Relativistic Self-Focusing of Hermite-cosh-Gaussian Laser Beam in Magnetoplasma with Exponential Plasma Density Ramp

In the present manuscript,we analyse the effect of exponential plasma density ramp for relativistic selffocusing of Hermite-cosh-Gaussian laser pulse in magnetoplasma.The exponential plasma density ramp is found to be more prominent in achieving the stronger self-focusing of Hermite-cosh-Gaussian laser beam in comparison to the tangential plasma density ramp.We propose a theoretical model for propagation of Hermite-cosh-Gaussian laser pulse in magnetoplasma with exponential density ramp.The nonlinearity in the medium arises because of the relativistic motion of electrons,being responsible for relativistic self-focusing.Equation of the beam width parameter is set up by taking the expression for the dielectric function and following Wentzel-Kramers-Brillouin(WKB) with paraxial ray approximations for mode indices m=0,1 and 2.Effect of decentered parameter is also analysed,which results in stronger self-focusing of the Hermite-cosh-Gaussian laser beam.Stronger self-focusing of laser beam is more pronounced in high density plasma with higher magnetic field.