The phenomenon of self-focusing has been extensively studied in a variety of non-linear media and its understanding is key to several issues in ICF, space communications, spatial solitons
etc. Most popular models [1-3] are not applicable for high power laser beams. Variational approach, which though an approximately analytical in nature, is more suitable to describe self-focusing as well as self-phase modulation. Authors have studied self-focusing and self-phase modulation of an elliptic Gaussian laser beam in collisionless magnetized plasma using variational approach. The dynamics of combined effects of nonlinearity and spatial diffraction is presented. With 'a' and 'b' as the beam width parameters of the beam along x and y directions respectively, the phenomenon of cross-focusing is observed, where focusing of 'a' results in defocusing of 'b' and vice versa. For cylindrically symmetric beam, stationary self-trapping is observed for critical power. However, exact self-trapping is not observed for elliptical Gaussian beam as 'a' and 'b' keep on oscillating infinitely. For higher value of the applied magnetic field more oscillatory self-focusing is observed. Further, with increase in ellipticity, strong oscillatory self-focusing/defocusing of 'a' as well as 'b' is observed. Substantial change in self-phase modulation is also observed. Finally, it is observed that regularized phase is always negative for different values of intensity parameter.

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