Nonlinear effects of dipole magnet edge field in charged particle cyclic accelerators and storage rings

It is well-known that nonlinear effects influence the process of slow resonance extraction of charged particles from accelerators and storage rings. Nonlinear effects caused by boundary fields of dipole magnets are theoretically considered. Dependence of betatron oscillation frequencies on their amplitudes, characteristics of the boundary field and betatron functions of the facility is determined. The frequency of radiation oscillations is shown to remain the same, and vertical - to grow with the amplitude increase. Nonlinear resonances which can be excited by the boundary fields are considered. Estimations of the theory are confirmed by the results of experimental determination of nonlinear characteristics of betatron oscillations carried out at N-100 storage ring of KPTI