The effect of tune modulation in two-dimensional symplectic maps has been studied by using the concept of chaotic transport in terms of flux across resonances. When a single resonance is dominant, the particle escape due to the tune modulation can be characterized by the increment of the flux induced by the modulation. The parameter dependence of the particle escape rate obtained by using the transport theory agrees well with the result of the multiparticle tracking study and the beam study experiments at the CERN Super Proton Synchrotron. This study showed that the transport theory provides a computationally efficient means of studying the particle escape due to the tune modulation and estimating the parameter dependence of the escape rate.
Shi, Jack J. Chaotic transport in time-dependent symplectic maps. PHYSICAL REVIEW LETTERS. MAY 20 1996. 76(21): 3971-3974.