Quantum beamstrahlung from ribbon pulses.

IR this paper the high energy expansion introduced in our previous paper is i used to describe to the problem of beamstrahlung due to an extended pulse with an elliptical cross section of arbitrary eccentricity. We show that the transverse . geometry of the pulse enters in a remarkably simple scaling manner. This case _ is of interest because the radiative energy loss can be markedly reduced while simultaneously keeping a fixed luminosity if the beam pulses are very thin in one transverse direction, i.e., shaped like ribbons. Effects of other types of beam shaping are briefly discussed and the physics of the process is emphasized.