Experimental measurement of resonance islands induced by rf voltage modulation

Quadrupole-mode transfer function and the nonlinear Mathieu instability

We show that the quadrupole-mode transfer function (QTF) is a powerful nondestructive tool to measure properties of dynamical systems. In particular, we discuss the feasibility of using the QTF to measure the betatron tunes and the beam emittances with a beam-position monitor system. The QTF can also be used to compensate the optical mismatch during the beam injection process. However, it is less effective than the rf dipole method in overcoming the intrinsic spin resonances for polarized beam acceleration.

Effects of overlapping parametric resonances on the particle diffusion process

The evolution of the beam distribution in a double-rf system with a phase modulation on either the primary or secondary rf cavity was measured. We find that the particle diffusion process obeys the Einstein relation if the phase space becomes globally chaotic. When dominant parametric resonances still exist in the phase space, particles stream along the separatrices of the dominant resonance, and the beam width exhibits characteristic oscillatory structure. The particle-tracking simulations for the double-rf system are employed to reveal the essential diffusion mechanism. Coherent octupolar motion has been observed in the bunch beam excitation. The evolution of the longitudinal phase space in the octupole mode is displayed.