Role of reconnection in inertial kinetic-Alfvén turbulence

Stanislav Boldyrev,Nuno F Loureiro

doi:10.1103/physrevresearch.1.012006

Abstract

In a weakly collisional, low-electron-beta plasma, large-scale Alfv\'en turbulence transforms into inertial kinetic-Alfv\'en turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from $(d_e/a)^{1/2}$ to $d_e/a$ depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from $k^{-8/3}$ to $k^{-3}$, and the corresponding spectral anisotropy with respect to the strong background magnetic field from $k_z\lesssim k_\perp^{2/3}$ to $k_z\lesssim k_\perp$.

Highlights

Large-scale low-frequency fluctuations in astrophysical systems such as the interstellar medium, the solar wind, and others, are associated with nearly incompressible magnetohydrodynamic (Alfvén) turbulence (e.g., Refs. [1,2,3])
We have proposed a conceptual framework to describe a turbulent cascade in the inertial kinetic-Alfvén regime—relevant to the Earth’s magnetosheath region and to the solar wind in the proximity of the solar corona
As in previous recent work [35,40], we conjecture that the turbulent cascade is determined by the timescale associated with the fastest tearing instability at each scale

Summary

Rapid Communications

We propose that at such kinetic scales, the nonlinear dynamics tends to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale a in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from (de/a)1/2 to de/a depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from k−8/3 to k−3, and the corresponding spectral anisotropy with respect to the strong background magnetic field from kz k⊥2/3 to kz k⊥

Introduction

Published by the American Physical Society

Discussion and conclusion