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The combined PTC-ORBIT code has been developed a few years ago to study the dynamics of the high intensity proton beams in synchrotrons, including the nonlinear machine resonances and the space charge effects in the self-consistent manner. In order to extend the code abilities the time variation of the main elements of the synchrotron has been introduced into the PTC module of the code. This feature opens the direct way to model the multi-turn injection process and the slow extraction process by using realistic machine description, in particular the dynamic variation of the betatron tunes, strength of the bump magnets, dynamic resonance correction or resonance excitation. To demonstrate the code abilities the corresponding simulations for CERN PS Booster and for J-PARC Main Ring are discussed.
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