  Compton scattering of a laser beam with a relativistic electron beam has been
used to generate intense, highly polarized and nearly monoenergetic x-ray or
gamma-ray beams at many facilities. The ability to predict the spatial,
spectral and temporal characteristics of a Compton gamma-ray beam is crucial
for the optimization of the operation of a Compton light source as well as for
the applications utilizing the Compton beam. In this paper, we present two
approaches, one based upon analytical calculations and the other based upon
Monte Carlo simulations, to study the Compton scattering process for various
electron and laser beam parameters as well as different gamma-beam collimation
conditions. These approaches have been successfully applied to characterize
Compton gamma-ray beams, after being benchmarked against experimental results
at the High Intensity Gamma-ray Source (HIGS) facility at Duke University.
