Observational quantification of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

TL;DR

This study uses five years of MMS data to statistically analyze the three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales, revealing scale-invariant perpendicular anisotropy and elongated eddies along the magnetic field.

Contribution

First quantification of 3D anisotropies and scalings of space plasma turbulence at sub-ion scales using multi-point structure functions.

Findings

Eddies are elongated along the magnetic field and shortened perpendicular to it.

Perpendicular anisotropy remains scale-invariant across scales.

Quantitative anisotropy relations for magnetic field structures at kinetic scales.

Abstract

A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years measurements from MMS in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion-scales ($<$ 100 km). In the local reference frame $(\hat L_{\perp}, \hat l_{\perp}, \hat l_{\parallel})$ defined with respect to local mean magnetic field $\boldsymbol {B}_0$ (Chen et al. 2012), the "statistical eddies" are found to be mostly elongated along $\boldsymbol {B}_0$ and shortened in the direction perpendicular to both $\boldsymbol {B}_0$ and local field fluctuations. From several $d_i$ (ion inertial length) toward $\sim$ 0.05 $d_i$, the ratio between eddies' parallel and perpendicular lengths features a trend of rise then fall, whereas the anisotropy in the perpendicular plane appears scale-invariant. Specifically, the anisotropy relations for the total magnetic field at 0.1-1.0 $d_i$ are obtained as $l_{\parallel} \simeq 2.44 \cdot l_{\perp}^{0.71}$, and $L_{\perp} \simeq 1.58 \cdot l_{\perp}^{1.08}$, respectively. Our results provide new observational evidence to compare with phenomenological models and numerical simulations, which may help to better understand the nature of kinetic scale turbulence.