Effect of parametric resonances on the bunched beam dilution mechanism

Abstract

Controlled beam-bunch dilution has been proved to be essential in the acceleration of high intensity beams in many high energy accelerators such as the AGS and the CERN PS for transition energy crossing. A secondary RF cavity operating at 200 MHz has been used routinely to blow up the longitudinal phase space for the transition energy crossing. In our recent experiments, we have observed a non-diffusive mechanism in the beam dilution process. As part of a new proposal, we will devote more effort to understand the importance of parametric resonances in bunched-beam dilution.Double RF systems were used in accelerator physics to decrease space-charge effects by reducing the peak current or to overcome multi-bunch instability by modifying the time structure of the beam. Double RF systems were also found to be a very effective tool for increasing synchrotron tune spread and enchancing the Landau damping rate. In a series of Cooler experiments, we investigated a possibile use of double RF systems in order to stimulate longitudinal beam dilution by modulating the secondary high frequency RF cavity. The experiment described in this paper was motivated by recent theoretical and experimental studies in the field.This progress report discusses experimental measurements of the evolution of the bunch profile while a modulating secondary RF system is acting on the beam. The experiment was conducted at IUCF and used a bunched proton beam with a kinetic energy of 45 MeV. The revolution frequency for the synchronous particle was fo = 1.03168 MHz.The frequency of the primary RF cavity was 1.03168 MHz with hl = 1, and the harmonic number of the secondary rf cavity was h = 9. The voltage of the main RF cavity was set at about 300 V, which resulted in a synchrotron frequency of about 705 Hz while operating with the primary RF cavity alone. The total beam current was about 100 PA, or equivalently 6 x 10' protons per bunch. The accelerator was operated with a cycle time of 10 s; the injected beam was electron-cooled for about 3 s (the rms equilibrium bunch length was about 10 -20 ns); then the phase modulation was applied and beam profiles were digitized for a few hundred milliseconds. To measure the time evolution of the bunch, we used a BPM sum signal passing through a low loss cable (7/B1' heliax high bandwidth, low attenuation cable). Then the signal was amplified by an amplifier with a bandwidth of 150 MHz and digitized by a fast sampling scope at a time step of 1 ns. The system

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.…”

“…(6) implies that the phases of both rf cavities are being simultaneously modulated in the model. 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].…”

“…The strengths of parametric resonances driven by rf phase modulation are functions of the action J [8] [see Eq. (17) and Fig.…”

“…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.…”

“…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.…”