## 3 Results
### Temporal Distribution  
To acquire the temporal distribution characteristics of electron radiation, observations should be conducted in the direction of the maximum radiation power. As depicted in Figure 6, the main peak is essentially located approximately at 50 fs. Simultaneously, two secondary peaks symmetrically distributed at positions approximately 0.5 fs on either side of the main peak can be observed. This exhibits a \"mountain-shaped\" symmetrical three-peak structure relative to the main peak. When \(b_{0}\) is extremely small, the height of the secondary peaks will be very low or even vanish directly. This indicates that at this stage, the majority of the electron radiation power is concentrated on a single central pulse, which can be considered as a separate ultrashort attosecond pulse. Concurrently, it can be observed that when the radius of the tight focusing beam waist is large until it reaches non-tight focusing, the heights of the two secondary peaks, that is, the radiation intensity, are relatively high compared to the main peak. This implies that the radiation power of the central pulse is not substantial, and the energy is more dispersed, making it infeasible to consider it as a single ultrashort attosecond pulse.  
It is noteworthy that as the beam waist radius \(b_{0}\) keeps increasing, the height difference between the two secondary peaks will correspondingly decrease. When \(b_{0}\) is larger than or equal to 7, the heights of the two secondary peaks are essentially equal. Overall, the height of the secondary peaks increases relatively as \(b_{0}\) becomes larger. The greater the beam waist radius is, the longer the period of the largest electron trajectory in the center will be. A longer trajectory implies a stronger interaction, resulting in stronger radiation. Consequently, the heights of both the secondary peak and the main peak will grow. This is because the increase in \(b_{0}\) will lead to a longer interaction time between the electron and the linearly polarized Gaussian pulse, strengthening the deflection influence of the laser on the electron, and eventually the electron will diverge from the direction of maximum power radiation at a later time.  
As the focus varies from tight to non-tight, the height of the main peak will continuously increase. This is because as \(b_{0}\) increases, the duration during which electrons interact with the linearly polarized Gaussian pulse will be longer, and the corresponding total radiation intensity will increase accordingly.  
Figure 6: The temporal distribution graphs of peak radiation power under different beam waist radii and their magnified figures.  
In order to observe the double-peak structure of the main peak of the temporal spectrum more clearly [27], we present the magnified graphs of these time spectra. As depicted in Figure 6, it can be discovered that the energy of the two main peaks is relatively high, reaching the order of \(10^{9}\).  
In reality, as depicted in Figure 7, the three-peak structure is multi-peak, except that the other peaks are extremely tiny. When observing the electron trajectory, each oscillation of the electron gives rise to a peak (actually two peaks that are very close to each other). The amplitudes generated by the three oscillation trajectories in the center are significantly greater than those of the other oscillation trajectories [27].