Collisions of short, intense laser pulses with electron beams have recently been proposed for various purposes, such as high-quality, Compton-Backscattered Xray sources CBX, or coherent pair production positron sources for future e + e , Linear Colliders. For such i n tense laser elds, few-photon perturbative treatments do not su ce, and nonperturbative e ects in the elds must be modeled. These e ects have, until recently, only been modeled within the'local plane wave', or Volkov,

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... in which ponderomotive i.e. laser intensity gradient effects are ignored. A systematic quantum treatment of the'post-Volkov' e ects occurring in such collisions has recently been initiated by Ben-Menahem 1 . In the present paper, we use the results of 1 to render a simpli ed treatment o f the leading ponderomotive corrections to electron trajectories during the electronlaser collision, and estimate the rami cations for CBX sources which utilize such collisions. We also apply to the CBX case some recently derived estimates of three non-ponderomotive e ects: two body collisions in the laser-induced shower; EM self-forces of this shower; and back-reaction of linac-laser collisions upon the laser elds. All three e ects are shown to be negligible for the numerical examples considered here. 2