Cascades in decaying three-dimensional electron magnetohydrodynamic turbulence

Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k(-2) law with increasing R-B, the ratio of the nonlinear to linear time scales in the governing equation, consistent with theoretical predictions. No evidence is round or a, dissipative cutoff, consistent with non-local spectral energy transfer and recent studies of 2D EMHD turbulence. Dissipative cutoffs found in previous studies are explained as artificial effects of hyperdiffusivity. In another similarity to 2D EMHD turbulence, relatively stationary structures are found to develop in time, rather than the variability found in ordinary or MHD turbulence. Further cascades of energy in 3D EMHD turbulence am found to be suppressed in all directions under the influence of a uniform background Held. Energy transfer is further reduced in the direction parallel to the field displaying scale-dependent anisotropy. Finally, the governing equation is found to yield a weak inverse cascade, at least partially transferring magnetic energy from small to large scales.