Relativistic effects on the magnetisation current in a plasma

Abstract: When a high frequency electromagnetic wave propagates through a plasma (for example a radio wave that enters the ionosphere, or an energetic laser beam that propagates through a fusion plasma) the nonlinearity of the medium give rise to low frequency perturbations of the background state of the plasma. Among other things a low frequency nonlinear current is created. This current in turns creates a low frequency magnetic field that can affect the propagation characteristics of the original high frequency wave. In this degree assignment we have considered, starting from the relativistic Vlasov equation, the case of a collisionless, weakly relativistic electron plasma (with immobile ions constituting a neutralising background) through which two high frequency waves are propagating. The low frequency nonlinear current density which is then created, and the corresponding quasi static magnetic field, have a relativistic contribution. During certain conditions this effect is more important than the non-relativistic contribution. An instructive example of this effect is also given.