Calculation of integrated luminosity for beams stored in the Tevatron collider

A model for calculating the integrated luminosity of beams stored in the Tevatron collider is presented. The model determines the instantaneous luminosity by calculating the overlap integral of bunched beams passing through the interaction region. The calculation accounts for the variation in beam size due to the beta functions and also for effects due to finite longitudinal emittance and nonzero dispersion in the interaction region. The integrated luminosity is calculated for the beams as they evolve due to processes including collisions and intrabeam scattering. The model has been applied to both the existing and upgraded Tevatron collider, but is not limited to them. It is concluded that, in the Tevatron, the integrated luminosity is determined by more than collisions losses, intrabeam scattering, and gas scattering. Postulating an additional source of transverse emittance growth of about 0.3 π mm-mrad/h brings the model closer to the observations. In the upgraded collider, the integrated luminosity per day could approach 1/pb. This may be compared to the 6.6/pb delivered so far in the run