Abstract: A method for controlling a density distribution of electrons provided by an electron source for use in hard X-ray, soft X-ray and/or extreme ultraviolet generation, the method comprising generating a plurality of electrons from a pattern of ultracold excited atoms using an ionization laser inside a cavity, wherein the electrons have a density distribution determined by at least one of the patterns of excited atoms and the ionization laser, and accelerating the electrons out of the cavity using a non-static acceleration profile, wherein the acceleration profile controls the density distribution of the electrons as they exit the cavity.