Laser-driven high-power X- and gamma-ray ultra-short pulse source
  A novel ultra-bright high-intensity source of X-ray and gamma radiation is suggested. It is based on the double Doppler effect, where a relativistic flying mirror reflects a counter-propagating electromagnetic radiation causing its frequency multiplication and intensification, and on the inverse double Doppler effect, where the mirror acquires energy from an ultra-intense co-propagating electromagnetic wave. The role of the flying mirror is played by a high-density thin plasma slab accelerating in the radiation pressure dominant regime. Frequencies of high harmonics generated at the flying mirror by a relativistically strong counter-propagating radiation undergo multiplication with the same factor as the fundamental frequency of the reflected radiation, approximately equal to the quadruple of the square of the mirror Lorentz factor. 
Timur Zh. Esirkepov, Sergei V. Bulanov, Alexei G. Zhidkov, Alexander   S. Pirozhkov, Masaki Kando