Nonstationary self-focusing of a Gaussian pulse in a plasma

In this paper the self−focusing of a cylindrically symmetric Gaussian (in space and time) electromagnetic pulse in collisionless and collisional plasmas has been studied by considering the ponderomotive force and the nonuniform heating (and consequent redistribution of electrons) as the sources of nonlinearity. The duration of the pulse is considered larger than the characteristic time of nonlinearity; the WKB and paraxial ray approximations have been used to solve the wave equation. It is found that the beam is focused in a moving filament. Because of relaxation effects the peak of the pulse is shifted to higher values of t−z/vg (in the case of collisional plasmas) and the pulse is severely distorted because of self−focusing; the shift of peak in the case of collisionless plasmas is not significant.