Effects of overlapping parametric resonances on the particle diffusion process

Abstract

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.

Method of phase space beam dilution utilizing bounded chaos generated by rf phase modulation

“…Only a few-fold increase in emittance was observed as particles traveled into nonoverlapping resonant islands. This result was supported by experiments at the IUCF CSR [8,9], where a huge emittance increase was observed at some optimal rf phase difference Δϕ o as depicted in Fig. 1.…”

“…We suggest driving the bunch into large chaotic regions that are bounded by well-behaved tori. The diffusion of particles by phase modulation applied to a single cavity in a double rf system has been observed experimentally at the Indiana University Cyclotron Facility (IUCF) cooler storage ring (CSR) in 1997 [8,9]. Figure 1 shows the square of the rms bunch length exhibiting linear growth as a function of time.…”

“…It has been shown that applied phase modulation will excite parametric resonances in a particle bunch [8]. When a multitude of parametric resonances are strongly driven and overlap, large regions of chaotic particle motion are generated [9]. In order to facilitate particle diffusion, the relative phase difference between the two rf cavities will need to deviate from zero, resulting in an asymmetric potential [10].…”

“…An alternate method exists that applies phase modulation to only the secondary rf system. This method has been explored at the IUCF CSR in 1997 [8,9]. Both methods indicate that the rf phase difference Δϕ o must be nonzero to generate overlapping resonant island chains that form large chaotic regions for particles diffusion.…”

Anomalous beam diffusion near beam-beam synchrobetatron resonances

“…Diffusion due to nonlinear resonances is more complex and the study of this phenomenon has a long history, see e.g. [7][8][9][10][11]. Resonances when modulated, either by dynamical effects such as synchrobetatron coupling or due to ripple in magnet currents, can sweep across phase space and transport particles to large amplitudes [12,13].…”