Abstract
This article presents the paraxial theory of the propagation of an initially Gaussian electromagnetic beam in an inhomogeneous plasma with an overdense region; in contrast to earlier work on penetration in overdense plasma, higher order terms (up to r(4)) in the expansion of the dielectric function and the eikonal have been taken into account. Three types of nonlinearities, viz., collisional, ponderomotive, and relativistic, have been considered. As expected the higher order terms do not affect the critical curves, corresponding to initial propagation without convergence or divergence. It is seen that the inclusion of higher order terms does significantly affect the dependence of the beam width on the distance of propagation. Corresponding to the case of ponderomotive nonlinearity numerical results for the dependence of beam width parameter and the axial dielectric function on the distance of propagation have been presented for specific values of the initial beam width and axial irradiance and specific spatial dependence of the electron density in the absence of the beam. Both the situations, viz., formation of bright or dark rings in the transverse irradiation pattern, have been considered. From a parametric analysis the dependence of the maximum penetration (when the axial dielectric function tends to zero) on the axial irradiance and an inhomogeneity parameter has been graphically illustrated. (C) 2008 American Institute of Physics.