Bending magnet edge field nonlinear effects in cyclic accelerators and storage rings

It is known that bending magnet edge fiels decrease axial focusing and axial betatron oscillation frequency. The aim of the study is to consider resonances excited by edge fields, to determine amplitude-frequency characteristics of betatron motion, and to estimate edge field effect on the process of slow extraction of particles from an accelerator. The vector potential of a dipole magnet edge field is found; it is shown that in case of a plane magnet the edge field is completely described by the function determining an axial component in a median plane. The amplitude-frequency characteristics of betatron oscillations are found on the base of Hamiltonian formalism; it is shown that the edge field doesn't effect the nonlinearity of radial oscillations. Types and forces of resonances excited by the edge field are found. Comparison of the theoretical results obtained with the experimental data shows good agreement. Conclusions about essential draw backs during beam extraction in the axial plane, if compare with aradial one, are made. It is caused, firstly, by the presence of relatively high nonlinearity stabilizing the resonance of slow extraction. It will lead to increase of particle losses in septum magnet and to increase of extracted beam emittance