Influence of asymmetric HF-oscillations in the resonator of a storage element on the stability of transverse motion of the particles

Abstract

frapid attenuation of betatron oscillations in the storage ring of VEPP-2 of the Institute of Nuclear Physics of the Siberian Branch of the Academy of Sciences of the USSR [4], It was shown in [5] that the cause of such attenuation is interaction of coherent betatron oscillations with external systems (resonator and inf[ector plates). Here azimuthaliy asymmetric HF-osciilations arise in the external systems; these oscillations, for certain conditions, lead to attenuation of the betatron oscillations. A determination was made in [5] of the power for excitation of an I-IF-field by infinitely short-duration clusters, whose motion is regarded as given. Since asymmetrical oscillations have an appreciable effect on the transverse motion of the particles, it is expedient to make an exact analysis of the excitation of these oscillations, based on the solution of the self-consistent problem, We shall assume, for simplicity, that an ordinary cylindrical resonator of height h and radius a is used in the storage ring, A beam of charged particles, passing close to the resonator axis, excites in it mainly oscillations of electric type, whose vector potential can be written in the form