Scale-dependent Skewness and Kurtosis in Kinetic Plasmas and Magnetohydrodynamic Systems

Turbulence systems are known to exhibit fluctuations which deviate from Gaussian statistics and display intermittency at small scales. Strong intermittency driven by coherent structures, such as vortices and current sheets, is frequently observed in simulations and space measurements, and is central to understanding turbulent energy dissipation and particle energization. High-order structure functions, particularly the third- and fourth-order moments -- skewness (S) and kurtosis (K) -- provide accessible, partial quantification of non-Gaussianity. In hydrodynamic turbulence, S and K display well-established behaviors depending on Reynolds number, and are theoretically predicted to asymptote to fixed values at sub-inertial scales. We aim to extend this framework to collisionless space plasmas by examining the scale-dependent S and K of magnetic field fluctuation increments. High-resolution in situ measurements from different spacecraft enable study of the asymptotic behavior of S and K toward small spatial lag. Preliminary analysis of the MMS unbiased campaign indicates a power-law scaling relationship between S and K at around half the ion inertial scale. From both Cluster and MMS measurements, there is a tendency for S to re-Gaussianize toward smaller scales, possibly caused by wave interactions and thermalization. We also aim to complement the observations with magnetohydrodynamic (MHD) and particle-in-cell (PIC) simulations to understand the relationship of S and K between fluid and collisionless environments.