New Feature of the Oscillating Synchrotron Motion Derived from the Hamiltonian Composed of Three Motions

摘要

Equations for the synchrotron motion are derived from the Hamiltonian, which was composed of coasting, betatron and synchrotron motions. The synchrotron oscillation is not only an oscillation of the revolution frequency but also an oscillation of the average radius. The synchrotron oscillation, which is both longitudinal and horizontal oscillations, can exchange energy with the betatron oscillation, which is a horizontal oscillation. The synchrotron oscillation occurs under a constant particle velocity and the s description is equivalent to the t description. Coriolis like force acting on its horizontal oscillation brings out its longitudinal oscillation.