Time evolution of the luminosity of colliding heavy-ion beams in BNL Relativistic Heavy Ion Collider and CERN Large Hadron Collider

We have studied the time evolution of the heavy ion luminosity and bunch intensities in the Relativistic Heavy Ion Collider (RHIC), at BNL, and in the Large Hadron Collider (LHC), at CERN. First, we present measurements from a large number of RHIC stores (from Run 7), colliding 100 GeV/nucleon {sup 197}Au{sup 79}+ beams without stochastic cooling. These are compared with two different calculation methods. The first is a simulation based on multi-particle tracking taking into account collisions, intrabeam scattering, radiation damping, and synchrotron and betatron motion. In the second, faster, method, a system of ordinary differential equations with terms describing the corresponding effects on emittances and bunch populations is solved numerically. Results of the tracking method agree very well with the RHIC data. With the faster method, significant discrepancies are found since the losses of particles diffusing out of the RF bucket due to intrabeam scattering are not modeled accurately enough. Finally, we use both methods to make predictions of the time evolution of the future {sup 208}Pb+{sup 82+} beams in the LHC at injection and collision energy. For this machine, the two methods agree well.