## 3 Results
### Motion Trajectory Analysis
As the pulse width increases, \(E_{0}\) increases, enhancing the laser pulse's binding force on the electron. The electron is unable to escape the laser's capture, and the motion trajectory becomes confined to a helical motion around the z-axis. As shown in Figure 2 for \(L=4\lambda_{0}\) and \(L=6\lambda_{0}\), after the interaction with the laser pulse ends, the electron no longer has radial velocity and transitions to uniform linear motion along the z-axis. On this basis, chirp is added to explore the influence of chirp parameters on electron motion trajectory under different pulse widths. The main effect of chirp on pulse generation is that the pulse frequency changes with time. Therefore, in the process of interaction between a chirped pulse and an electron, because the pulse frequency is no longer fixed, the motion state of the electron under the action of pulse under different time nodes is different from that of a non-chirped pulse. Based on the trajectory changes shown in Figure 2 after adding the chirped pulse, we summarize the effects of the chirped pulse on the electron's motion trajectory. Under all pulse width conditions, the addition of a chirped pulse has the following effects on the electron's motion trajectory: After the addition of a chirped pulse, the radial motion of electrons is more regular and tends to be circular, and the radial motion radius of the electrons decreases with the increase in chirped pulse compared with the non-chirped state. We can see that the trajectory of electrons with a pulse width of \(2\lambda_{0}\) changes obviously after the chirp is added. When the chirp with an absolute value of 0.01 is added, the original movement of electrons deviating from the z-axis due to the smaller pulse width is bound back to the \(z\)-axis, and the movement in the xy direction is finally reduced to 0, which produces an effect similar to that of increasing the pulse width. Figure 2: (**I**). Comparison of the electron motion tracks with different pulse widths under different chirp parameters: the pulse width \(L\) is taken as three sets of values, group (_a_) corresponds to \(2\lambda_{0}\), group  
(_b_) corresponds to 4\(\lambda_{0}\), and group (\(\epsilon\)) corresponds to 6\(\lambda_{0}\). The corresponding pulse durations are 6.7\(f\)/s, 13.3\(f\)/s, and 20 \(f\)/s. All the different trajectory colors represent different chirp parameters. The colors of the motion trajectories under different chirped parameters are marked in the upper right corner of the figure. (**II**). Expansion diagram of the electron motion trajectory with different pulse widths under different chirped parameters. The effect of the chirp is very obvious. When the pulse width is 2\(\lambda_{0}\), 4\(\lambda_{0}\), 6\(\lambda_{0}\), the motion trajectory becomes more continuous and regular after adding a small chirp parameter. With the increase in pulse width, the effect of radial contraction of the chirp becomes more and more obvious. This is because the addition of the chirp causes the instantaneous frequency of the pulse to change, and the instantaneous frequency of the chirped pulse changes. Under the same pulse width action condition, the action of the electron receiving the pulse in the same action time changes in a relatively continuous way, so the trajectory of the electron movement tends to be continuous and regular. With the increase in pulse width, the chirp frequency change in the action time becomes longer, resulting in the radial action time on the electron becoming longer, the radial binding effect on the electron is enhanced, the radial radius decreases to a greater extent on the trajectory, and the distance required for radial contraction becomes shorter. In the direction of the electron \(z\)-axis, the distance required for the electron trajectory to reach stability becomes shorter due to the addition of a chirped pulse, and the shortening effect tends to be obvious with the increase in the chirped-pulse intensity.