Abstract
In this paper, the longitudinal and transverse variation of Laguerre Gaussian laser pulse has been investigated, when it is propagating inside the nonlinear plasma medium under the united impact of both relativistic and ponderomotive nonlinearity. Two second-order differential equations for transverse and longitudinal pulse width parameters have been derived using the approach of method of moments. The solution of both equations are obtained numerically and variation in spatio-temporal pulse width parameters is obtained. The excited plasma wave generated by the laser-plasma interaction, accelerate the plasma electrons to high gradients. The effect of the spatio-temporal variation on electron acceleration has also been studied and it has been observed that the laser pulse with smaller pulse duration results in better energy gain by the electrons.
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