Abstract
The action-angle variables for the longitudinal motion in synchrotrons are defined to conform with that of the transverse degrees of freedom. The Hamiltonian due to synchro-betatron coupling resonances is formulated in terms of these action-angle variables. A method for the calculation of the synchro-betatron resonance strength is discussed. The dynamics of particle motion near a resonance condition in the presence of nonlinear detuning is studied. The hysteresis phenomena associated with these resonances are discussed and employed to deduce the resonance Hamiltonian from experimental data.
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