Cascade conditions in electron magneto-hydrodynamic turbulence

The basic features of electron whistler waves can be described by electron magneto-hydrodynamics. In terms of this model, we discuss criteria and relevant parameter ranges for dual and forward cascades in electron whistler turbulence. It is an advantage to use the set of eigenfunctions for the “curl” operator in the analysis. It is demonstrated that three wavemodes with same helicity support a dual cascade as know also from spatially two dimensional turbulence, while modes with mixed helicities include the classical cascade of energy from long to shorter wavelengths. The analysis is based on the conservation of energy and magnetic helicity during the wave interactions. For stationary conditions in large closed systems, a detailed balance can be expected. It is, however, possible for large-scale self-organized structures to develop as transient phenomena. These can be found when solving initial value problem with a strong imbalance of positive and negative helicities. For plasmas in nature or laboratory, similar conditions can occur when the system has boundary conditions with preference for emission of oscillations with one sign of helicity.