A compensated dispersion-free long insertion for an FFAG synchrotron

An FFAG synchrotron differs from a synchrocyclotron by having a large radial field gradient; this large gradient greatly reduces the magnet volume while maintaining stable orbits for all energies, but it does induce substantial nonlinearities. A decade ago, the author proposed a dispersion-free insertion for an FFAG that provides regions of small volume for RF cavities, strippers, and injection and extraction elements, similar to a normal synchrotron. Here we exploit this insertion to provide compensation of the lower order nonlinear driving fields, thereby greatly increasing the dynamic aperture as compared to an FFAG without insertions. The correction fields may be programmed to track the momentum or may be static, providing full compensation at the injection energy