Theory and simulations of whistler wave propagation

A linear theory of whistler waves is developed within the paradigm of a two-dimensional incompressible electron magnetohydrodynamics model. Exact analytic wave solutions are obtained for small-amplitude whistler waves that exhibit magnetic field topological structures consistent with the observations and our simulations in a linear regime. In agreement with experiment, we find that the parallel group velocity of the wave is large compared to its perpendicular counterpart. Numerical simulations of collisional interactions demonstrate that the wave magnetic field either coalesces or repels depending upon the polarity of the associated current. In the nonlinear regime, our simulations demonstrate that the evolution of the wave magnetic field is governed essentially by the nonlinear Hall force.