Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

TL;DR

This study analyzes magnetic field fluctuations in Earth's magnetosheath at kinetic scales, demonstrating that turbulence can be modeled by Markov processes, with results aligning with theoretical Fokker-Planck solutions and revealing universal scale invariance.

Contribution

It applies Markov process analysis to kinetic-scale turbulence in Earth's magnetosheath, extending previous large-scale studies and confirming the universality of turbulence characteristics across scales.

Findings

Markov processes describe turbulence at kinetic scales.

Fokker-Planck solutions match observed probability densities.

Turbulence exhibits universal scale invariance across kinetic regimes.

Abstract

In our previous studies we have examined solar wind and magnetospheric plasmas turbulence, including Markovian character on large inertial magneto-hydrodynamic scales. Here we present the results of statistical analysis of magnetic field fluctuations in the Earth's magnetosheath based on Magnetospheric Multiscale mission at much smaller kinetic scales. Following our results on spectral analysis with very large slopes of about -16/3, we apply Markov processes approach to turbulence in this kinetic regime. It is shown that the Chapman-Kolmogorov equation is satisfied and the lowest-order Kramers-Moyal coefficients describing drift and diffusion with a power-law dependence are consistent with a generalized Ornstein-Uhlenbeck process. The solutions of the Fokker-Planck equation agree with experimental probability density functions, which exhibit a universal global scale invariance through the kinetic domain. In particular, for moderate scales we have the kappa distribution described by various peaked shapes with heavy tails, which with large values of kappa parameter are reduced to the Gaussian distribution for large inertial scales. This shows that the turbulence cascade can be described by the Markov processes also on very small scales. The obtained results on kinetic scales may be useful for better understanding of the physical mechanisms governing turbulence