Relativistic self-focusing of a rippled laser beam in a plasma

This paper presents an analysis of the relativistic self-focusing of a ripp led Gaussian laser beam in a plasma. Considering the nonlinearity as arisin g owing to relativistic variation of mass, and following the WKB and paraxi al-ray approximations, the phenomenon of self-focusing of rippled laser bea ms is studied for arbitrary magnitude of nonlinearity. Pandey et al. [Phys. Fluids 82, 1221 (1990)] have shown that a small ripple on the axis of the main beam grows very rapidly with distance of propagation as compared with the self-focusing of the main beam. Based on this analogy, we have analysed relativistic self-focusing of rippled beams in plasmas. The relativistic i ntensities with saturation effects of nonlinearity allow the nonlinear refr active index in the paraxial regime to have a slower radial dependence, and thus the ripple extracts relatively less energy from its neighbourhood.