## 3 Results
### Space Radiation Characteristics of Electron  
Figure 3 shows the spatial radiation map corresponding to the electron at \(\mathrm{L}=1\lambda_{0}\), \(\mathrm{L}=2\lambda_{0},\mathrm{L}=3\lambda_{0},\mathrm{L}=4\lambda_{0}, \mathrm{L}=5\lambda_{0},\mathrm{L}=6\lambda_{0},\mathrm{L}=10\lambda_{0}, \mathrm{L}=15\lambda_{0},\mathrm  
It can be seen from the figure that the radiation of electrons is concentrated in a narrow cone in the direction of motion of electrons (Z-axis), and the size of the angle between the central axis of the cone and the generatrix can be judged by the degree of energy concentration.  
It is worth noting that the electron radiation power in Figure 3 is normalized by the maximum radiation power of the corresponding parameter itself. The specific values will be introduced in Section 3.3.  
The maximum value of the color bar in the figure is 1, and the minimum value is 0.  
We can find that the collimation of spatial radiation radiated by electrons without magnetic field is not strong and vortex-like. In contrast, the collimation of the energy radiated by electrons under the combined effect of laser and magnetic fields is significantly better.  
Moreover, the collimation of electron radiation is slightly worse when \(\mathrm{L}=\lambda_{0},2\lambda_{0},3\lambda_{0}\) under the combined effect of laser field and applied magnetic field. When \(\mathrm{L}>3\lambda_{0}\), the collimation of the electron radiation improves significantly, i.e., the angle between the central axis of the cone and the generatrix becomes smaller. We also find that when \(\mathrm{L}>5\lambda_{0}\), the collimation of the electron space radiation does not change much. There is a similarity with the electron motion trajectory shown in Figure 2.  
However, we also find that as \(\mathrm{L}\) increases, especially when \(\mathrm{L}=10\lambda_{0},15\lambda_{0}\) there appears an asymmetric in the radiation trajectory of the electrons, and in the positive direction of the z axes, we find less radiation from the electrons. Therefore, we consider the best outcome to be when \(\mathrm{L}=6\lambda_{0}\).  
Since the direction of radiation of an electron is the direction of the velocity of the electron's motion [24]. Therefore, the greater the velocity of the electron in the z-axis direction compared to the velocity in the x-axis and y-axis directions, the better the collimation of the electron radiation. Whereas the intensity of electron radiated power is related to the velocity and acceleration of the electron, I will discuss the maximum electron radiated power intensity in Section 3.3.  
The change of the shape and collimation of the electron space radiation is because when \(\mathrm{L}=\lambda_{0},2\lambda_{0},3\lambda_{0}\) its electron trajectory is an unstable spiral combined with a stable spiral column. Therefore, its radiation is perturbed by the electron motion trajectory. As a result, the collimation is slightly poor. When \(\mathrm{L}>4\lambda_{0}\), the electron trajectory is a stable spiral column, the trajectory is stable, so the radiation collimation is better. In contrast, the electrons without magnetic field are not stable in their trajectory, so the collimation is worse than the electron radiation under the action of laser field and magnetic field.