Self‐distortion of a whistler pulse in a plasma

Following the technique used by Akhmanov et al. to solve the nonlinear wave equation, we have investigated the propagation of temporally and spatially gaussian whistler pulses in a plasma. In the linear case the temporal width of the pulse is enhanced (due to dispersion) at a distance R ˜ τ 2 v 3 g /(∂ 2 ω/∂ k 2 ) whereas its size is enhanced (due to diffraction) over a length R d ∼ 2 kr 2 0 /(1 + ϵ + /ϵ zz ); τ, r 0 , k , v g , ϵ + , and ϵ zz are the initial time width, size, wave vector, group velocity, and the components of the dielectric tensor of the plasma. In the case of a high‐power whistler, the ponderomotive nonlinearity causes self‐focusing (for all values of ω/ω c ) of the whistler and results in severe distortion of the pulse shape.