## 3 Results
### Spatial Distribution of Radiation  
At the same time, the study of radiation spatial distribution in the process of electron motion also found that the chirped parameter has an effect on radiation spatial distribution. It is worth noting that we have used a cylindrical coordinate system to plot the spatial distribution of radiation, aiming to investigate the radiation behavior of electrons under the influence of the laser. In the absence of a chirped pulse, the spatial distribution of electron radiation is affected by the pulse width. On the one hand, the radiation peak decreases with the increase in pulse width. At the same time, with the increase in pulse width, the vortex phenomenon becomes gradually obvious, and the spiral distribution tends to be closer. When the radiation is affected by a chirped pulse, in the process of increasing the absolute value of the chirped pulse, the number of rotational layers of radiation increases, the angular gap of vortex radiation shrinks significantly, the vortex structure is rich, the spiral distribution is tighter, and the coupling phenomenon gradually begins to appear. As the pulse width increases, the effect of the chirped parameters on vortex coupling is gradually obvious, and the effect of positive and negative chirps is different. When the pulse width is 2\(\lambda_{0}\), the vortex density increases obviously with the increase in the absolute value of the chirp parameter. When the chirp parameter reaches \(\pm\)0.03, the vortex disappears, and the radiation distribution is circular. However, compared with Figure 3_(a2,a4)_, although the absolute value of the chirp is the same, the radiation distribution of the electron radiation increasessignificantly. However, the effect of positive and negative chirps is obviously asymmetrical, and the vortex coupling effect of negative chirps is stronger than that of positive chirps, which is similar to the motion trajectory. There is also a symmetry axis at the negative chirp, and the coupling effect of chirped parameters on space radiation is also symmetrical. Figure 3: **(I)**. Front view and top view of the spatial distribution of electronic radiation, group (_a_) corresponds to \(2\lambda_{0}\), group (_b_) corresponds to \(4\lambda_{0}\), and group (_c_) corresponds to \(6\lambda_{0}\). **(II)**. Histogram of the peak value of the spatial distribution of electron radiation under different parameters. Each point is the logarithm of the peak value of the spatial distribution of radiation under different pulse widths and chirp parameters with a base of 10 for comparison. In addition, it can be seen that the morphometric transformation effect of radiation distribution is more obvious under the influence of a chirped pulse. This is because the chirped pulse causes the instantaneous frequency of the laser to change, and the electrons are subjected to higher-intensity laser action per unit of time, resulting in an increase in the energy peak of the electron radiation. At the same time, because the electrons are affected by the chirped pulse, the spiral motion frequency of the electrons increases. The spiral distribution of electron radiation tends to be tight, and the coupling occurs in the process of adjacent radiation gradually approaching, forming a circular distribution. Although the vortex phenomenon becomes more obvious when the pulse width increases, it can be seen that the coupling effect of the same chirp parameter on the spatial distribution of radiation is more obvious when the pulse width increases. Compared with Figure 3(\(a\)4-\(c\)4), the radiation coupling of group (\(a\)4) with a pulse width of 2\(\lambda_{0}\) occurs under the chirp of +0.01. The spatial distribution of radiation in group (\(b\)4) with a pulse width of 4\(\lambda_{0}\) begins to appear as a concentric circular-like distribution, and the radiation coupling degree in group (\(c\)4) with a pulse width of 6\(\lambda_{0}\) is extremely high--and the vortex phenomenon could not be observed.