In situ observation of three-dimensional anisotropy and scalings of space plasmas turbulence at kinetic scales

Abstract:

The energy distribution at a certain scale (or wave number space) is known to be not isotropic in the turbulence of magnetized plasma, also known as spectral anisotropy. At kinetic scales, the turbulence still remains or becomes much anisotropic than at large magento-fluid scales. In this work, we surveyed the kinetic scale spectral anisotropy of the space plasma turbulence based on five years measurements from Magnetospheric Multiscale mission 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 $\bm{B}_0$, the “statistical eddies” are found to be mostly elongated along $\bm{B}_0$ and shortened in the direction perpendicular to both $\bm{B}_0$ 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. As shown in the median value of the statistical results, the anisotropy relations for the total magnetic field at 0.1-1.0 $d_i$ obey $l_{\parallel} \simeq 2.44 \cdot l_{\perp}^{0.71}$, 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.