Growth of a Gaussian ripple on a uniform-plane wave front in plasmas

Abstract

This paper presents an investigation of the growth of a Guassian ripple on a uniform-plane electromagnetic wave front in plasmas. The redistribution of electron density in a plasma because of nonuniform intensity distribution along an electromagnetic wave front gives rise to a nonlinear dependence of the effective dielectric constant on the intensity. The redistribution in collisionless plasmas takes place because of ponderomotive force; this is also true in collisional plasmas for periods less than the energy relaxation time τε. The redistribution in collisional plasmas for periods greater than the energy relaxation time τε is on account of the nonuniform heating of electrons along the wave front. This nonlinearity in the effective dielectric constant makes a ripple of a given radius to self-focus, when the initial power of the ripple (P) is between two critical powers (Pcr1<P<Pcr2). When P≳Pcr2 or P<Pcr1, respectively, oscillatory and monotonic defocusing of the ripple occurs. For powers P lying between Pcr1<P<Pcr2, oscillatory self-focusing of the ripple takes place. The critical power for self-focusing of the ripple and the nature of self-focusing is highly dependent on the power of the main beam, the phase difference between the electric vector of the ripple and main beam, and the absorption. The analysis is also valid for a weakly inhomogeneous plasma within the WKB approximation.