Three-dimensional theory of emittance in Compton scattering and x-ray protein crystallography

A complete, three-dimensional theory of Compton scattering is described, which fully takes into account the effects of the electron beam emittance and energy spread upon the scattered x-ray spectral brightness. The radiation scattered by an electron subjected to an arbitrary electromagnetic field distribution in vacuum is first derived in the linear regime, and in the absence of radiative corrections; it is found that each vacuum eigenmode gives rise to a single Doppler-shifted classical dipole excitation. This formalism is then applied to Compton scattering in a three-dimensional laser focus, and yields a complete description of the influence of the electron beam phase-space topology on the x-ray spectral brightness; analytical expressions including the effects of emittance and energy spread are also obtained in the one-dimensional limit. Within this framework, the x-ray brightness generated by a 25 MeV electron beam is modeled, fully taking into account the beam emittance and energy spread, as well as the three-dimensional nature of the laser focus; its application to x-ray protein crystallography is outlined. Finally, coherence, harmonics, and radiative corrections are also briefly discussed.