Comparative MMS analysis of Markov turbulence in the magnetosheath on kinetic scales

Abstract

We apply Fokker-Planck equation to investigate processes responsible for turbulence in space plasma. In our previous studies, we have shown that turbulence in the inertial range of hydromagnetic scales exhibits Markov properties [1,2]. We have also extended this statistical approach on much smaller scales, where kinetic theory should be applied. Namely, we have already obtained the results of the statistical analysis of magnetic field fluctuations in the Earth’s magnetosheath based on the Magnetospheric Multiscale (MMS) mission [3]. Here we compare the characteristics of turbulence behind the bow shock, inside the magnetosheath, and near the magnetopause. We check whether the second order approximation of the Fokker-Planck equation leads to kappa distribution of the probability density function provided that the first Kramers-Moyal coefficient is linear and the second term is quadratic, describing drift and diffusion correspondingly, which is a generalization of Ornstein-Uhlenbeck process. In some cases the power-law distributions are recovered. For moderate scales we have the kappa distributions described by various peaked shapes with heavy tails. In particular, for large values of the kappa parameter this is reduced to the normal Maxellian distribution. The obtained results on kinetic scales could be important for a better understanding of the physical mechanism governing turbulent systems in laboratory and space.Keywords: Kinetic scales, Markov processes, MMS probe, Plasmas, Solar wind, Turbulence.Acknowledgments. This work has been supported by the National Science Centre, Poland (NCN), through grant No. 2021/41/B/ST10/00823.