## 3 Results and Discussion  
### Electrons Injection and Acceleration  
Plasma mirrors have been proven as fantastic electron injectors for vacuum laser accelerations [26, 27]. However, as the electrons propagate with the reflected laser, the electron slice is defocused and its density decreases rapidly. Therefore, a cone-like target may localize the electrons' motions and act as a brilliant light source by utilizing the dense electron pulses. As shown in Figure 2a, when the incident laser irradiates on the inner side of the target, the reflected part \(E_{x}\) gathers into the center area and gets superimposed with the part \(E_{y}\) that still propagates forward. Additionally, under the action of the laser's ponderomotive force, Lorentz force and the ions' electrostatic force, quite a large amount of the electrons can be observed to escape out of the inner side after the reflection of the electromagnetic field and then constitute dense electron pulses traveling with the reflected field. If we define the electromagnetic field perpendicular to the target's inner side, it can be written as  
\[\begin{split} E_{\perp}&=E_{x}\cos\alpha+E_{y}\sin \alpha\qquad(y>12\lambda_{0}),\\ E_{\perp}&=E_{x}\cos\alpha-E_{y}\sin\alpha\qquad(y <12\lambda_{0}),\end{split} \tag{1}\]  
where \(\alpha=45^{\circ}\) is half of the open angle. It is comprehensible that, when \(E_{\perp}>0\), the electrons are pulled out of the target, and when \(E_{\perp}<0\), the electrons are pushed into the target. Since \(E_{x}\) and \(E_{y}\) are both periodic functions about \(T_{0}\), \(E_{\perp}\) periodically reaches its largest point and the electron pulses separated by \(T_{0}\) are formed outside the surface. Regarding the ponderomotive force, whose period is \(T_{0}/2\), it only provides the electrons with relatively rapid oscillations. Therefore, the electron pulses appear synchronously with the peaks of \(E_{\perp}\) (Figure 2a). Furthermore, due to the similarity parameter \(S=n_{e}/n_{e}a_{0}\) being 1.3, this setup is in favor of high harmonic generations (HHG). Therefore, the reflected field \(E_{x}\) appears as attosecond pulse trains, whose spectrum is consistent with the power-law under the mechanism of a relativistic oscillation mirror (Figure 2b), i.e., \(I\propto(\omega/\omega_{0})^{-8/3}\), and we can know that the peaks in \(E_{\perp}\) originate from the reflected attosecond pulses.  
Particle tracking is carried out to further understand the emission of HHG and electron escaping and subsequent motions. An effective process begins with the electron acceleration from the interior of the target towards the surface (Figure 3a). Due to the decrease in the ponderomotive force, the compressed electron bunches are mainly under the action of the charge separation field, which accelerates the electrons to tens of MeV. After a transverse acceleration induced by the incident laser, electrons experience an attosecond pulse emission along with an energy decrease. Typical electron trajectories are illustrated in Figure 3a to demonstrate this emission process, after which, part of them fall back to the target because of energy loss, whereas the others achieve second accelerations to escape from the target.  
Figure 3b-d demonstrates the electron's behavior after leaving the target surface. Before reaching the position labeled as time \(t_{1}\), the electron energy decreases due to the negative work carried out by the y-direction electric field, which is superimposed by the electrostatic field and the incident laser's electric field. After the direction change in the laser's electric field, the electron energy gets restored to a certain extent until the time \(t_{2}\). This is exactly the second acceleration that we called, and this process is an account for the electron's escaping, which has not been specifically investigated before.