Xue-Ren Hong et al. [EPL, 139 (2022) 14001] Details of the electron dynamics and Thomson backscattering of electrons moving in a combined field of a tightly focused Gaussian laser pulse and an external uniform magnetic field are investigated. It is found that electrons can be pushed out from the laser pulse by a qualitative dynamic, leading to the phenomenon that the symmetry of the electron dynamics from the Gaussian envelope is broken. In this comment, we investigate the motion law of electrons under precise laser pulses, and we find that the longitudinal vector potential of electrons has a non-negligible effect on the electron motion, especially when the laser peak amplitude is enhanced, the laser pulse width becomes wider, the beam waist of the laser pulse becomes tighter. In addition, we explain the reason for such a large effect of the longitudinal vector potential from the point of view of electron dynamics.

The collision between relativistic electrons and a tightly focused linearly polarized laser pulse produced nonlinear inverse Thomson scattering (NITS), which generates backward x-rays. The effects of the initial transverse position of electrons with varied initial energy on the angular distribution of radiation power and spectrum are studied through numerical simulation. For the electrons with low initial energy (i.e. 2.56  MeV ), the off-axis collision breaks the spatial symmetry of x-ray radiation compared with the axial collision, the radiation direction is also torqued towards the same off-axis direction. There exists an optimal initial transverse position of electrons, which means the electron emitted from this position obtains greater radiation power. For the high-energy ( > 10  MeV ) electrons, the effect of torsion is not significant. The impact of off-axial is mainly manifested in the high-order harmonic spectrum. These findings help obtain high quality x-rays and modulate NITS radiation symmetry by electron parameters.

The effects of longitudinal fields on electron dynamics, power, and radiation spectrum in tightly-focused circularly polarized laser pulses are investigated in detail. When the longitudinal field vector potential is not considered at the intense relativistic laser field, the longitudinal acceleration of the electron subjected to the ponderomotive force is oscillatory, and the electron will be pushed out of the laser field. The peak radiation power, along with peak angle, varies exponentially with the laser peak amplitude. The longitudinal field leads to the appearance of spatial radiation vortex states when the laser peak is strong, increasing the collimation of the power and spectrum of spatial radiation as well as the focus.

This paper presents a novel view of the impact of electron collision off-axis positions on the dynamic properties and relativistic nonlinear Thomson inverse scattering of excited electrons within tightly focused, circularly polarized laser pulses of varying intensities. We examine the effects of the transverse ponderomotive force, specifically how the deviation angle and speed of electron motion are affected by the initial off-axis position of the electron and the peak amplitude of the laser pulse. When the laser pulse intensity is low, an increase in the electron’s initial off-axis distance results in reduced spatial radiation power, improved collimation, super-continuum phenomena generation, red-shifting of the spectrum’s harmonic peak, and significant symmetry in the radiation radial direction. However, in contradiction to conventional understandings, when the laser pulse intensity is relatively high, the properties of the relativistic nonlinear Thomson inverse scattering of the electron deviate from the central axis, changing direction in opposition to the aforementioned effects. After reaching a peak, these properties then shift again, aligning with the previous direction. The complex interplay of these effects suggests a greater nuance and intricacy in the relationship between laser pulse intensity, electron position, and scattering properties than previously thought.

The properties of nonlinear inverse Thomson scattering (NITS) are investigated in the collision between a circularly polarized tightly focused intense laser pulse and a relativistic off-axis electron with numerical simulations. Due to the asymmetric effect of the laser field on the off-axis electrons, the electron trajectory is torqued to the off-axis direction, and the symmetry of the spatial radiation is also destroyed, which causes the concentrations of the radiation in the off-axis direction. With the increase of laser intensity, the torsion effect is more obvious, the radiation collimation improves, the direction turns to sideways. With the increase of electron’s initial energy, the direction turns back to backwards and the degree of off-axis effect decreases. In both cases, the power exponentially enhances, the pulse width shortens, the spectrum broadens and super-continuity appears. With the laser intensity, the duration of sideways X-ray pulse from the low-energy (2.61MeV) electron is only 0.2 as, and the normalized intensity reaches 109. While using ultra-high-energy (100MeV) electrons, the duration of backwards γ-ray pulse reaches 1.22 zs, and the normalized intensity reaches 1017. These results help the understanding of nonlinear Thomson scattering and provide important numerical references for the research of NITS as high-quality X-ray and γ-ray sources.