  We present a model which describes proton scattering data from ISR to
Tevatron energies, and which can be applied to collimation n high energy
accelerators, such as the LHC and FCC. Collimators remove beam halo particles,
so that they do not impinge on vulnerable regions of the machine, such as the
superconducting magnets and the experimental areas. In simulating the effect of
the collimator jaws it is crucial to model the scattering of protons at small
momentum transfer~$t$,as these protons can subsequently survive several turns
of the ring before being lost. At high energies these soft processes are well
described by Pomeron exchange models. We study the behaviour of elastic and
single-diffractive dissociation cross sections over a wide range of energy, and
show that the model can be used as a global description of the wide variety of
high energy elastic and diffractive data presently available. In particular it
models low mass diffraction dissociation, where a rich resonance structure is
present, and thus predicts the differential and integrated cross sections in
the kinematical range appropriate to the LHC.We incorporate the physics of this
model into the beam tracking code MERLIN and use it to simulate the resulting
loss maps of the beam halo lost in the collimators in the LHC.
