Fig. 1. Top: two electrons that are close to one another in a phase space and interact with a laser can radiate coherently. Bottom: spectrum of a large number (N) of electrons colliding with a laser pulse for various densities of electron bunch. Dashed magenta curve: spectrum without accounting for coherency (N times the single-particle spectrum). The dot-dashed red curve shows the dependence of the highest coherently enhanced frequency on the density. The surface combines coherent (to the left of the dashed red curve) and incoherent (to the right) spectra. Laser intensity 10¹⁹ W/cm², electron energy 50 MeV.