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All-optical ideas provide a potential to dramatically cut off the size andcost of x-ray light sources to the university-laboratory scale, with thecombination of the laser-plasma accelerator and the laser undulator. However,the large longitudinal energy spread of the electron beam from laser-plasmaaccelerator may hinder the way to high brightness of these all-optical lightsources. In this paper, the beam energy spread effect is proposed to besignificantly compensated by the natural transverse gradient of a laserundulator when properly transverse-dispersing the electron beam. Theoreticalanalysis and numerical simulations on conventional laser-Compton scatteringsources and high-gain all-optical x-ray free-electron lasers with the electronbeams from laser-plasma accelerators are presented.

Compensating the electron beam energy spread by the natural transverse gradient of laser undulator in all-optical x-ray light sources