Luminosity optimisation for storage rings with low-s sections and small crossing angles

The luminosity of storage rings with intersections having small values of the amplitude function and the crossing angle is optimised imposing upper limits on the line density in the two beams and on the linear beam-beam tune shift. It is found that the luminosity is proportional to the energy of the stored particles. It depends on the beam-beam tune shift, the amplitude function the length of the crossing region, the beam emittance and the line density more weakly than one might expect from simple-minded formulae. In 300 GeV proton storage rings a luminosity above 10/sup 33/ cm/sup -2/ s/sup -1/ should be possible. (6 refs).