Simultaneous treatment of betatron and synchrotron motions in circular accelerators

In this paper a general theory for the description of coupling and resonance effects in circular accelerators is developed. Therefore, a simultaneous treatment of all three oscillation modes has been set up with the use of the Hamilton formalism taking curvilinear coordinates as canonical variables and the time as independent variable. The theory - which takes into account the rf accelerating electric field and the time dependence of the magnetic field - shows various transverse-longitudinal coupling effects and sources that can excite synchro-betatron resonances. (orig.)