Synchrotron-radiation limit of the luminosity in TeV linear colliders

In linear colliders in the TeV region, the synchrotron radiation occuring in the final quadrupole magnet limits the smallest vertical RMS beam size which can be reached at the interaction point. Due to the same effect, however, the distribution does not remain gaussian, which helps the luminosity: it is much larger than what is expected from the RMS beam size, but much smaller than the value without radiation in the quadrupole. The luminosity is still limited from above, but the maximum occurs at a much smaller value of the nominal beam size. A simple approximate expression for the luminosity is also proposed