Whistler turbulence inverse cascade: Three-dimensional particle-in-cell simulations

Three-dimensional particle-in-cell (PIC) simulations of whistler turbulence have been carried out in a magnetized, homogeneous, collisionless plasma of initial $\beta_e =$ 0.10. The simulations begin with anisotropic bi-Maxwellian electron velocity distributions with $T_{\perp e}/T_{\parallel e} >$ 1, leading to the growth of the whistler anisotropy instability. The simulations follow the temporal evolution of the field fluctuations as they grow and saturate with largest amplitudes at $kbzero$ and $k_{\parallel} c/\omega_{pe} \simeq$ 1.0. The counter-propagating enhanced fluctuations drive an inverse cascade to longer wavelengths at $k_{\parallel} c/\omega_{pe} <<$ 1 with $k_{\perp} > k_{\parallel}$. Computations have been done at various values of the electron electron temperature anisotropy, and physical interpretations for the results of these simulations will be provided.