  Tracking studies have indicated that for a lattice whose elements all have a
single field multipole present, all having the same order k, the dynamic
aperture approaches a non zero limit when k becomes very large. The dynamic
aperture and other properties of the lattice, as k becomes large, will be
called the high multipole limit. It will be shown that the high multipole limit
provides a reasonable estimate of the dynamic aperture of an accelerator, and
the other properties of the high multipole limit found below are useful for
understanding the stability of the accelerator. The high multipole limit is
easily computed and it also provides an estimate of how much can be gained by
correcting the lower field multipoles. The above results will be illustrated by
tracking studies done with a simple one cell lattice, and with a RHIC lattice
having six low beta insertions.
