This paper presents an investigation of self-focusing of Gaussian laser beam in collisional plasma and its effect on second harmonic generation. Due to non-uniform heating, collisional non-linearity arises, which leads to redistribution of carriers and hence affects the plasma wave, which in turn affects the second harmonic generation. Effect of the intensity of the laser beam/plasma density on the harmonic yield is studied in detail. We have set up the non-linear differential equations for the beam width parameters of the main beam, plasma wave, second harmonic generation and second harmonic yield by taking full non-linear part of the dielectric constant of collisional plasma with the help of moment theory approach. It is predicted from the analysis that harmonic yield increases/decreases due to increase in the plasma density/intensity of the laser beam respectively.

The presence of an axial magnetic field in a laser beat wave accelerator enhances the oscillatory velocity of electrons due to cyclotron resonance effect leading to higher amplitude of the ponderomotive force driven plasma wave, and higher energy of accelerating electrons. The axial magnetic field inhibits the transverse escape of electrons and thus causes a growth of the interaction length. The surfatron acceleration of electrons also shows a similar enhancement. A surfatron transverse magnetic field deflects the electrons parallel to the phase fronts of the accelerating wave keeping them in phase with it. However, the electron continues to move away radially.