Abstract
The ring is symmetric with two interacting regions op- posite each other as shown in Fig. 1. Distances are meas- ured from one of the interaction regions. The main accel- crating cavity gap is situated an integral number of half- wavelengths from the interaction region. The frequency- splitting cavities are placed in some straight sections. For the general case, the ith cavity gap is placed at a position Li from the interaction region. The voltage on the gap is where X is the particle position and the independent vari- able is t IT e turn number. (Y is the momentum compaction and Es the energy of the synchronous particle. The phase tra- jectories are curves defined in the E-X, phase space for constant values of the above Hamiltonian, and the phase tra- jectory enclosing the maximum area is called the separatrix. The small amplitude synchrotron oscillation frequencies are given by
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