Sensitiveness of Decentered Parameter for Relativistic Self-Focusing of Hermite-cosh-Gaussian Laser Beam in Plasma

Sensitiveness of the decentered parameter for relativistic self-focusing of Hermite-cosh-Gaussian beam in the plasma is investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices 0, 1, and 2. The plot between the beam width parameter and the normalized propagation distance for different values of the decentered parameter and intensity has been reported and results obtained indicate the dependency of the self-focusing of the laser beam on the decentered parameter. The selection of the decentered parameter is more sensitive to self-focusing. For the mode indices ${\rm m}={0}$ and 1, self-focusing becomes stronger and for ${\rm m}={2}$ , self-focusing becomes weaker as the diffraction term becomes more dominant. Our emphasis is on the selection of the decentered parameter at which stronger self-focusing of laser beam is observed which might be very useful in the applications, such as the generation of inertial fusion energy driven by lasers, laser driven accelerators, and so on.