# Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations

## Abstract

This paper presents numerical simulations of the nonlinear cyclokinetic equations in the cyclotron harmonic representation [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Simulations are done with a local flux-tube geometry and with the parallel motion and variation suppressed using a newly developed rCYCLO code. Cyclokinetic simulations dynamically follow the high-frequency ion gyro-phase motion which is nonlinearly coupled into the low-frequency drift-waves possibly interrupting and suppressing gyro-averaging and increasing the transport over gyrokinetic levels. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the breakdown of gyrokinetics at high turbulence levels is quantitatively tested over a range of relative ion cyclotron frequency 10 < Ω*{sup }< 100 where Ω*{sup }= 1/ρ*, and ρ* is the relative ion gyroradius. The gyrokinetic linear mode rates closely match the cyclokinetic low-frequency rates for Ω*{sup }> 5. Gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω*{sup }≥ 50) and low turbulence level as required. Cyclokinetic transport is found to be lower than gyrokinetic transport at high turbulence levels and low-Ω* values with stable ion cyclotron (IC) modes. The gyrokinetic approximation is found to break down when the density perturbations exceed 20%. For cyclokinetic simulations with sufficiently unstable IC modes and sufficientlymore »

- Authors:

- State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China)
- General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States)

- Publication Date:

- OSTI Identifier:
- 22410382

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BREAKDOWN; COMPUTERIZED SIMULATION; CYCLOTRON FREQUENCY; DENSITY; DISTURBANCES; GYROFREQUENCY; IONS; L-MODE PLASMA CONFINEMENT; NONLINEAR PROBLEMS; TURBULENCE; WAVE PROPAGATION

### Citation Formats

```
Deng, Zhao, E-mail: zhao.deng@foxmail.com, and Waltz, R. E.
```*Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations*. United States: N. p., 2015.
Web. doi:10.1063/1.4917176.

```
Deng, Zhao, E-mail: zhao.deng@foxmail.com, & Waltz, R. E.
```*Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations*. United States. doi:10.1063/1.4917176.

```
Deng, Zhao, E-mail: zhao.deng@foxmail.com, and Waltz, R. E. Fri .
"Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations". United States. doi:10.1063/1.4917176.
```

```
@article{osti_22410382,
```

title = {Testing the high turbulence level breakdown of low-frequency gyrokinetics against high-frequency cyclokinetic simulations},

author = {Deng, Zhao, E-mail: zhao.deng@foxmail.com and Waltz, R. E.},

abstractNote = {This paper presents numerical simulations of the nonlinear cyclokinetic equations in the cyclotron harmonic representation [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 (2013)]. Simulations are done with a local flux-tube geometry and with the parallel motion and variation suppressed using a newly developed rCYCLO code. Cyclokinetic simulations dynamically follow the high-frequency ion gyro-phase motion which is nonlinearly coupled into the low-frequency drift-waves possibly interrupting and suppressing gyro-averaging and increasing the transport over gyrokinetic levels. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the breakdown of gyrokinetics at high turbulence levels is quantitatively tested over a range of relative ion cyclotron frequency 10 < Ω*{sup }< 100 where Ω*{sup }= 1/ρ*, and ρ* is the relative ion gyroradius. The gyrokinetic linear mode rates closely match the cyclokinetic low-frequency rates for Ω*{sup }> 5. Gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (Ω*{sup }≥ 50) and low turbulence level as required. Cyclokinetic transport is found to be lower than gyrokinetic transport at high turbulence levels and low-Ω* values with stable ion cyclotron (IC) modes. The gyrokinetic approximation is found to break down when the density perturbations exceed 20%. For cyclokinetic simulations with sufficiently unstable IC modes and sufficiently low Ω*{sup }∼ 10, the high-frequency component of cyclokinetic transport level can exceed the gyrokinetic transport level. However, the low-frequency component of the cyclokinetic transport and turbulence level does not exceed that of gyrokinetics. At higher and more physically relevant Ω*{sup }≥ 50 values and physically realistic IC driving rates, the low-frequency component of the cyclokinetic transport and turbulence level is still smaller than that of gyrokinetics. Thus, the cyclokinetic simulations do not account for the so-called “L-mode near edge short fall” seen in some low-frequency gyrokinetic transport and turbulence simulations.},

doi = {10.1063/1.4917176},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}