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We treat here the process of simulation of charged particle dynamics using so called hybrid system. Hybrid system is a system with continuous and discrete parts, described by differential and difference equations, respectively. In this case new mathematical model of beam dynamics optimization is suggested. The main parameters of optimization are: coefficient of particle capture in the acceleration mode, phase and energy spectra of particles at the exit of the accelerator, the transverse beam characteristics, etc. Optimization was carried out for the drift tubes accelerator.
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