Emittance in Nonlinear Thomson Scattering

Inverse Compton scattering sources are finding increasing use as intense sources of high-energy photons. When operated at high field strength, ponderomotive detuning of the scattered emission can lead to decreased source performance. Up to now, the calculations of spectra for such nonlinear Thomson scattering have been done assuming a perfectly aligned electron interacts with the incident laser beam and several authors have investigated whether pondermotive detuning may be mitigated or cured by suitable incident laser chirping prescriptions. In order to determine if these chirping prescriptions are suitable in real beams with nonzero emittance, it is necessary to include misaligned boundary conditions in the electron motion and calculate the resulting spectra from the exact motion. In this paper we provide the exact solution for the electron equations of motion in the case of a misaligned electron passing through a laser pulse of high field strength. This solution is then used to calculate the scattered radiation distribution and we determine the emittance limits for the simplest chirping prescription