Transverse self-focusing and filamentation of a laser beam in a collisional magnetoplasma

Anisotropic self-focusing of a Gaussian laser beam in a collisional magnetoplasma is examined analytically. The laser propagates transverse to the static magnetic field. The nonlinearity arises through the Ohmic heating of electrons and subsequent redistribution of plasma along the magnetic field. The magnetic field enhances the rate of self-focusing to a large extent. In the case of a plane-uniform laser beam, it is seen that it is unstable for small scale fluctuations, and the growth rate of instability increases rapidly with magnetic field.