The motion of trapped secondary particles in a storage ring

The longitudinal motion of secondary electrons and ions trapped by an electric circulating beam field in a nonuniform magnetic field of a storage ring is studied analytically. Conditions for their reflection in the fringe field of the storage ring magnet and in the sign-alternating field of an undulator have been determined. Calculations have been made for the probability of reflection in the case of an ion generated in a straight section, i.e. in a region of zero magnetic field.