Characterizing Luminosity Evolution in the Tevatron

We derive an approximate form of a luminosity evolution in a high intensity hadron collider taking into account the most important phenomena of intrabeam scattering (IBS), beam burn-up due to luminosity and beam-beam effects. It is well known that an exponential decay does not describe luminosity evolution very well unless the lifetime is allowed to vary with time. However, a "1/time" evolution, which this derivation shows is a good approximation, fits data from the Tevatron well.