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The principle of using multiple partial helical magnets to preserve the polarization of the proton beam during its acceleration was applied successfully to the alternating gradient synchrotron (AGS) which currently operates with two partial helical magnets. In this paper we further explore this idea by using four partial helical magnets placed symmetrically in the AGS ring. This provides many advantages over the present setup of the AGS, which uses two partial helical magnets. First, the symmetric placement of the four helical magnets and their relatively lower field of operation allows for better control of the AGS optics with reduced values of the beta functions especially near beam injection and allows both the vertical and horizontal tunes to be placed within the ``spin tune gap,'' therefore eliminating the horizontal and vertical intrinsic spin resonances of the AGS during the acceleration cycle. Second, it provides a wider spin tune gap. Third, the vertical spin direction during beam injection and extraction is closer to vertical. Although the spin tune gap, which is created with four partial helices, can also be created with a single or two partial helices, the high field strength of a single helical magnet which is required to generate such a spin tune gap makes the use of the single helical magnet impractical, and that of the two helical magnets rather difficult. In this paper we will provide results on the spin tune and on the optics of the AGS with four partial helical magnets, and compare them with those from the present setup of the AGS that uses two partial helical magnets. Although in this paper we specifically discuss the effect of the four partial helices on the AGS, this method which can eliminate simultaneously the vertical and horizontal intrinsic spin resonances is a general method and can be applied to any medium energy synchrotron which operates in similar energy range like the AGS and provides the required space to accommodate the four helices. In addition, the four partial helix solution is an optimum solution because it eliminates all the spin resonances for any synchrotron which operates in the same energy range as the AGS.

Since 2001, the Relativistic Heavy Ion Collider has experienced electron cloud effects, some of which have limited the beam intensity. These include dynamic pressure rises (including pressure instabilities), tune shifts, a reduction of the instability threshold for bunches crossing the transition energy, and possibly incoherent emittance growth. We summarize the main observations in operation and dedicated experiments as well as countermeasures including baking, nonevaporable getter coated warm beam pipes, solenoids, bunch patterns, antigrazing rings, prepumped cold beam pipes, scrubbing, and operation with long bunches.

The four electron stripping stages leading to fully stripped gold ions in the Relativistic Heavy Ion Collider (RHIC) are briefly described. The third stripper, which removes 46 electrons from the ${\mathrm{Au}}^{31+}$ ions leading to heliumlike ${\mathrm{Au}}^{77+}$, offers the greatest challenges in terms of energy loss and induced energy spread. These problems are described in detail as well as recent advances in the design and performance of this stripper. Measurements performed with several carbon and aluminum strippers show general agreement with a semiempirical model but small systematic deviations suggest that some model adjustments may be in order. The best performance is predicted and obtained with a combined carbon-aluminum foil system. Measurements showing the enhanced performance in the alternating gradient synchrotron are described. The stripper that removes the last two electrons has also been improved and the results of relevant calculations and measurements are presented.

Two partial Siberian snakes were used to avoid all the spin imperfection and vertical intrinsic resonances in the alternating gradient synchrotron (AGS) at Brookhaven National Laboratory. However, the horizontal betatron motion can cause polarization loss resulting from the nonvertical stable spin direction in the presence of two partial snakes. This type of resonance, called a horizontal intrinsic spin resonance, was observed and systematically studied in the AGS. A simplified analytic model and numerical simulation have been developed to compare with experimental data. Properties of the horizontal intrinsic resonance are discussed.

We describe a fast and robust global decoupling scheme, coupling angle modulation. This novel technique introduces an extra rotating coupling coefficient into the coupled optics to determine the global decoupling strengths. The eigentune split is used as the observable during the modulation. The two eigentunes are tracked with a high-resolution phase locked loop tune measurement system. In the article, the principle of coupling angle modulation is presented, followed by its application to the Relativistic Heavy Ion Collider (RHIC). Coupling angle modulation coupling correction has been used for the global coupling correction on the nonstop RHIC ramp.

Measurement of the residual betatron coupling with skew quadrupole modulation is a new diagnostics technique. It was developed and tested at the Relativistic Heavy Ion Collider (RHIC) as a promising method for measuring coupling on the ramp. By modulating the strengths of skew quadrupole families, the two tunes' responses are precisely measured with the phase lock loop system. The projection ratio of the residual coupling coefficient onto the coupling modulation direction can be determined. In this article, the analytical solution to the skew quadrupole modulation is given. Dedicated beam studies were carried out in RHIC Run'04 and the results are presented. The ability to measure coupling on the ramp opens the possibility of continuously correcting coupling during acceleration.

An 11.4% partial Siberian snake was used to successfully accelerate polarized protons through a strong intrinsic depolarizing spin resonance in the Alternating Gradient Synchrotron (AGS). No noticeable depolarization was observed. This opens up the possibility of using a 20% to 30% partial Siberian snake in the AGS or other medium energy proton synchrotrons to overcome all weak and strong depolarizing spin resonances.

Response is made to J. A. MacLachlan's preceding Comment [Phys. Rev. ST Accel. Beams 4, 017001 (2001)]. We are gratified to see that high quality simulations, as presented by MacLachlan, verify our experimental results.