X-ray generation in strongly nonlinear plasma waves.

We show that a laser wake field in the "bubble" regime [Appl. Phys. B 74, 355 (2002)]], works as a compact high-brightness source of x-rays. The self-trapped relativistic electrons make betatron oscillations in the transverse fields of the bubble and emit a bright broadband x-ray radiation with a maximum about 50 keV. The emission is confined to a small angle of about 0.1 rad. In addition, we make simulations of x-ray generation by an external 28.5 GeV electron bunch injected into the bubble. gamma quanta with up to GeV energies are observed in the simulation in good agreement with analytical results. The energy conversion is efficient, leading to a significant stopping of the electron bunch over 5 mm interaction distance.