Recent significant improvements of the contrast ratio of chirped pulse amplified pulses allows us to extend the applicability domain of laser accelerated protons to very thin targets. In this framework, we propose an analytical model particularly suitable to reproducing ion laser acceleration experiments using high intensity and ultrahigh contrast pulses. The model is based on a self-consistent solution of the Poisson equation using an adiabatic approximation for laser generated fast electrons which allows one to find the target thickness maximizing the maximum proton (and ion) energies and population as a function of the laser parameters. Model furnished values show a good agreement with experimental data and 2D particle-in-cell simulation results.
Andreev, A., Levy, A., Ceccotti, T., Thaury, C., Platonov, K., Loch, R. A., & Martin, P. (2008). Fast ion energy flux enhancement from ultra thin foils irradiated by intense and high contrast short laser pulses. Physical review letters, 101(15), 155002-1-155002-4. https://doi.org/10.1103/PhysRevLett.101.155002