Abstract
Relativistic self focusing and frequency shift of laser beam having super-Gaussian profile in space and Gaussian profile in time is studied in a plasma. The relativistic mass nonlinearity is found to cause time dependent self focusing of the laser pulse and the saturation effect of nonlinearity avoids point focusing of the beam. For ultrashort laser pulse, the front of the pulse undergoes frequency down shift while that of the tail undergoes up shift. Frequency shift increases and self focusing becomes stronger for higher intensity of the laser. The self focusing is also stronger for the laser beam carrying larger wavelength.
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