Phase mixing of relativistically intense waves in a cold homogeneous plasma

Breaking of upper hybrid oscillations in the presence of an inhomogeneous magnetic field

We present space-time evolution of large-amplitude upper hybrid modes in a cold homogeneous plasma in the presence of an inhomogeneous magnetic field. Using the method of Lagrange variables, an exact space-time-dependent solution is obtained in parametric form. It is found that the magnetic field inhomogeneity causes various nonlinearly excited modes to couple, resulting in phase mixing and eventual breaking of the initially excited mode. The occurrence of wave breaking is seen by the appearance of spikes in the density profile. These results will be of relevance to laboratory and space plasma situations in which the external magnetic field is inhomogeneous.

Breaking of longitudinal Akhiezer-Polovin waves

The breaking of longitudinal Akhiezer-Polovin (AP) waves is demonstrated using a one-dimensional simulation based on the Dawson sheet model. It is found that the AP longitudinal waves break through the process of phase mixing at an amplitude well below the breaking amplitude for AP waves, when subjected to arbitrarily small longitudinal perturbations. Results from the simulation show a good agreement with the Dawson phase mixing formula modified to include relativistic mass variation effects. This result may be of direct relevance to the laser- or particle-beam plasma wakefield experiments.