Ultrashort pulse propagation in a magnetized plasma

The theoretical description of the propagation of an ultrashort pulse in a dispersive and dissipative medium, e.g. a plasma, in the presence of a magnetic field is performed in the space-time domain using a Green's function approach. For the purpose a model equation is constructed in which the source term is represented by a delta-function in space and time. The model equation, which is of the Klein-Gordon type can be given an explicit solution directly in the form of a delta-function part and a wake-field part, for which the argument of a Bessel function contains all the parameters of the problem. The results thus reveal the influence on the Green's function of the plasma frequency, the gyro-magnetic frequency and the damping rate. The resulting Green's function can then be used to derive the plasma response of an ultrashort pulse of arbitrary shape and structure by direct integration of the product of the Green's function and the initial pulse over the spatial source domain. The results should be of interest for diagnostics of plasmas and other media with dispersive and dissipative properties.