## 3 Results
### Spatial and Angular Distribution  
In order to maximize the electron radiation power, it is necessary to set an appropriate laser delay time to control the timing impact between the laser and the electron. Through tests, when the laser delay time is set at 5 fs, the electron precisely collides with the central position of the laser pulse, resulting in the maximum radiation power. During the collision process, the different collision parts between the electron and the laser pulse exert a considerable influence on the generated electron radiation power. Hence, for the purpose of investigating the characteristics of the electron radiation angle and spatial distribution, the normalized spatial angular distribution of the radiation power under the maximum radiation scenario, that is, when the delay time of laser emission is set at 5 fs, is plotted. It can be derived from Figure 4 that with the gradual increase in the laser amplitude, the peak value of the normalized radiation power keeps escalating. Observing the scale of the coordinate axes, the peak radiation power rapidly surges from the order of \(10^{6}\) to the order of \(10^{9}\), constituting a considerable variation. This is due to the fact that the increase in the laser amplitude intensifies the interaction between the laser and the electron, thereby leading to a more intense electron radiation during the collision. Figure 3: The energy variations in electron motion under diverse laser amplitudes. \(\Delta\gamma\) represents the energy of the electron’s change. By observing the angular distribution of the polar angle \(\theta\) and azimuthal angle \(\Phi\) in Figure 4, it can be observed that when the laser amplitude is extremely low, the electron radiation power is concentrated at \(\Phi=0^{\circ}\) and \(\theta=90^{\circ}\). This is attributed to the fact that the laser amplitude at this moment is very low, and its deflection effect on the fast-moving electron is extremely weak. The electron almost passes through the laser without deflection. Simultaneously, the radiation produced by the cross-collision between the laser and the electron is basically concentrated in the positive direction of the x-axis. With the enhancement of the laser amplitude, a certain degree of differentiation emerges in the electron radiation adjuncts in both the \(\theta\) and \(\Phi\) directions. The spatial angular distribution diagram of the electron radiation presents a comet-like image, with the radiation peak located at the head of the comet. Gradually, the comet moves toward the region of low \(\theta\) values. As the laser amplitude intensifies, the peak of the polar angle decreases continuously and significantly. According to the expression of radiation power, the radiation power is mainly influenced by two parameters: the energy of electron motion and the z-axis acceleration. In this article, the initial energy of electron motion remains invariant. Nevertheless, the increase in the laser amplitude will lead to the enhancement of the z-axis ponderomotive force that the electron undergoes when interacting with the laser pulse. Consequently, the electron will possess a greater z-axis acceleration, and the peak value of the generated radiation power will also become larger. In the direction of the polar angle, the increase in \(a_{0}\) causes a substantial increase in the ponderomotive force along the z-axis, elongating the electron trajectory in the z-axis. Subsequently, the direction of the electron radiation power approaches the z-axis, indicating that more radiation is concentrated in the region with a smaller polar angle. Meanwhile, as the polarization plane of the linearly polarized laser is the XOZ plane, the radiation along the tangential direction of the electron trajectory lies in the XOZ plane, thereby resulting in the concentration of the radiation in the region where \(\Phi=0\).