Pair production in bunch crossing

Electron-positron colliders operating in the multi-TeV range, at the required very high luminosity, will have to contend with an intense beamstrahlung. Serious problems will originate from the energetic electrons and positrons which the radiated photons will produce before they leave the bunch. We calculate the pair production rate by a photon traversing a bunch, focusing here on the contribution proportional to the bunch length, in the deep quantum regime. The probability for pair production is of the same order as that for beamstrahlung. It is considerable. (orig.)