Relativistic interaction of rippled laser beams with plasmas

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.