A comprehensive study of magnetic field-induced modifications in sin-Gaussian pulse-driven laser wakefield acceleration

The presence of an external magnetic field exerts a substantial influence on the phenomenon commonly referred to as nonlinear laser plasma interaction. External magnetic field exerts a notable influence on the efficiency of THz creation, harmonic generation, self-focusing, and electron acceleration by laser wakefield acceleration (LWFA). An analytical study is conducted to examine the impact of an external magnetic field on the acceleration of the laser wakefield. This investigation utilized a sin-Gaussian pulse profile. To achieve this objective, a fundamental second-order differential equation is generated for the wake potential. Furthermore, equations describing the wakefield generated and the resulting increase in electron energy are derived. The sin-Gaussian pulse is used in the appropriate equations to derive an analytical solution for the laser wakefield, the electron energy gain, and the laser wake potential. Curves have been constructed using experimentally tractable parameters to show the variation in LWFA. The findings of this study indicate a positive correlation between the presence of an external magnetic field and the laser wake potential, laser wakefield, and electron energy gain. Moreover, the optimization of parameters related to the sine function and the Gaussian function is achieved. Improved electron acceleration can be achieved when the value of L is equal to \(0.2 {\lambda }_{{\text{P}}}\) $0.2{\lambda }_{\text{P}}$ ( \({\lambda }_{{\text{P}}}\) ${\lambda }_{\text{P}}$ is plasma wavelength) and the value of \({r}_{0}\) $r_0$ exceeds \(0.5 {\lambda }_{{\text{P}}}\) $0.5{\lambda }_{\text{P}}$ . Our findings will enable the researchers to employ an external magnetic field and improve the laser characteristics to obtain energy efficient electron acceleration.