The dynamic aperture and the high multipole limit

Tracking studies have indicated that for a lattice whose elements all have a single field multipole present, all having the same order {kappa}, the dynamic aperture approaches a non zero limit when {kappa} becomes very large. The dynamic aperture and other properties of the lattice, as {kappa} 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.