Diffusion Dynamics in a Tevatron Store

A separator failure during a store in 2002 led to a drop in luminosity, to increased emittance growth and to a drop in beam lifetimes. We show that a simple diffusion model can be used to explain the changes in beam lifetimes. Emittance growth of beams when they are in collision occurs due to many sources: beam-beam interactions, magnetic nonlinearities, intra-beam scattering, scattering off the residual gas and possibly others. The dynamics of the emittance growth is complicated and it depends strongly on the tunes. It is not always clear that the dynamics can be described by a diffusion process at all particle amplitudes in each beam. However in one store early in Run II, there was a sudden drop in a separator voltage in the Tevatron and the subsequent enhanced emittance growth and intensity lifetime drop could be described by a simple diffusion model. In this report we analyze the luminosity drop, compare the measured value with the expected drop and analyze the change in beam lifetimes. We show how a simple model of diffusive emittance growth and a change in physical aperture provides a quantitative explanation for the change in lifetimes.