Optimization of compton source performance through electron beam shaping

We investigate a novel scheme for significantly increasing the brightness of x-ray light sources based on inverse Compton scattering (ICS) - scattering laser pulses off relativistic electron beams. The brightness of ICS sources is limited by the electron beam quality, since electrons traveling at different angles, and/or having different energies, produce photons with different energies. Therefore, the spectral brightness of the source is defined by the 6D electron phase space shape and size, as well as laser beam parameters. The peak brightness of the ICS source can be maximized, then, if the electron phase space is transformed in a way such that all electrons scatter off the x-ray photons of same frequency in the same direction, arriving to the observer at the same time. We describe the x-ray photon beam quality through the Wigner function (6D photon phase space distribution), and derive it for the ICS source when the electron and laser rms matrices are arbitrary.