A. Riabko

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.

The Indiana University Cooler injection synchrotron RF cavity

A small 2.2 Tesla-meter booster synchrotron is under construction at the Indiana University Cyclotron Facility to boost polarized beam performance in the electron cooled Indiana University Cooler Synchrotron. Polarized light proton or deuteron beam from a high intensity polarized ion source will be preaccelerated to 7 and 6 MeV respectively by an RFQ/DTL accelerator. The beams are then debunched to reduce the energy spread and strip-injected into the booster synchrotron. The booster RF system must accomplish the tasks of beam capture and acceleration. At the end of the acceleration cycle, the beam phase needs to be aligned to the Cooler synchrotron RF for bucket-to-bucket beam transfer. A single RF cavity in the ring will provide the necessary RF field to accomplish the above tasks.

The Indiana University Cooler injector synchrotron RF system

A 2.2 Tesla-meter synchrotron with 17.4 m circumference is being built at the Indiana University Cyclotron Facility (IUCF). The purpose of the project is to achieve higher luminosity for nuclear physics experiments using electron cooled polarized light ion beams in the IUCF Cooler synchrotron. The injection line for the booster synchrotron consists of an RFQ/DTL linear accelerator delivering a 7 MeV proton beam and a 6 MeV deuteron beam for the booster injection. A debunching system will be installed in the injection beamline to reduce the energy spread of beams out of the linear accelerators. Charge-exchange injection is used for high intensity multiturn beam accumulation. The booster output beams, 200 MeV for protons and 105 MeV for deuterons, will be transferred bucket to bucket to the IUCF Cooler synchrotron. The rf system design for the booster synchrotron is presented in this paper.

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.

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.

Modeling of the IUCF cooler synchrotron

Measurements of lattice parameters for the Indiana University Cyclotron Facility (IUCF) Cooler synchrotron at betatron tunes close to a sum resonance line are discussed. The measured beta functions at 36 quadrupole locations and the dispersion functions at 35 Beam Position Monitor (BPM) locations are compared with calculations. The methods used to make the above measurements and the data analysis are described.

Nonlinear dynamics issues for quasi-isochronous storage rings

The synchrotron equation of motion in quasi-isochronous (QI) storage rings was transformed to a universal Weierstrass equation, where solution is given by Jacobian elliptic functions. Scaling properties of QI Hamiltonian were derived. The effects of phase space damping and the sensitivity of particle motion to external harmonic modulation were studied. We found that rf phase modulation is particularly enhanced in QI storage rings. This means that the operators of QI storage rings should pay special attention to rf phase modulation. Exact formulae and sum rules for resonance strength coefficients were derived. In the presence of radiation damping and rf phase modulation, the QI system exhibits a sequence of period-two bifurcations enroute to global chaos (instability) in a region of modulation tune. The critical modulation amplitude for the onset of global chaos shows a cusp as a function of modulation tune. This cusp was shown to arise from the transition from the 2:1 to the 1:1 parametric resonances. We also studied the effect of rf voltage modulation and found that the tolerance of rf voltage modulation is much larger than that of rf phase modulation.

Particle dynamics inside a quasi-isochronous storage ring

Quasi-isochronous {alpha}-like bucket can be important in providing ultra short bunches. the instability of a bunch inside the bucket is found to be severely affected by rf phase modulation. The synchrotron tune drops to zero at the bucket edge very rapidly, indicating the possibility of a thick chaotic layer due to overlapping of resonance islands. The approach to chaos comes from a sequence of bifurcation into 2:1 parametric resonances. When quantum excitation is included in addition to radiation damping, the instability is worsened. the steady-state particle distribution in the longitudinal phase space is Gaussian in the phase coordinate and non-Gaussian in the momentum coordinate, unless the bunch is small. The size of the bunch is governed only bye the ``thermal energy`` {ital E{sub th}} = D{sup 2}/2A, where D and A are, respectively, the normalized diffusion and damping coefficients. The quantum lifetime of the particle bunch, for the D and A that have been enhanced by the smallness of the phase- slip factor, is studied and turns out to be much longer than expected. Phase modulation tends to enhance quantum diffusion at high frequencies, but leads to stochastic resonances instead at low frequencies.

The lattice design of Indiana University Cyclotron Facility Cooler Injector Synchrotron

This paper reports lattice design studies of a low energy booster at the Indiana University Cyclotron Facility (IUCF). This booster will be used as an injector, which is named as Cooler Injector Synchrotron (CIS), for the existing IUCF Cooler ring. The IUCF CIS will be able to accelerate high-intensity polarized protons or deuterons coming from a RFQ linac from 7 MeV (6 MeV) to 200 MeV (105 MeV). The beam bunch then will be extracted and injected into the Cooler ring for further acceleration. The finalized lattice design for the CIS has four superperiods. Each period is composed of a drift space and a dipole magnet which has 90/spl deg/ bending angle and 12/spl deg/ edge angle at both ends. The circumference of the CIS is 17.364 meters, one fifth of that of the Cooler ring. The designed horizontal and vertical tunes are 1.463 and 0.779, respectively. Possible effects from the employment of trim quadrupoles, which will be located between dipoles, are also discussed.