Abstract
In the process of bunching an intense beam, the betatron oscillation frequency of particles changes due to a growth in their momentum rejection (in the presence of chromaticity) and changes in the Coulomb shift. These changes lead to the intersection of nonlinear betatron resonances. A mathematical model of the dynamics of ions in the process of bunching an intense beam has been built in order to assess the influence of transverse betatron resonances on the motion of particles. This model takes into account the influence of space charge on the longitudinal and transverse oscillations of particles in the presence of one- and two-dimensional betatron resonances. An analysis of the motion of particles near the one- and two-dimensional third-order resonances is given. Results of the numerical simulation of particle losses and emittance growth in the process of bunching an intense beam in the storage ring at the Institute for Theoretical and Experimental Physics (ITEP) are presented.
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