FINDING THE CIRCULAR MAGNET APERTURE WHICH ENCLOSES AN ARTITRARY NUMBER OF MIDPLANE-CENTERED BEAM ELLIPSES

In specifying the magnets for an accelerator, one must be able to determine the aperture required by the beam. In some machines, in particular FFAGs, there is a significant variation in the closed orbit and beta functions over the energy range of the machine. In addition, the closed orbit and beta functions may vary with the longitudinal position in the magnet. It is necessary to determine a magnet aperture which encloses the beam ellipses at all energies and all positions in the magnet. This paper describes a method of determining the smallest circular aperture enclosing an arbitrary number of midplane-centered ellipses