In this research, the process of electron acceleration and wakefield generation by Gaussian-like (GL), super-Gaussian (SG) and Bessel–Gaussian (BG) laser pulses through cold collisionless plasma in the presence of a planar magnetostatic wiggler are studied. Three different types of laser spatial profiles, GL, SG and BG, are considered. Additionally, using the hydrodynamics fluid equations, Maxwell's equations as well as the perturbation technique for GL, SG and BG laser pulses in the weakly nonlinear regime and in the presence of a planar magnetostatic wiggler, governing equations for analysing the laser wakefield and electron acceleration have been derived and compared correspondingly. In addition, the effect of some important factors, including the wiggler field strengths, laser intensity, pulse length, plasma electron density and laser frequency on the wakefield and the electron energy gain, have been investigated. Numerical results show that enhancing the wiggler magnetic field results in an increase in the amplitude of the wakefield. Furthermore, it is observed that in comparison with the wakefield amplitude excited by SG and GL laser pulses, the amplitude of the wakefield excited by BG laser pulse is larger when the wiggler field is enhanced. Moreover, it is realized that the type of the laser profile, selected laser parameters and wiggler magnetic field are the most decisive and effective factors in the wakefield amplitude and shape of wakefield generation through cold collisionless plasma. Also, it is seen that as the pulse length declines, the amplitude of the wakefield increases, and correspondingly the resonance positions shift to higher ${({\varOmega _w}/{\varOmega _p})_{max}}$ values.

Evolution of longitudinal electrostatic wakefields, due to the propagation of a linearly polarized super-Gaussian laser pulse through homogeneous plasma has been presented via two-dimensional particle-in-cell simulations. The wakes generated are compared with those generated by a Gaussian laser pulse in the relativistic regime. Further, one-dimensional numerical model has been used to validate the generated wakefields via simulation studies. Separatrix curves are plotted to study the trapping and energy gain of an externally injected test electron, due to the generated electrostatic wakefields. An enhancement in the peak energy of an externally injected electron accelerated by wakes generated by super-Gaussian pulse as compared to Gaussian pulse case has been observed.