Coherent radiation of an electron bunch colliding with an intense laser pulse

We study the conditions for coherent radiation of an electron bunch driven by a counterpropagating strong pulsed electromagnetic plane wave. We derive the spectrum of the coherent radiation and show that it is emitted backwards with respect to the laser propagation direction and has a very narrow angular spread. We demonstrate that for a solid density plasma coherent radiation extends to frequencies up to hundreds of keV thereby enhancing the low-frequency part of the spectrum by many orders of magnitude. Our analytical findings are tested with 3D particle-in-cell simulations of an electron bunch passing through a laser pulse, clearly demonstrating how the coherence can essentially modify the observed radiation spectrum.