Relativistic nonlinearity and wave-guide propagation of rippled laser beamin plasma

In the present paper we have investigated the self-focusing behaviour of ra dially symmetrical rippled Gaussian laser beam propagating in a plasma. Con sidering the nonlinearity to arise from relativistic phenomena and followin g the approach of Akhmanov et al, which is based on the WKB and paraxial-ra y approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focu sing of laser beam has been studied for arbitrary large magnitude of nonlin earity. Results indicate that the medium behaves as an oscillatory wave-gui de. The self-focusing is found to depend on the position parameter of rippl e as well as on the beam width. Values of critical power has been calculate d for different values of the position parameter of ripple. Effects of axia lly and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.