Autoresonant excitation of nonlinear beam motion in storage rings

Understanding and controlling of nonlinear beam dynamics are essential to the performance of storage ring light sources. In order to measure and correct limitations due to nonlinear beam dynamics, an effective method is needed to excite the beam oscillation to large amplitudes. Autoresonance is a method that enables the control of the amplitude of a driven nonlinear oscillator by sweeping the frequency of the driver. In this study, autoresonant excitation of beam transverse oscillations in storage rings is studied. The threshold of the drive amplitude for autoresonance is theoretically obtained, for cases with or without damping. The results are in good agreement with simulations for a simple storage ring model, as well as for models of actual storage rings. Application of the theory to experimental data on the SPEAR3 storage ring also validates the results.