Forward and Inverse Cascades of Whistler Turbulence: Three-Dimensional Particle-in-Cell Simulations

Three-dimensional particle-in-cell (PIC) simulations of decaying whistler turbulence in a magnetized, homogeneous, collisionless plasma have been carried out to study the simultaneous processes of forward cascade to shorter wavelength and inverse cascade to longer wavelengths. An initial relatively isotropic spectrum of narrowband whistler mode fluctuations is imposed upon the system. The simulations follow the temporal evolution of the field fluctuations as they decay by cascade processes. The forward cascade yields the usual broadband, short-wavelength spectrum with the usual wavevector anisotropy in the sense of $k_{\perp} >> k_{\parallel}$ where the subscripts denote directions relative to the background magnetic field. The inverse cascade involves a much weaker energy density and a considerably weaker wavevector anisotropy than the forward cascade.