Magnet fringe fields, nonlinear effects, and compensation in large acceptance rings

The importance of nonlinear effects has been well known in the field of modern high resolution spectrography and in other areas requiring the precise manipulation of large phase space volumes. Simulations for such devices require treating the field as precisely as possible; furthermore the required large aperture of the appearing magnets usually makes the consideration of fringe fields crucial. In conventional proton beam rings, many of the nonlinear effects can often be safely neglected because of the relatively small emittances. This is not the case anymore in large acceptance rings such as those to be used for the various muon accelerator scenarios, where the difficulty and expense of cooling requires the ability to manipulate a beam of unusually large emittance. We will discuss various nonlinear effects including those due to fringe fields and the so-called kinematic correction for proposed muon storage rings, and present novel methods of symplectic tracking and other nonlinear analysis tools as well as schemes to compensate the nonlinear effects.