Temporal growth of filamentation instability in plasmas

In this paper we have derived an expression for the growth rate of filamentation instability, valid for arbitrary intensity of the electromagnetic wave and upto plasma resonance (ω/sub p/> or =ω0 here ω/sub p/ and ω0 are the field free plasma frequency and EM wave frequency respectively). In a collisionless plasma and on the short time scale (ttau/sub epsilon/, tau/sub epsilon/ being the energy relaxation time) in a collisional plasma, the nonlinearity arises on account of pondermotive force and consequent depletion of electrons in regions of large wave amplitude. On the time scale of energy relaxation time in a collisional plasma, the dominant nonlinearity arises on account of preferential heating electrons. It is found that (i) maximum growth rate attains it's maximum for an optimum intensity of the beam (ii) filamentation is predicted in the over dense plasmas