Coherent frequency combs from electrons colliding with a laser pulse

Highly coherent and powerful light sources capable of generating frequency combs in the soft x-ray domain are essential for advancing high precision measurements and conducting rigorous tests of fundamental physics. In this work, we derive the analytical conditions required for the emission of coherent radiation, including coherent frequency combs, from an electron beam colliding with a laser pulse, modeled as a plane wave. Using numerical simulations, we demonstrate that this scheme can produce a coherent soft x-ray frequency comb, provided the electron beam is sufficiently monoenergetic and electrons in the beam are regularly spaced. Furthermore, we highlight the advantageous role of employing few-cycle laser pulses in relaxing the stringent monoenergeticity requirements for coherent emission. The conditions derived here can also be used to optimize coherent emission from electron beam-laser interactions in other frequency ranges, such as the terahertz domain.