Self-focusing of Q-Gaussian Laser Beam in Relativistic plasma using exponential density based transition

We have investigated self-focusing of a q-Gaussian laser beam in a relativistic plasma channel using exponential density based transition. The present paper is devoted to the importance of using a ramp density profile in decreasing the beam width parameter considerably. The preference of ramp type plays a better role in guiding the high intensity laser pulses to several Rayleigh lengths. Our results obtained from numerical analysis show that laser self-focusing can be controlled by varying laser intensity parameter, q-values and suitable density ramp parameter. We have derived the nonlinear differential equation for the beam width parameter using WKB and Paraxial ray approximation and solved it numerically using the Runge Kutta method to study the nature of self-focusing and defocusing. It is observed that self-focusing of q-Gaussian laser beam can be increased with increasing laser intensity parameter. Moreover, in case of q-Gaussian laser beam, it is easier to focus lower q-values using suitable type of plasma density ramp.