## 3 Results
### Time Spectrum Analysis  
At the same time, it can be seen that the time spectrum of the chirp parameter changes under the same pulse width (Figure 4). In the process of chirp parameters changing from negative to positive, the magnitude and time of the peak power of the main peak change. The time range after the expansion of the main radiation peak is attached to the upper right corner of each complete time spectrum, from which we can observe that one of the specific manifestations of the chirp pulse on the time distribution is that the time of the peak changes under the conditions of the three groups of pulse widths.  
Compared with no chirp and added chirp conditions, the peak radiation of the main peak appears earlier, but the effect of different chirp parameters is different. When the absolute value of the chirp parameter increases, it is found that the occurrence time of the main peak of the positive chirp pulse is delayed with the increase in the positive chirp value, and the occurrence time of the negative chirp pulse is advanced with the increase in the negative chirp value. Therefore, it can be seen that the occurrence time of the peak pulse of the main peak is simultaneously affected by the compound effect of the chirp and pulse width. Under certain circumstances, the combination of the chirp and pulse width may delay or advance the appearance of the main peak. Further research will be conducted on the movement of the peak pulse of the main peak. For the peak of the main peak power, with an increase in the absolute value of the chirp parameter, no matter whether the added chirp is positive or negative, the peak of the radiated power gradually increases. The main influencing factors are the change in pulse effect due to the change in the frequency and the broadening effect of chirping on the pulse.  
The negative chirp means that the pulse in the high-frequency part interacts with the electron first, followed by the pulse in the low-frequency part. Therefore, the interaction between the pulse front and the electron is obvious, and the speed of electron movement to the peak is faster. At the same time, due to the action of a high-frequency pulse, the electron absorbs more energy per unit of time so that the radiation power peak appears in advance, and the peak value is greater than that of the pulse without a chirp.  
The principle of positive chirping is that the frequency of the pulse front is relatively low, the wavelength is relatively long, and the wavelength is relatively short along the frequency. Therefore, the position where the energy effect is most obvious is delayed, and the time when the power peak appears is delayed. At the same time, due to the characteristics of the normal dispersive medium, the long wavelength of the front will lead to faster pulse propagation, which will cause the pulse front to move further forward, while the short wavelength part of the propagation is slow, which makes the pulse back edge more backward, resulting in the pulse broadening. This broadening gives the electrons more time to interact with the laser field, which allows them to absorb more energy, resulting in an increase in the peak power of the electrons. In addition to the change in the main peak, another obvious change is the radiation, with a relatively low amplitude appearing at different times, which is defined in this paper as the side peak. With an increase in the absolute value of the chirped parameter, the side peak appears, and the occurrence frequency increases. In the time spectrum, multiple spectral lines appear, and with an increase in the absolute value of the chirped parameter, the envelope tends to be a Gaussian-like distribution with the same main peak.