B. Hamilton

Effects of rf voltage modulation on particle motion

Abstract The effects of rf voltage modulation on synchrotron motion were studied experimentally. The experimental data revealed the resonance islands generated by the rf voltage modulation. With electron cooling, beam particles were observed to damp to the basins of these resonance islands or attractors, which were observed to rotate about the origin of the phase space at a half of the modulation frequency. The measured amplitude of the attractors as a function of the modulation frequency agreed very well with the theoretical prediction. The Poincare maps in the resonance rotating frame were obtained from the experimental data and compared with tori of the Hamiltonian flow. Based on our theoretical formulation, slow beam extraction using rf voltage modulation and a bent crystal are also studied.

Experimental results of the betatron sum resonance

The experimental observations of motion near the betatron sum resonance, /spl nusub x/+2/spl nusub z/=13, are presented. A fast quadrupole (Panofsky-style ferrite picture-frame magnet with 8 pulsed power supplies) producing a betatron tune shift of the order of 0.03 at rise time of 1 /spl mu/s was used. This quadrupole was used to produce betatron tunes which jumped past and then crossed back through a betatron sum resonance line. The beam response as function of initial betatron amplitudes were recorded turn by turn. The correlated growth of the action variables, J/sub x/ and J/sub z/, was observed. The phase space plots in the resonance frame reveal the features of particle motion near the nonlinear sum resonance region.<<ETX>>

Space charge effects and intensity limits of electron-cooled bunched beams

For stripping injection of proton beams in the IUCF Cooler, electron cooling permits us to accumulate beam currents several times higher than what can be obtained without cooling. Paradoxically, the electron cooling system also appears to be responsible for limiting peak currents in the ring at 45 MeV to about 6 mA. Thus the tool which allows us to accumulate beam also prevents us from accumulating more beam. At this point we can account for some of the observed beam features when we include space charge effects. Presently, we do not, however, have any techniques to counteract the space charge effects and thus raise this intensity limit.

Nonlinear beam dynamics studies at the IUCF cooler ring

The nonlinear beam dynamics of transverse betatron oscillations were studied experimentally at the IUCF Cooler Ring. Particles were kicked onto resonance islands and the properties of these islands were studied. The island tune was determined with high precision by Fourier analyzing the spectrum containing the islands and the properties of these island were studied. The island tune was determined with high precision by Fourier analyzing the spectrum containing the island oscillations. The island width was estimated based on a single resonance model. The Hamiltonian of particle motion near a resonance condition was thus deduced.

First test of orbit response matrix in proton storage ring

The orbit response matrix method is applied to experimentally determine the Cooler Ring optics at the Indiana University Cyclotron Facility (IUCF). We have carried out two experiments in Oct. And Nov. 1996 to measure the orbit response of the IUCF Cooler Ring. An analysis software was adopted from the NSLS, BNL. In our analysis, strength error in quadrupoles and steering dipoles, and amplifier gain in BPMs are included as fitting parameters. However, effects of the linear and non-linear coupling are excluded in our preliminary analysis. Since the resolution of our BPM system is of the order of 10 /spl mu/m, we will address the effect of BPM resolution on the applicability of the orbit response matrix method in proton storage rings.

A method of detecting coherent synchrotron modes

Abstract A method for measuring coherent longitudinal synchrotron modes is developed and tested at the Indiana University Cyclotron Facility Cooler Ring. This method can be used to detect the onset of coherent instability and can provide important diagnosis for the control of beam brightness. Some possible improvement of this technique is discussed.

Beam diagnostic systems and their use in the new IUCF beam line

Diagnostic tools developed for and being used in a new 30 m beam line (BL1C) connecting the IUCF high intensity polarized ion source (HIPIOS) with the injector cyclotron are described and the results obtained with them are detailed. These devices include non-intercepting beam position monitors, wire scanners, and beam sweeper systems. Studies of rf beam bunching have been performed using a high bandwidth current readout. Programs have been developed for automatic emittance measurements and beam centering in the beam line.

Experimental simulation of ground motion effects

Synchro-betatron coupling in a proton storage ring with electron cooling was studied by modulating a transverse dipole field close to the synchrotron frequency. The combination of the electron cooling and transverse field modulation on the synchrotron oscillation is equivalent to a dissipative parametric resonant system. The proton bunch was observed to split longitudinally into two pieces, or beamlets, converging toward strange attractors of the dissipative system. These phenomena might be important to understanding the effect of ground vibration on the SSC beam, where the synchrotron frequency is about 4/spl sime/7 Hz, and the effect of power supply ripple on the RHIC beam, where the synchrotron frequency ramps through 60 Hz at 17 GeV/c.<<ETX>>

Determination of the linear coupling resonance strength using 2D invariant Tori

Experimentally obtained Poincare maps in the resonant precessing frame for particle motion with linear coupling revealed invariant tori of the 2D Hamiltonian. Using these tori, we obtained the linear coupling strength, the tune shift with betatron amplitude coefficient and the proximity parameter to the resonance. The coupling strengh obtained with this method agreed well with that obtained from measuring the betatron tune separation of the normal modes.

Longitudinal phase‐space measurements at IUCF

Synchrotron motion in the IUCF cooler ring was studied using turn‐by‐turn beam tracking on ten‐turn intervals, where the beam phase relative to the rf and the closed‐orbit position in a high‐dispersion region were measured. The synchrotron tune shift with amplitude was measured and is compared with theory. The driven response of the system was also studied using the same techniques, and was found to share many of the same characteristics of other parametric resonant systems. The experimental results did not exhibit any effects of bunch decoherence expected from the tune shift with amplitude.