Orbit properties of non-scaling FFAG accelerators using constant-gradient magnets

Very high momentum compaction can be obtained in non-scaling FFAG accelerators using constant-gradient magnets with their field strengths decreasing outwards - sufficiently high that the magnet apertures (and vacuum chamber) need be little wider than in a strong-focusing synchrotron. Such machines are of great potential interest for applications in the 0.1 - 50 GeV energy range requiring higher pulse repetition rates or intensities than synchrotrons can provide. Explicit formulae have been developed for the equilibrium orbit properties, particularly their momentum dependence, in various lattices, and give accurate enough results to provide a useful tool for choosing the magnet parameters. In this paper the dependences of orbit offset and circumference on momentum are explored for doublet lattices, and numerical results from the formulae are compared with those from lattice codes.