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The nonlinear interaction of a circularly polarized Gaussian
intense laser pulse in a collisionless cold plasma with immobile
ions is analyzed. The laser beam is assumed to have a nonuniform
intensity distribution (along its wave front) in a plane
transverse to the direction of propagation. To properly include
the nonuniformity of the laser field, the wave equation is
integrated over the transversal distribution. In this way, the
mean transversal effects are taken into account. In this frame of
work the relativistic modulational instability (RMI) of a long
pulse is analyzed. A general dispersion relation is derived and
solved. Plots of the temporal growth rate as a function of the
laser beam power and the modulation wavenumber are presented and
compared with the case when a uniform intensity distribution along
the laser wavefront is assumed. It is found that the nonuniformity
of the laser beam has a significant effect on the characteristics
of RMI. It is shown as a conclusion that the effect of transverse
distribution in the growth rate reduction, in comparison with the
case when it was neglected, becomes more significant for shorter
wavelength of the RMI and stronger pump waves.
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