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.