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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.

In this work, the influence of a non‐uniform magnetic field on the self‐focusing of relativistic q‐Gaussian (QG) laser pulse propagating in magnetized plasma is studied. Utilizing the non‐linear Schrodinger equation with higher‐order paraxial approximation, the higher‐order terms of the dielectric function and the eikonal in the presence of a non‐uniform magnetic field have been obtained. Numerical results reveal that while the non‐uniform magnetized field decreases, the pulse width parameter (g) decreases, and subsequently the spot‐size of the laser declines too. As a consequence, the QG laser pulse will be more focused. Besides, it is shown that increasing the values of q‐parameter leads to a decline in self‐focusing qualities and, at lower values of q‐parameter, sharp self‐focusing of QG laser pulse is observed. Furthermore, it is found that when the QG laser pulse is propagated in the magnetized plasma, the amplitude of the pulse width decreases with decreasing the δ‐parameter, and consequently, the laser pulse becomes more compressed. Moreover, it is observed that the application of a non‐uniform magnetic field improves the self‐focusing of the QG laser pulse propagated through magnetized plasma.

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