The synchrotron equation of motion in quasi-isochronous (QI) storage rings is transformed to a universal Weierstrass equation, where the solution is given by Jacobian elliptic functions. Scaling properties of the QI Hamiltonian are derived. The effects of phase space damping and the sensitivity of particle motion to external harmonic modulation are studied. We find that the rf phase modulation is particularly enhanced in QI storage rings. Exact formula and sum rules for resonance strength coefficients are derived. When the QI dynamical system is subject to harmonic modulation, it exhibits a sequence of period-2 bifurcations leading to global chaos in a region of modulation tune. This means that the operators of QI storage rings should pay special attention to rf phase noise. {} 1996 The American Physical Society.
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Riabko et al. (1996) studied this question.
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