Hamiltonian Formulation for Synchrobetatron Resonance Driven by Dispersion in RF Cavities

Synchrobetatron resonance driven by dispersion in RF cavities is studied by using the Hamiltonian formalism. Explicit expressions are given for the growth rate of betatron and synchrotron oscillation amplitudes on resonance and on fast-crossing of the resonance. The effect of distributed RF cavities is also studied, and it is shown that the resonance can be suppressed by proper arrangement of RF cavities. The theory is shown to agree fairly well with the computer simulation for PETRA and some numerical examples are given for the booster of the TRIUMF Kaon Factory project. This paper is an abridged version of Ref. (1), and readers are referred to Ref. (1) for more details.