Steady regime of radiation pressure acceleration with foil thickness adjustable within micrometers under 10-100 PW laser

Quasi-monoenergetic GeV-scale protons are predicted to efficiently generate via radiation pressure acceleration (RPA) when the foil thickness is matched with the laser intensity, e.g., $L_{mat}$ at several nm to 100 nm with $10^{19}-10^{22} \rm ~W cm^{-2}$ available in laboratory. However, non-monoenergetic protons with much lower energies than prediction were usually observed in RPA experiments, because of too small foil thickness which is hard to bear insufficient laser contrast and foil surface roughness. Besides the technical problems, we here find that there is an upper-limit thickness $L_{up}$ derived from the requirement that the laser energy density should dominate over the ion source, and $L_{up}$ is lower than $ L_{mat}$ with the intensity below $10^{22} \rm~ W cm^{-2}$, which causes inefficient or unsteady RPA. As the intensity is enhanced to $\geq 10^{23} \rm ~W cm^{-2}$ provided by 10-100 PW laser facilities, $L_{up}$ can significantly exceed $L_{mat}$ and therefore RPA becomes efficient. In this regime, $L_{mat}$ acts as a lower-limit thickness for efficient RPA, so the matching thickness can be extended to a continuous range from $L_{mat}$ to $L_{up}$; the range can reach micrometers, within which foil thickness is adjustable. This makes RPA steady and meanwhile the above technical problems can be overcome. Particle-in-cell simulation shows that multi-GeV quasi-monoenergetic proton beams can be steadily generated and the fluctuation of the energy peaks and the energy conversation efficiency remains stable although the thickness is taken in a larger range with increasing intensity. This work predicts that near future RPA experiments with 10-100 PW facilities will enter a new regime with the adjustable and large-range foil thickness for steady acceleration.