Fig. 1: Microbunching and X-ray power evolution in a laser-driven free-electron laser (LDFEL).
From: X-ray free-electron lasing in a flying-focus undulator
A relativistic electron beam (blue dots) traveling at a velocity v0 collides head-on with the phase fronts of a laser pulse traveling at vph = −c. a A conventional laser pulse with a stationary focus, Rayleigh range ZR equal to the saturation length Lsat, and an energy U = 88 J (red). b A flying-focus pulse with a moving focus traveling at vf = c, a focal range Lf = Lsat, and U = 8 J (green). Both pulses have the same maximum amplitude a0 and wavelength λL. With the conventional pulse, the longitudinal uniformity of the undulator can only be improved by increasing the spot size and Rayleigh range. With the flying-focus pulse, the peak amplitude travels with the electron beam, allowing the pulse to have a much smaller spot size while still ensuring a longitudinally uniform undulator. Despite having 11× more energy, the conventional pulse results in a ~10× lower X-ray power P than the flying focus due to the spatial variation in a(x) experienced by the electron beam (see Fig. 2). Note that the length of the electron beam and period of the microbunches has been elongated for illustrative purposes.
