Numerical methods for nonlinear simulations of cyclokinetics illustrating the breakdown of gyrokinetics at high turbulence levels
This paper presents the numerical methods for the nonlinear simulations of cyclokinetic [Waltz and Zhao Deng (2013)] equations in Fourier harmonics of the gyro-phase. A parallel processed, implicit time advanced, Eulerian (or continuum) code (rCYCLO) is developed. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantees accurate conservation of the incremental entropy. By comparing the cyclokinetic simulations with the corresponding gyrokinetics, we quantitatively test the breakdown of gyrokinetics at high turbulence levels over a range of large relative ion cyclotron frequency (10<??<100 10 < ? ? < 100 where ?? ? ? =1/?? = 1 / ? ? , and ?? ? ? is the relative ion gyroradius). As an important code verification, the rCYCLO gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency (???50 ? ? ? 50 ) and low turbulence levels. In the case of linearly stable ion cyclotron modes, the cyclokinetic transport is lower (not higher) than the gyrokinetic transport at high turbulence levels and low-?? ? ? values.
cyclokinetics gyrokinetics turbulence ion cyclotron modes drift-waves