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During the past decade, the interaction of high-intensity lasers with solidtargets has attracted much interest, regarding its potential in acceleratingcharged particles. In spite of tremendous progress in laser-plasma basedacceleration, it is still not clear which particle beam quality will beaccessible within the upcoming multi petawatt (1 PW = 10$^{15}$ W) lasergeneration. Here, we show with simulations based on the coupled relativisticequations of motion that protons stemming from laser-plasma processes can beefficiently post-accelerated using crossed laser beams focused to spot radii ofa few laser wavelengths. We demonstrate that the crossed beams producemonoenergetic accelerated protons with kinetic energies $> 200$ MeV, smallenergy spreads ($\approx$ 1$%$) and high densities as required for hadroncancer therapy. To our knowledge, this is the first scheme allowing for thisimportant application based on an all-optical set-up.

Intense high-quality medical proton beams via laser fields