landau collision operator in conservative form},

author = {Pan, Qingjiang and Ernst, Darin R.},

abstractNote = {A gyrokinetic linearized exact (not model) Landau collision operator is derived by transforming the symmetric and conservative Landau form. The formulation obtains the velocity-space flux density and preserves the operator’s conservative form as the divergence of this flux density. The operator contains both test-particle and field-particle contributions, and finite Larmor radius effects are evaluated in either Bessel function series or gyrophase integrals. While equivalent to the gyrokinetic Fokker–Planck form with Rosenbluth potentials [B. Li and D. R. Ernst, Phys. Rev. Lett. 106, 195002 (2011)], the gyrokinetic conservative Landau form explicitly preserves the symmetry between test-particle and field-particle contributions, which underlies the conservation laws and the H theorem, and enables discretization with a finite-volume or spectral method to preserve the conservation properties numerically, independent of resolution. The form of the exact linearized field-particle terms differs from those of widely used model operators. We show the finite Larmor radius corrections to the field-particle terms in the exact linearized operator involve Bessel functions of all orders, while present model field-particle terms involve only the first two Bessel functions. This new symmetric and conservative formulation enables the gyrokinetic exact linearized Landau operator to be implemented in gyrokinetic turbulence codes for comparison with present model operators using similar numerical methods.},

doi = {10.7910/DVN/H4TFRB},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2019},

month = {4}

}

Works referencing / citing this record:

##
Gyrokinetic Landau collision operator in conservative form

journal, February 2019

- Pan, Qingjiang; Ernst, Darin R.
- Physical Review E, Vol. 99, Issue 2