INVERSE ENERGY CASCADE AND IMBALANCED ELECTRON MAGNETOHYDRODYNAMIC TURBULENCE

Electron magnetohydrodynamic (EMHD) turbulence provides a fluid-like description of small-scale magnetized plasmas. Most EMHD turbulence studies consider "balanced" EMHD turbulence. However, imbalanced EMHD turbulence has never been studied. In this study, we numerically study "imbalanced" EMHD turbulence. Imbalanced turbulence means that wave packets moving in one direction have high amplitudes or strong perturbations than the others. In driven imbalanced EMHD turbulence, non-zero magnetic helicity is injected. When magnetic helicity is injected at a scale, we expect to have inverse cascade of magnetic helicity, as well as magnetic energy, in three-dimensional (3D) EMHD turbulence. For no helicity injection, we do not observe inverse energy cascade. However, when magnetic helicity is injected, inverse cascade of magnetic helicity is clearly observed. Magnetic energy also shows inverse cascade. In EMHD turbulence, it is well known that magnetic energy on scales smaller than the energy injection scale is forward-cascading quantity and the magnetic energy spectrum follows a k^{-7/3} one. On the other hand, the inverse-cascading entity on scales larger than the energy injection scale is uncertain. If the magnetic helicity is inverse-cascading quantity, we will obtain a k^{-5/3} magnetic energy spectrum. In our simulations, we do observe energy spectrum consistant with k^{-5/3} on large scales. Therefore, we confirm that magnetic helicity indeed is the inverse-cascading entity in 3D EMHD turbulence.