M. Bai

Overcoming intrinsic spin resonance by using an AC dipole

Depolarization from an intrinsic spin resonance can be avoided by adiabatically exciting a coherent betatron oscillation. Experimental results of creating sustained coherent betatron oscillations in the Brookhaven National Laboratory AGS, and relevant spin tracking calculations are discussed.

Spin Coupling Resonance and Suppression in the AGS

Spin depolarizing resonances due to coupling may account for as much as a 30 percent loss in polarization in the AGS. The major source of coupling in the AGS is the solenoidal snake. In the past some preliminary work was done to understand this phenomena [1], and a method to overcome these resonances was attempted [2]. However, in the polarized proton run of 2002, the response of these coupled spin resonances to the strength of the solenoidal snake, skew quadrupoles and vertical and horizontal betatron tune separation was studied to provided a benchmark for a modified DEPOL program [3]. Then using the new DEPOL program, a method method to cure the coupled spin resonances in the AGS via spin matching rather than global or local decoupling was explored.

Overcoming weak intrinsic depolarizing resonances with energy-jump

In the recent polarized proton runs in the AGS, a 5% partial snake was used successfully to overcome the imperfection depolarizing resonances. A polarized proton beam was accelerated up to the required RHIC injection energy of 25 GeV. However, a significant amount of polarization was lost at 0+/spl nu//sub y/, 12+/spl nu//sub y/ and 36+/spl nu//sub y/, which is believed to be partially due to the coupling resonances. To overcome the coupling resonance, an energy-jump was generated by rapidly changing the beam circumference using the powerful AGS RF system. It clearly demonstrates that the novel energy-jump method can successfully overcome coupling resonances and weak intrinsic resonances.

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.