# Enhanced Proton Acceleration from Laser Interaction with a Tailored Nanowire Target
## 3 Results and Discussions
### Robustness of the CNT  
To study the robustness of the CNT, a series of PIC simulations with different laser and target parameters were implemented. Firstly, the amplitude of the corrugated surface (expressed as \(x=10\lambda_{0}+A\ \cos(2\pi Ky)\)) was varied from \(A=0\) to \(A=5\lambda_{0}\), and \(K\) was fixed as \(K\lambda_{0}=0.25\), where \(A=0\) denotes the PNT. Figure 5a,b show the simulation results. The cut-off energy of the accelerated protons increases with \(A\), and the conversion efficiency also increases, meaning that more high-energy protons can be generated with larger \(A\). It is worth noting that both the conversion efficiency and cut-off energy tend to converge to a constant value with increasing \(A\), as shown in Figure 5b. This is because the laser reflectivity cannot be suppressed infinitely, and the absorption of the laser pulse also has an upper limit. When \(A\) is large enough, the incident laser pulse can be almost totally absorbed, leading to the maximum conversion efficiency and cut-off energy. Figure 5c,d show the cut-off energy of the accelerated protons and the conversion efficiency versus intensity of the incident laser. The cut-off energies of both targets increase nearly linearly with laser intensity, but changes in the conversion efficiency are relatively weak. It is clear that both the cut-off energy and conversion efficiency can be significantly enhanced in the CNT for different laser intensities. Figure 4: (**a–f**) Temporal evolution of energy density (normalized by \(n_{c}m_{g}c^{2}\)) at different times for the PNT (**a–c**) and the CNT (**d–g**) energy spectra of protons at the end of simulation. In experimental conditions, the laser pulse usually has a long pre-pulse of low intensity. This pre-pulse can pre-heat the target and generate low density plasmas that fill the gaps between the nanowires, which may impair the laser absorption and hot electron generation. [PERSON] et al. [29] have studied the effect of pre-pulses on laser absorption and TNSA of nanowire targets by filling the gaps with prescribed low-density plasma. They found that the prescribed plasma can inhibit laser propagation in the nanowires and significantly reduce the proton energy. In the discussions above, the effect of the pre-pulse is not taken into consideration. Here, a set of simulations were carried out to briefly investigate the influence of pre-plasma. The density and profile of the pre-plasma are influenced by many factors such as the contrast of the laser pulse and target material. However, in typical experiments on nanowire targets, the requirement for the contrast of the laser pulse is rather strict, even above 1\(\times\)10\({}^{12}\)[23,39]. For simplicity, we set the density of pre-plasma as \(n_{c}\) and distributed it uniformly in the gaps. The simulation parameters are identical to those introduced in Section 2, except that the gaps are filled with plasma with an electron density of 1\(n_{c}\) to represent the pre-plasma created by a laser pre-pulse. The energy spectra of the protons at the end of the simulation are shown in Figure 6a. The CNT can still generate much more energetic protons than the PNT. Furthermore, compared to the cases without pre-plasma, the cut-off energies of the protons are only slightly decreased, meaning that the influence of pre-plasma is not significant. This can be understood from the laser propagation in under-critical plasma. The non-relativistic critical density is \(n_{c}\), while for a laser pulse with large intensity, this value should thus be modified as \(\gamma n_{c}\), where \(\gamma=\sqrt{1+a_{0}^{2}}\) is the relativistic factor [40]. In our case, \(a_{0}=8\), and the corresponding relativistic critical density is approximately 8 \(n_{c}\), much larger than the density of filled pre-plasma. This means that the laser pulse can propagate through the gaps, and the pre-plasma does not have much influence on the absorption.