This paper presents an interaction between two Gaussian electromagnetic beams in relativistic magnetoplasma, when the axes of the two beams are initially (z=0) parallel along the z-axis in the x-z plane; the beams are initially propagating in the z-direction. The coupled wave equations corresponding to the parallel Gaussian electromagnetic beam have been solved in the paraxial approximation, yielding a system of coupled second order differential equations for the beam width. The equations have been solved numerically for a range of parameter. Lastly, the results have been presented in the form of graphs.
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