Self focusing of a quadruple Gaussian laser beam in a plasma

The self focusing of a quadruple Gaussian laser beam, comprising four coherent identical Gaussian beams with axes parallel to z but shifted from z-axis by −x0x,x0x,−x0y,x0y in a collisionless plasma, is investigated in the paraxial ray approximation. The nonlinearity arises through the ponderomotive force led plasma density redistribution. As the beam propagates, it maintains the shape of its intensity profile with spot size r0 of each of the four distributions modified from r0 to r0f, x0, modified to x0f and the axial intensity enhanced by 1/f2, where f is the beam width parameter. In the regime of quadratic nonlinearity, the threshold beam power for self focusing, Pth, increases with x0 as the laser intensity gradient decreases and the ponderomotive force becomes weaker. At beam power greater than Pth, the beam focuses in an oscillatory manner, i.e., f varies periodically with z due to the saturating effect of nonlinearity. The locations of intensity maxima of the four beams also vary periodically ...