Analytic model for quadrupole fringe-field effects

The linear-field non-scaling FFAG lattices originally proposed for multi-GeV muon acceleration are now being modified for sime 200 MeV/u proton or carbon medical applications. The momentum range is large and the chromatic tune variation is significant. In the medical case, the issue of resonance crossing is acute owing to the lower rate of energy gain. Quadrupole magnets with non-normal entry/exit faces are considered as means to reduce the tune variation. Thus one is motivated to study the fringe-field effects of quadrupole magnets with rotated entry/exit faces. However, just as a bending (dipole) magnet fringe-field B_f prop taue^ithetas is found to give a focusing effect, so we expect the fringe field of a quadrupole magnet, B_f prop tau²e^i2thetas, with rotated pole faces to give amplitude-dependent impulses reminiscent of a sextapole magnet. This note is a precis of two laboratory reports[l 1, 12].