Forward and Inverse Cascades in EMHD Turbulence

Abstract

Electron magnetohydrodynamics (EMHD) provides a simple fluid-like description of physics below the proton gyro-scale in collisionless plasmas, such as the solar wind. In this paper, we discuss forward and inverse cascades in EMHD turbulence in the presence of a strong mean magnetic field. Similar to Alfvén waves, EMHD waves, or EMHD perturbations, propagate along magnetic field lines. Therefore, two types of EMHD waves can exist: waves moving parallel to and waves moving anti-parallel to the the magnetic field lines. For energy cascade in EMHD turbulence, the relative amplitudes of opposite-traveling waves are important. When the amplitudes are balanced, we will see fully-developed forward cascade with a k-7/3 energy spectrum and a scale-dependent anisotropy. On the other hand, when the amplitudes are imbalanced, we will see inverse cascade, as well as (presumably not fully developed) forward cascade. The underlying physics for the inverse cascade is magnetic helicity conservation.