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ON THE DYNAMIC APERTURES OF CIRCULAR ACCELERATORS

One of the preoccupations of the circular accelerator designers is to estimate the influence of nonlinear forces on the single particle’s motion. Even though the nonlinear forces compared with the linear ones are usually very small, what is observed in reality, however, is that when the amplitudes of the transverse oscillation of a particle are large enough, the transverse motions might become unstable and the particle itself will finally be lost on the vacuum chamber. In the following sections we will show how the nonlinear forces limit the dynamic apertures and what is the relation between them.