摘要
Cyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 （2013）]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlineaxly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency （ion cyclotron frequency） regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1. This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22（5）, 056101 （2015）] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian （or continuum） scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 （2015）]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω＊ values with stable ion cyclotr
Cyrokinetics is widely applied in plasma physics. However, this framework is limited to weak turbulence levels and low drift-wave frequencies because high-frequency gyro-motion is reduced by the gyro-phase averaging. In order to test where gyrokinetics breaks down, Waltz and Zhao developed a new theory, called cyclokinetics [R. E. Waltz and Zhao Deng, Phys. Plasmas 20, 012507 （2013）]. Cyclokinetics dynamically follows the high-frequency ion gyro-motion which is nonlineaxly coupled to the low-frequency drift-waves interrupting and suppressing gyro-averaging. Cyclokinetics is valid in the high-frequency （ion cyclotron frequency） regime or for high turbulence levels. The ratio of the cyclokinetic perturbed distribution function over equilibrium distribution function δf/F can approach 1. This work presents, for the first time, a numerical simulation of nonlinear cyclokinetic theory for ions, and describes the first attempt to completely solve the ion gyro-phase motion in a nonlinear turbulence system. Simulations are performed [Zhao Deng and R. E. Waltz, Phys. Plasmas 22（5）, 056101 （2015）] in a local flux-tube geometry with the parallel motion and variation suppressed by using a newly developed code named rCYCLO, which is executed in parallel by using an implicit time-advanced Eulerian （or continuum） scheme [Zhao Deng and R. E. Waltz, Comp. Phys. Comm. 195, 23 （2015）]. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantee saccurate conservation of incremental entropy. By comparing the more fundamental cyclokinetic simulations with the corresponding gyrokinetic simulations, the gyrokinetics breakdown condition is quantitatively tested. Gyrokinetic transport and turbulence level recover those of cyclokinetics at high relative ion cyclotron frequencies and low turbulence levels, as required. Cyclokinetic transport and turbulence level are found to be lower than those of gyrokinetics at high turbulence levels and low-Ω＊ values with stable ion cyclotr
作者
Zhao Deng
R. E. Waltz
Xiaogang Wang
赵登;R. E. Waltz;王晓钢(Institute of Fluid Physics, China Academy of Engineering Physics, P.O. Box 919-108, Mianyang 621900, China;State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China;General Atomics, P.O. Box 85608, San Diego, CA 92186-5608, USA;Department of Physics, Harbin Institute of Technology, Harbin 150001, China)
