## 5 Conclusions  
In summary, we demonstrate significant improvement in proton acceleration from thin solid targets using a double plasma mirror (DPM) [34] to enhance the temporal contrast of the ultrashort (24 fs), ultraintense (\(>\)\(10^{21}\,\mathrm{W\,cm^{-2}}\)) F2 Apollon laser beam. This improvement is observed simultaneously in terms of maximum energy, conversion efficiency, and beam quality. The DPM mitigates the impact of the \(\sim\)1 ps long, relativistic-intensity (\(\sim\)\(10^{3}\) contrast) laser pulse preceding the main pulse, thereby enabling solid foils as thin as 20 nm to be used. In contrast, the minimum target thickness exploitable under standard irradiation conditions is 800 nm. With the DPM, we were able to accelerate protons up to 15 MeV from a 20 nm thick foil, and achieved a peak proton energy of 35 MeV from a 250 nm foil, with only 5 J of laser energy. Remarkably, this maximum proton energy is \(\sim\)40% higher than without the DPM, despite 50% less laser energy. Two-dimensional (2D) PIC simulations attribute the superior performance of the DPM configuration to a stronger effective longitudinal electrostatic field and its closer overlap with the expanding proton bunch when the main laser pulse interacts with the sharp-gradient solid foil. These results pave the way for optimizing laser-driven X-ray and neutron sources [11], opening new perspectives in nuclear material interrogation [66; 67; 13; 68] and medicine [7]. Furthermore, we can expect even further improvements in laser-proton acceleration at higher intensities, such as with the upcoming 10 PW-scale F1 beam of the Apollon facility.  
Conceptualization, J.F.; methodology, J.F., F.M. and A.A.; software, W.Y., Y.Y., P.A., E.d., X.D. and L.G.; investigation, R.L., T.W., J.F., W.Y., I.C., A.B., E.C., C.G., I.P., D.P., D.M. and L.G.; data curation, P.K., F.T., W.Y., J.F., Q.D., E.F., S.P. and R.L.; writing--original draft preparation, W.Y., J.F., R.L., E.F. and L.G.; writing--review and editing, all. All authors have read and agreed to the published version of the manuscript.  
Figure 12: Longitudinal (\(x-p_{x}\)) phase-space distribution of protons for (**a**) a direct shot on a 1.5 \(\upmu\)m thick Al target and (**b**) a DPM shot on a 200 nm Si + 50 nm Al target.  
**Funding:** This work was supported by funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant Agreement No. 787539, Project GENESIS), by CNRS through the MITI interdisciplinary programs and by IRSN through its exploratory research program. The project was also made possible thanks to the credits of the Hubert Curien Mainiomides program made available by the French Ministry of Europe and Foreign Affairs and the French Ministry of Higher Education and Research. We acknowledge the financial support of the IdEx University of Bordeaux/Grand Research Program \"GPR LIGHT\", and of the Pazy Foundation Grant No. 435/2023. The computational resources of this work were supported by the National Sciences and Engineering Research Council of Canada (NSERC) and Compute Canada (Job: pve-323-ac, PA).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.  
**Acknowledgments:** The authors acknowledge the national research infrastructure Apollon and the LULI staff for their technical assistance.  
**Conflicts of Interest:** Author [PERSON] was employed by the company HB11. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.