Abstract
A generalization of the paraxial approximation based on a stationary transverse distribution of a laser pulse in laserplasma interaction is addressed. The laser beam is assumed to have a nonuniform intensity distribution along its wave front in a plane transverse to the direction of propagation. The conditions are considered in such a way that the pulse variation in the perpendicular direction is negligible. Accordingly, the study is based on an approach that accounts for the transversal effects in an average manner. The dispersion relation is presented in this frame of work by which the electron parametric instability can be studied. It is shown that the correction terms regarding the spot size is just negligible near the symmetry axis, and as off axis points come to play, they grow and consequently their effect might have significant influence in different aspects of the instabilities.
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