The effect of displacement current on whistler propagation of a fast-rising magnetic field

Abstract

The effect of the displacement current on the magnetic field propagation into plasmas in the form of a whistler wave is studied. For times between the electron and the ion cyclotron periods and if the plasma is tenuous so that the electron plasma frequency is smaller than the cyclotron frequency, the magnetic field is shown to be governed by the Telegraph equation with complex coefficients. The propagation of a fast-rising magnetic field is examined and at early times the magnetic field is shown to propagate as a left-polarized wave with the light velocity. At a later time the magnetic field propagates as the dispersive whistler wave and is governed by the diffusion equation with a complex coefficient [Fruchtman and Maron, Phys. Fluids B 3, 1546 (1991)]. As expected, the front of the wave keeps propagating with the finite velocity of light. The effect of collisional resistivity is also considered.