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.

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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

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Fast bunch to bunch feedback is necessary to control instabilities caused by coupled bunch oscillations in high intensity machines. A time domain active feedback scheme is discussed with focus on effective error detection using simple analog filters. Fast electronic switches direct each beam bunch signal from a beam pickup to a corresponding filter. The filters are excited at steady states. The output of the filters are steady sine waves tracking the phase and amplitude variations of individual bunches, allowing easy phase comparison with a reference rf signal. Amplitude detection of the signals yields valuable information of higher order beam oscillation modes. The beam motion information is processed and multiplexed to a fast phase or amplitude modulator that drives a wideband kicker. The feedback system can also be used to correct individual bunch oscillations caused by injection errors in larger machines filled by a number of booster cycles.