  With the emergence in the next few years of a new breed of high power laser
facilities, it is becoming increasingly important to understand how interacting
with intense laser pulses affects the bulk properties of a relativistic
electron beam. A detailed analysis of the radiative cooling of electrons
indicates that, classically, equal contributions to the phase space contraction
occur in the transverse and longitudinal directions. In the weakly quantum
regime, in addition to an overall reduction in beam cooling, this symmetry is
broken, leading to significantly less cooling in the longitudinal than the
transverse directions. By introducing an efficient new technique for studying
the evolution of a particle distribution, we demonstrate the quantum reduction
in beam cooling, and find that it depends on the distribution of energy in the
laser pulse, rather than just the total energy as in the classical case.
