## 3 Results  
### Spatial Radiation Angle Distribution  
In the numerical simulation, we select a laser pulse with a normalized peak intensity (a = 5) in a light period. In Figure 2, we plot the motion trajectories of electrons in different CE phases of \(\phi_{0}=0\), \(\phi_{0}=\pi/3\), and \(\phi_{0}=\pi/2\), and the pictures show the polarization characteristics of the electron motion consistent with the laser pulse. At the same time, by observing the two-dimensional diagram of the motion trajectory, we find that the motion trajectory has symmetry about the 0 axis. As shown in Figure 2, the movement direction of the electron is along the z-axis direction from right to left. In our research, the analysis of the trajectories of electrons plays a critical role in deriving crucial physical quantities pertaining to the radiation field. Through the numerical simulation of the electron trajectories in the presence of a circularly polarized, tightly focused laser pulse, we are able to track the intricate dynamics of these relativistic particles as they interact with the laser's electromagnetic fields. This serves as the foundation for our subsequent research. Figure 3a-h depict the spatial radiation angle distribution of \(\phi_{0}=0\), \(\phi_{0}=\pi/3\), \(\phi_{0}=\pi/2\), \(\phi_{0}=2\pi/3\), \(\phi_{0}=\pi\), \(\phi_{0}=4\pi/3\), \(\phi_{0}=3\pi/2\), and \(\phi_{0}=5\pi/3\) at the initial laser phase, given an initial electron energy of \(20\times 0.511\ \mathrm{MeV}\). Significantly, when an electron traveling in the negative z-axis direction collides with a circularly polarized laser in the positive z-axis direction, the radiation energy attains its peak at a specific angle \(\theta_{M}\) of around \(167.75^{\circ}\). As the initial phase increases, the polar angle \(\theta_{M}\) remains constant at the point of maximum radiation energy, while the azimuth angle \(\psi\) varies from 0 to \(2\pi\). Furthermore, our calculations reveal a linear positive correlation between the azimuth angle corresponding to the maximum radiation and the initial phase. Moreover, it indicates that the radiation peaks in the direction of laser incidence. This phenomenon emerges due to the modulation of the laser field's polarization direction by varying the initial phase of the laser pulse. Specifically, when the polarization direction of the laser field aligns with the chirality of the electron's spiral orbit, the force exerted on the electron within the laser field attains its maximum. This alignment leads to a pronounced electron scattering effect and maximizes the radiation energy. Consequently, the location of the peak radiation energy exhibits a strong correlation with the initial phase of the laser pulse. We further obtained the spatial radiation angle distribution diagram at different initial phases when the initial electron energy was 40, 60, 80, and 100 \((\times 0.511\ \mathrm{MeV})\). It is also consistent with the fact that the polar angle corresponding to the maximum radiation energy is fixed and the azimuth angle moves from 0 to \(2\pi\) in the process of the initial phase change. Based on the preceding analysis, the initial phase does not affect the polar angle at the maximum radiation. We further plotted the correlation between the radiation energy and polar angle for varying initial electron energies, with the initial phase angle fixed at 0, as shown in Figure 4. Observing the figure, it becomes apparent that as the initial electron energy rises, the polar angle at the point of maximum radiation converges towards \(\pi\). Meanwhile, the radiation distribution exhibits increasingly pronounced collimation. Concomitantly, the maximum radiation quantity surges, escalating by several orders of magnitude, specifically from \(10^{11}\) to \(10^{12}\), \(10^{13}\), \(10^{14}\), and ultimately \(10^{15}\). This noteworthy trend underscores the superior collimation properties of radiation emitted by higher-energy electrons.