Intensity scaling limitations of laser-driven proton acceleration in the TNSA-regime

We report on experimental results laser-driven proton acceleration using high-intensity laser pulses. present power law scalings of the maximum energy with pulse and show that scaling exponent $\ensuremath{\xi}$ strongly depends scale length preplasma, which is affected by temporal intensity contrast. At lower intensities, a shortening leads to transition from square root toward linear scaling. Above certain threshold, however, significant deviation this observed. Two-dimensional particle-in-cell simulations that, in case, electric field accelerating ions generated earlier has higher amplitude. However, since process starts as well, fastest protons outrun region highest strength, ultimately rendering less effective. Our investigations thus point principle limitation target normal sheath regime, would explain why increase above limit $100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ not yet been achieved.