Filling Schemes, Collision Schedules and Beam-beam Equivalence Classes

Several filling schemes are under consideration for the LHC, each
leading to a different bunch train structure.  The collision schedule is
a description of when and where the bunches encounter each other,
whether separated or head-on.  In the LHC, matters are complicated by
the large number of bunches and the path-length differences between
inner and outer arcs of the rings.  The complexity of the problem is
broken down by computing the beam-beam equivalence classes, i.e., sets
of bunches that see identical---or sufficiently similar---sequences of
beam-beam encounters.  This is a refinement of the classification into
"normal" and "Pacman" bunches.  The analysis generates the detailed MAD
description of the encoun ters in each class. Various filling schemes
will be compared from this perspective.