Self-focusing of radiation beams in plasmas

In laser driven accelerators it is highly desirable to transport an intense radiation beam over a distance of many Rayleigh lengths. Without additional focusing mechanisms, a laser beam in vacuum diffracts on the scale of a Rayleigh length. For certain accelerator schemes, such as the beat wave accelerator, it is possible for the background plasma to provide the necessary focusing for laser transport over many Rayleigh lengths. The transport of laser beams through plasmas is studied both analytically and numerically. This analysis is based on an envelope equation derived from the ray equations of geometric optics. The resulting envelope equation describes the evolution of the mean radius of a radiation field which can be approximated by a Gaussian profile. This formulation describes propagation through plasmas with arbitrary density profiles