Intense high-quality medical proton beams via laser fields

During the past decade, the interaction of high-intensity lasers with solid targets has attracted much interest, regarding its potential in accelerating charged particles. In spite of tremendous progress in laser-plasma based acceleration, it is still not clear which particle beam quality will be accessible within the upcoming multi petawatt (1 PW = 10$^{15}$ W) laser generation. Here, we show with simulations based on the coupled relativistic equations of motion that protons stemming from laser-plasma processes can be efficiently post-accelerated using crossed laser beams focused to spot radii of a few laser wavelengths. We demonstrate that the crossed beams produce monoenergetic accelerated protons with kinetic energies $> 200$ MeV, small energy spreads ($\approx$ 1$%$) and high densities as required for hadron cancer therapy. To our knowledge, this is the first scheme allowing for this important application based on an all-optical set-up.