Effect of self-focused Cosh-Gaussian beam on second harmonic generation in collisional plasmas

Effect of self-focused Cosh-Gaussian beam on second harmonic generation (SHG) in collisional plasma is investigated in present work. The plasma electrons get heated non-uniformly in presence of Cosh-Gaussian beam leading to focusing of beam. Further, there is generation of density gradients in normal direction to pump beam thereby exciting EPW at pump beam frequency. SHG is produced as a result of excited EPW interaction with main beam. We have obtained 2nd order differential equation representing beam waist's behavior by employing WKB and paraxial approaches. Influence of well known laser plasma parameters on beam's focusing behavior and SHG yield is also inspected.