Filamentation instability of extraordinary and ordinary modes in a magnetoplasma

The dispersion relation is derived for modulational instabilities of a Gaussian electromagnetic beam propagating in either of the two modes viz. extraordinary or the ordinary mode, along the externally applied d.c. magnetic field, in a homogeneous magnetoplasma. The dispersion relation has been obtained using Fourier analysis in WKB approximation with ksub(parallel) > > k0 and ksub(perpendicular)>>(r0f)-1 where k0 is the propagation vector of the main beam; ksub(parallel), ksub(perpendicular) are the parallel and normal components of the propagation vector of the fluctuation along and normal to the direction of propagation of the main beam and (r0f) is the effective beam width in the plasma. The nonlinearity arises on account of preferential heating and depletion of carriers on the time scale of the energy relaxation time (t>>tausub(E), tausub(E) being the energy relaxation time). On the short time scale (t>>tausub(E)) i.e. in a collisionless plasma, the nonlinearity arises due to ponderomotive force. Filamentation of these modes is predicted. Moreover, on account of self-focusing of the main beam the growth rate of filamentation gets considerably modified. (author)