An investigation of the growth of a radially symmetrical ripple, superimpos
ed on a Gaussian laser beam in a plasma is presented. Based on WKB and para
xial ray approximation the phenomenon of relativistic self-focusing (RSF) i
s analytically investigated. The differential equation for beamwidth parame
ter of rippled laser beam is evaluated. The ripple gets focused when the in
itial power of the ripple is greater than the critical power for focusing.
The focusing is found to be considerably affected by the power of the main
beam and the phase angle between the electric vectors of the main beam and
the ripple. At higher intensities the saturation effects of nonlinearity be
come predominant, making the nonlinear refractive index in the paraxial reg
ion have slower radial dependence, and thus the ripple extract relatively l
ess energy from its neighborhood. The case of magnetized plasmas is also pr
eliminarily discussed.