## 2 Materials and Methods  
In terms of data processing, all physical variables were normalized by \(k_{0}^{-1}~{}=~{}\lambda_{0}/2\pi\) and \(\omega_{0}^{-1}=\lambda_{0}/2\pi c\), where \(\lambda_{0}=1~{}\upmu\)m is the wavelength of the laser and \(c~{}=~{}2.998~{}\times~{}10^{8}\) m/s is the speed of light. This paper not only uses the observer as a reference, defining \(t\) as the time on the observer system, but also introduces the electronic reference frame, defining the time as \(t_{e}=t-R^{\prime}+\mathbf{n}\mathbf{j}\) with the electron as the reference frame, where \(R^{\prime}\) is the distance between the observer and the interaction center, and \(\mathbf{j}=(x_{t_{e}},y_{t_{e}},z_{t_{e}})\) is the electron displacement at \(t_{e}\) time. Radiation direction \(\mathbf{n}=(\sin\theta\text{cos}\,\phi,\sin\theta\text{sin}\,\phi,\cos\theta)\), where \(\theta\) is the polar angle, and \(\phi\) is the azimuth angle. The initial electron position \((x_{0},y_{0},z_{0})\) is set to \((0,0,0)\) to ensure that the pulse and electron begin to interact at the origin [30]. The chirped pulse and electron action process are shown in Figure 1. The initial position of the laser is on the negative half of the z-axis, propagating along the positive z-axis at the speed of light \(c\), interacting with the stationary electron at the origin and driving the electron's motion. In a tightly focused Gaussian laser field, the electric field \(\mathbf{E}\) and magnetic field \(\mathbf{B}\) satisfying [PERSON]'s equations can be expressed as follows [31]:  
\[\mathbf{E}=\
abla\times\mathbf{A} \tag{1}\]  
\[\mathbf{B}=\sqrt{\epsilon}[(i/k)\
abla(\
abla\cdot\mathbf{A})+ik\mathbf{A}] \tag{2}\]  
where \(\epsilon\) is the dielectric constant, we can use [PERSON]'s equation to obtain the solution for \(\mathbf{A}\):  
\[\
abla^{2}\mathbf{A}+k_{0}^{2}\mathbf{A}=0 \tag{3}\]  
In Cartesian coordinates, a circularly polarized laser can be decomposed into a pair of linearly polarized lasers with phase difference \(\pi/2\), whose polarization planes are parallel to \(x\) and \(y\), respectively. Therefore, the electromagnetic field circularly polarized laser can be decomposed into \(\mathbf{E}=\mathbf{E_{xp}}+\mathbf{E_{yp}}\) and \(\mathbf{B}=\mathbf{B_{xp}}+\mathbf{B_{yp}}\). The spot size of the Gaussian laser field in this model is \(2w_{0}\), the pulse width \(L\) and the intensity \(I\), so we can define  
\[E_{0}=a_{0}\frac{w_{0}}{w}\text{exp}\bigg{(}-\frac{\eta^{2}}{L^{2}}\bigg{)} \text{exp}\bigg{(}-\frac{\rho^{2}}{w^{2}}\bigg{)} \tag{4}\]  
where \(a_{0}=\sqrt{\big{(}I\lambda_{0}^{2}/1.384\big{)}}\times 10^{-9}\) is the peak amplitude, \(w=w_{0}~{}\sqrt{\big{(}1+z^{2}/z_{0}^{2}\big{)}}\) is the waist radius, and where [PERSON]'s distance \(z_{0}=k_{0}w_{0}^{2}/2\). The perpendicular distance \(\eta=z-ct\), the parallel distance \(\rho=\sqrt{(x^{2}+y^{2})}\), and the speed of light is \(c\). In the case of tight laser focus, the expression of the electromagnetic field must be expanded to a higher order, accurate to the diffraction angle \(\epsilon=w_{0}/z_{0}\). [PERSON] et al. [32] derived \(\mathbf{A}\), \(\mathbf{B}\), and \(\mathbf{E}\) in the X-axis polarization laser field from Equation (1) to Equation (3). [PERSON] [33] and [PERSON] [31] proposed an electromagnetic field expression for a Y-axis polarized laser field by using a symmetric expression. In summary, the fifth-order expansion of the electric field component \(\mathbf{E}=\{E_{x},E_{y},E_{z}\}\) can be obtained:  
\[\begin{array}{c}E_{x}=E_{0}\{S_{0}+\varepsilon^{2}[\alpha^{2}S_{2}-\frac{r^ {4}S_{5}}{4}  
\[