We investigate the target normal sheath acceleration of protons in thin aluminum targets irradiated at relativistic intensity by two time-separated ultrashort (35 fs) laser pulses. For identical laser pulses and target thicknesses of 3 and 6 $mu$m, we observe experimentally that the second pulse boosts the maximum energy and charge of the proton beam produced by the first pulse for time delays below $sim0.6-1$ ps. By using two-dimensional particle-in-cell simulations we examine the variation of the proton energy spectra with respect to the time-delay between the two pulses. We demonstrate that the expansion of the target front surface caused by the first pulse significantly enhances the hot-electron generation by the second pulse arriving after a few hundreds of fs time delay. This enhancement, however, does not suffice to further accelerate the fastest protons driven by the first pulse once three-dimensional quenching effects have set in. This implies a limit to the maximum time delay that leads to proton energy enhancement, which we theoretically determine.
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