  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 Au 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 Pb
beams in the LHC at injection and collision energy. For this machine, the two
methods agree well.
