# Enhanced Proton Acceleration from Laser Interaction with a Tailored Nanowire Target
## 3 Results and Discussions  
### Laser Absorption and Hot Electron Generation  
In typical TNSA, the laser pulse irradiates a solid target, usually a foil target. Electrons are heated via vacuum heating and the \(J\times B\) mechanism. Hot electrons propagate to the target rear side, establishing an intense sheath field for proton acceleration. Because the laser pulse can only reach several skin depths into the target, a large proportion of energy is reflected. However, for the nanowire target, the laser pulse can propagate in the vacuum gaps between the solid wires, leading to a significant suppression of the reflectivity. Typically, the reflectivity in the nanowire target can be reduced to under \(20\%\)[35]. Furthermore, the laser pulse propagates in the vacuum gaps and interacts with the solid wires, pulling out the electrons and accelerating them via Lorentz force over a long distance [36]. This mechanism makes it possible to generate much more energetic electrons. In the CNT, the tailored front surface is expected to further reduce the reflectivity of the incident laser.  
Figure 2 shows the simulation results at \(t=22T_{0}\). To compare the reflectivity, the normalized Poynting flux in the longitudinal direction (\(S_{x}\)) is shown in Figure 2a,b. It can be clearly seen that the reflected component is much weaker in the CNT compared to the PNT. The reflectivity can be estimated by integrating the Poynting flux propagating in the negative direction (blue components in Figure 2a,b, denoted as \(S_{-}\)) at the left boundary, expressed as \(R=\frac{\int\int S_{-}(x=0,\,y,\,z)dydzdt}{W_{0}}\), where \(W_{0}\) is the total energy of the incident laserpulse. The value of \(R\) determines the energy that flows into the target, and the latter corresponds to electron heating and determines the temperature of the electrons. The reflectivity in the PNT is 15%, while in the CNT it is only 5%. This result indicates that in the CNT, more energy is transferred to the electrons in the nanowires, and thus the temperature of the electrons is expected to increase. Furthermore, multiple reflections by the corrugated surface leads to the focusing and reinforcement of the laser pulse in each cavity of the front surface. To better illustrate this, Figure 2d,e show the zoom-in view of \(S_{x}\) at the region near the front surface in Figure 2a,b, and the colormap is also adjusted. It is clearly seen that the intensity of \(S_{x}\) is higher in the CNT, and the peak value of the laser electric field is estimated to increase by 50% comparatively.  
As discussed above, due to the multi-reflections and focusing of the incident laser pulse by the corrugated surface, the electrons in the CNT are heated more effectively and are able to gain higher energy than those in the PNT. This can be observed from the energy spectra of electrons exhibited in Figure 2c. The spectra are obtained by counting all electrons moving in the \(+x\) direction. In the CNT, hot electrons with energies as high as over 40 MeV are generated, compared to a maximum energy of only 15 MeV in the PNT. The energy spectra show significantly different spectra because a portion of low-energy energetic electrons is shifted to higher energies. The temperature of the hot electrons is given by fitting the spectra with a Maxwellian distribution, as labeled by dashed lines in the figure. It increased by as much as 3 times from 1.6 MeV to 4.9 MeV. The phase space (\(p_{x}-x\)) of the electrons is also shown in Figure 2g,f, which is consistent with the energy spectra. It is worth noting that the phase space features a periodical structure, and the period of electron bunches is approximately \(\frac{\lambda_{0}}{2}\). Similar results have also been demonstrated in previous work [36; 37] on nanowire targets. Since TNSA is directly affected by the temperature of hot electrons, an increased temperature will enhance the sheath field established at the target rear surface and the subsequent proton acceleration. This will be discussed in detail in the following section.