The dynamics and radiation of ultrarelativistic electrons in strong counterpropagating laser beams are investigated. Assuming that the particle energy is the dominant scale in the problem, an approximate solution of the equation of motion is derived and the characteristic features of the motion are examined. An analytical expression for the spectral distribution of spontaneous radiation is derived in the framework of the semiclassical operator method based on the classical trajectory.
The failure of the local constant field approximation is demonstrated in this field configuration due to the emergence of an additional small time scale in the electron dynamics. Moreover, we identify a class of anomalous LCFA violation in which electrons turn sharply and leave the radiation formation zone much earlier than in the LCFA estimation. In contrast to previous observations of LCFA violation in a single laser beam, resulting in new low-harmonic peaks in the spectrum, here deviations from LCFA results are seen across the whole spectrum. A similar phenomenon is also demonstrated for an electron colliding with an ultrashort laser pulse. These results indicate the necessity of amending laser-plasma kinetic simulations in multiple beam laser configurations.
We also put forward a realistic scheme involving two counter-propagating laser pulses at different intensity in the region of 10¹⁶ - 10¹⁹ W/cm²  and a relativistic electron beam with the energy about tens of MeV. There are two parameter regimes, which can lead to x-ray sources with different properties. In the first regime, when the electron co-propagates with the high intensity laser, a single peak x-ray source with 0.1% energy spreading can be realized in the keV energy regime. On the other hand, when the high intensity laser is counter-propagating with the electron, a comb-like x-ray source of around keV energy can be obtained. The obtained keV x-ray comb increases the conventional frequency comb energy by two orders of magnitude.
 

strong laser fields, relativistic electrons, nonlinear compton scattering, strong field QED