## 3 Results and Discussion
### Attosecond Gamma-Ray Source from ICS  
The microbunching of the electron beam fingerprint on the ICS radiation is analyzed by applying a thin Al plasma downstream of the LWFA stage at \(x=2.06\) mm. Figure 3a  
Figure 2: Dynamic evolutions of the micro-bunched electron beam in the LWFA stage. **(a)** Density distribution of the trapped nitrogen electron and the on-axis current density profile. **(b)** Initial phase space distribution of the injected electrons (\(\xi_{i}\), \(p_{x}\)) upon ionization in the electric field \(E_{y}\) of the driving laser. **(c)** Energy spectra of the electron beam during 3 mm acceleration. **(d)** Normalized transverse emittance and relative energy spread evolutions of the entire beam during the acceleration, and the inset: longitudinal phase space (\(x\), \(p_{x}\)) of the electron beam near \(x=2\) mm, where the relative energy spread of the electron beam is minimal. The individual micro bunches are highlighted in different colors. illustrates the evolutions of the normalized transverse emittance and relative energy spreads of the micro-bunched electron beam during the transition from LWFA to ICS process. Upon propagating into the vacuum, a head-on collision with the reflected laser pulse occurred at approximately \(x=2050\)\(\upmu\)m in front of the plasma mirror, ending before the electron beam entered the Al foil plasma, where the bremsstrahlung radiation should also be considered. As shown in Figure 3a, interactions with the reflected laser field during the head-on collision result in the increased emittance and relative energy spread of the electron beam. Electrons undergo oscillations in the field of the reflected laser, as the snapshots of the electron beam at different positions (pre-collision at \(x=2043\)\(\upmu\)m), during collision at \(x=2053\)\(\upmu\)m), and post-collision at \(x=2059\)\(\upmu\)m) depicted in Figure 3b-d. Electrons acquire additional transverse momentum during the ICS head-on collision. However, normalized emittance of the electron beam returns to 1.28 mm mrad when the head-on collision ends, with nearly zero net transverse momentum gained from the laser field throughout the process, as shown in Figure 3d. When the electrons enter the Al foil plasma, the normalized emittance increases rapidly again when the bremsstrahlung scattering occurs, as indicated by the phase spaces in Figure 3e. Furthermore, when the micro bunches interact with the reflected driving laser pulse, the energy spread of the beam gradually increases due to the deceleration of some electrons, as depicted in the energy spectra around \(x=2053\)\(\upmu\)m and \(x=2059\)\(\upmu\)m shown in Figure 3f. Energy spread degradation continues further as the beam penetrates the thin plasma mirror, influenced by electron-ion collisions within the foil. Nevertheless, it can be observed that the electron beam maintains a stable micro-bunched structure throughout the ICS head-on collision, as illustrated by Figure 3b-d, both in the temporal and spatial aspects. Such micro-bunches would potentially fingerprint the inherited structure onto the gamma-ray radiation. Figure 3: The dynamics of the micro bunches during the Inverse Compton scattering (ICS) process. (**a**) Evolutions of the normalized transverse emittance \(\epsilon_{xy}\) and the relative energy spread \(\Delta E/E\) of the entire beam, highlighting the DDR for the plasma density down-ramp region and gray area for the fully ionized Al plasma region. (**b–d**) Snapshots of the micro bunches at different times during the ICS with the reflected laser pulse. (**b**) pre-collision at \(x=2043\)\(\upmu\)m, (**c**) during collision at \(x=2053\)\(\upmu\)m, (**d**) post-collision at \(x=2059\)\(\upmu\)m. (**e,f**) Electron phase space (\(x,p_{y}\)) and (\(x,E\)) throughout the ICS process. Dots with different colors show electrons at different positions. Figure 4a,b verifies the isolated structures with snapshots of electron and gamma-ray photon densities at the post-collision position around \(x=2059\) um.