Generation of high-energy protons from the Coulomb explosion of hydrogen clusters by intense femtosecond laser pulses

The energy distributions of protons emitted from the Coulomb explosion of hydrogen clusters by an intense femtosecond laser have been experimentally obtained. Ten thousand hydrogen clusters were exploded, emitting 8.1 keV protons under laser irradiation of intensity $6\times {10}^{16}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$ The energy distributions are interpreted well by a spherical uniform cluster analytical model. The maximum energy of the emitted protons can be characterized by cluster size and laser intensity. The laser intensity scale for the maximum proton energy, given by a spherical cluster Coulomb-explosion model, is in fairly good agreement with the experimental results obtained at a laser intensity of ${10}^{16}–{10}^{17}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2$ and also when extrapolated with the results of three-dimensional particle simulations at ${10}^{20}–{10}^{21}{\mathrm{W}/\mathrm{c}\mathrm{m}}^2.$