  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.
