## 3 Results and Discussion
### \(\gamma\)-ray Pulses Generation
However, for the few-cycle laser pulses, this asymmetry will significantly affect the whole photon distribution, and the carrier-envelope phase (CEP) is also a nonnegligible parameter, as the time and intensity of the \(\gamma\)-ray that is generated strongly rely on it. Consequently, the CEP of a few-cycle laser pulse can probably be deciphered by detecting the intensities of the \(\gamma\)-ray from the two sides, i.e., \(p_{y}>0\) and \(p_{y}<0\). Figure 3: (Color online). (**a**) The electron trajectories during the emission of HHG. (**b**) The electron trajectories after leaving the target surface. (**c**) The variation in electron momentum \(p_{x}\) over time. (**d**) The work carried out by the electric field on the electrons. The values of \(t_{1}\), \(t_{2}\), \(t_{3}\), \(t_{4}\) and \(t_{5}\) are \(14.30T_{0}\), \(14.74T_{0}\), \(15.37T_{0}\), \(15.90T_{0}\), \(16.37T_{0}\), respectively. To explain the significance of \(\gamma\)-ray generation via the NCS, we make a comparative simulation by taking away the top half of the cone target, which corresponds to a laser irradiating a planar target obliquely at an angle of 45\({}^{\circ}\). All other parameters remain the same. Figure 5a,b demonstrates the electrons' behavior after leaving the target surface in the planar target case. The physical processes before \(t_{3}\) in Figure 5a,b are similar with those in the cone target case, while there are obvious differences after \(t_{3}\). The momentum \(p_{x}\) at \(t_{4}\) and \(t_{5}\) varies weakly since there is no counter-propagating attosecond electromagnetic pulses, and the NCS process cannot occur. The photon spectrum presented in Figure 5c shows that the photon yield decreases significantly and the maximum photon energy is reduced to the \(x\)-ray range (100 KeV\(\sim\)1 MeV). The energy conversion efficiency of the laser to the photon for the cone target and planar target is 0.24% and 0.02%, respectively, with a 12-fold difference between them. Compared to the scheme in ref. [22], the energy conversion efficiency 0.24% is an order of magnitude higher, although a less intense laser is used. Therefore, this indicates that high-energy photons are produced by the NCS mechanism in our cone target scheme, and the scheme is more effective in \(\gamma\)-ray production. Figure 4: (Color online). (**a**) The density distribution of photons at 19.24\(T_{0}\). There are three bunches of photons around \(y=8.3\lambda_{0}\), \(y=15.15\lambda_{0}\) and \(y=16.15\lambda_{0}\). (**b**) The density distribution of photons around \(y=8.3\lambda_{0}\); the FWHM is 0.1\(T_{0}\) (267 as). (**c**) The angular distribution of photons; the unit of radial scale is MeV. (**d**) The energy spectrum of photons; the cut-off energy is 6 MeV. \(p_{y}>0\) corresponds to the red curve, \(p_{y}<0\) corresponds to the green curve and the total momentum corresponds to the black curve. In addition, simulation results for five open angles of \(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\), \(120^{\circ}\) and \(150^{\circ}\) show that both the cut-off energy and energy conversion efficiency of the photon beam have a maximum value at \(90^{\circ}\), which can be seen from Figure 6. This is because, when the open angle is \(90^{\circ}\), the reflected laser and the reversed electron beam collide head-on and the chance of the NCS is the greatest. In addition, Figure 6 shows that the energy conversion efficiency at \(30^{\circ}\) is instead larger than that at \(60^{\circ}\). This is rational because the structure of the \(30^{\circ}\) cone target is closer to a cone channel, in which, more laser energy is transferred to the electrons [28], and the corresponding laser-to-photon energy conversion efficiency is increased, whereas the cut-off energy lies at a relatively low value. On the other hand, the \(\gamma\)-ray we obtain is of a higher energy and shorter FWHM compared to that of the two-laser scheme in ref. [29].