RHIC nine-magnet spin flipper has been operated successfully during RHIC polarized proton Run 17, with 97% spin flip efficiency achieved. The results show the importance of mirror resonance removal, small spin tune spread, and proper spin flipper driving tune sweep speed. Detailed spin tracking simulations, based on a Lorentz force and Thomas-BMT differential equation numerical solver code for accuracy, have been carried out to understand the experimental results. Agreement within measurement accuracy is obtained at injection energy, 23.8 GeV. It is not as tight at 255 GeV, reasons for that are exposed. These measurements and numerical studies allow to determine the sensitivity of spin-flip efficiency to the dispersion slopes at the two Siberian snakes and to the ac dipole frequency sweep speed. They also provide guidance for future developments at BNL's electron-ion collider.

The extensive APEX studies of the RHIC Spin Flipper were performed during FY17 achieving up to 97 % spin flip efficiency at both injection (23.8 GeV) and store (255 GeV) energy, using 9 MHz and 197 MHz RF system. The Zgoubi simulations were setup to reproduce the experimental conditions. The results of the APEX measurements and the numerical simulations are compared here, showing a good agreement especially at injection energy. The additional simulations of the spin flip efficiency, with the 28 MHz and 197 MHz RF system, show that a stronger Spin Flipper is needed in order to achieve good (|Pf /Pi| > 99 %) spin flip efficiency during the nominal physics store running conditions at 255 GeV. Tech. Note CA/AP/646 BNL C-AD

In order to minimize the systematic errors for the Relativistic Heavy Ion Collider (RHIC) spin physics experiments, flipping the spin of each bunch of protons during the stores is needed. Experiments done with single RF magnet at energies less than 2 GeV have demonstrated a spin-flip efficiency over 99%. At high energy colliders with Siberian snakes, a single magnet spin flipper does not work because of the large spin tune spread and the generation of multiple, overlapping resonances. Over past decade, RHIC spin flipper design has evolved and a sophisticated spin flipper, constructed of nine-dipole magnets, was developed to flip the spin in RHIC. A special optics choice was also used to make the spin tune spread very small. In recent experiment, 97% spin-flip efficiency was measured at both 24 and 255 GeV for the first time. The results show that efficient spin flipping can be achieved at high energies.

An ac dipole will be used for the efficient transport of polarized 3He in the AGS Booster as it is accelerated to |Gγ | = 10.5. The ac dipole produces coherent vertical beam oscillation for preservation of polarization by full spin flipping through the two intrinsic resonances: |Gγ | = 12 − νy and |Gγ | = 6+νy. The AGS Booster ac dipole will be tested with protons crossing the |Gγ | = 0 + νy intrinsic resonance, which has ac dipole requirements similar to polarized 3He crossing the |Gγ | = 12− νy resonance and provides a convenient proof of principle. Beam dynamics studies are planned for late 2019 and polarized proton experiments in early 2020. Part of this upgrade include magnets that will also be used by the vertical and horizontal tune kickers, providing higher kicker strength for tune measurements at higher rigidities. This paper gives a status of the project.

In polarized proton collision experiments, spin flip is needed to reduce the systematic errors. At high energy colliders with Siberian snakes, a single magnet spin flipper does not work . A more sophisticated spin flipper, constructed of nine-dipole magnets, was used to flip the spin in the BNL Relativistic Heavy Ion Collider. A 97% spin-flip efficiency was measured at both 24 and 255 GeV. The spin flip experiment results are presented in this paper.

This Letter reports the first spin tune measurement at high energies (24 and 255 GeV) with a driven coherent spin motion. To maintain polarization in a polarized proton collider, it is important to know the spin tune of the polarized proton beam, which is defined as the number of full spin precessions per revolution. A nine-magnet spin flipper has demonstrated high spin-flip efficiency in the presence of two Siberian snakes [H. Huang et al., Phys. Rev. Lett. 120, 264804 (2018).10.1103/PhysRevLett.120.264804]. The spin flipper drives a spin resonance with a given frequency (or tune) and strength. When the drive tune is close to the spin tune, the proton spin direction is not vertical anymore, but precesses around the vertical direction. By measuring the precession frequency of the horizontal component, the spin tune can be precisely measured. A driven coherent spin motion and fast turn-by-turn polarization measurement are keys to the measurement. The vertical spin direction is restored after turning the spin flipper off and the polarization value is not affected by the measurement. The fact that this manipulation preserves the polarization makes it possible to measure the spin tune during the operation of a high energy accelerator.

An ac dipole system will be installed in the AGS Booster in preparation for polarized helion experiments at RHIC and the future EIC. An ac dipole is a device that drives large amplitude betatron oscillations which cause all particles to sample the strong depolarizing horizontal fields in quadrupoles, resulting in a full spin flip of all particles. The amplitude of the vertical coherent oscillations induced by the ac dipole depends on the resonance proximity parameter, δm, which is the distance between the betatron tune and the modulated tune of the ac dipole. The rapid acceleration rate of the booster causes the modulated tune to decrease and δm to change. The absolute change in δm depends on the energy and the duration of the ac dipole cycle. Due to the non-zero momentum spread, particles with different momenta will have different value of δm and thus different coherent amplitudes. These effects are significant for helions crossing |Gγ | = 12 − νy and are simulated using zgoubi. A suitable range of δm values that optimize spin flip efficiency and minimize emittance growth are determined.

The proposed eRHIC project is an electron hadron collider to be built in the existing tunnel of the RHIC collider at Brookhaven National Laboratory (BNL). Polarized He-3(+2) ions are one of the hadron species to collide with the polarized electrons. To overcome the spin resonances during the pre-acceleration of polarized He-3(+2) ions in the AGS-Booster, an AC Dipole [2] is being built to create an artificial vertical intrinsic spin resonance which will eliminate the naturally occurring vertical intrinsic spin resonances during the acceleration. We will present an overview of the intrinsic spin resonances in the AGS-Booster, discuss the physics and the requirements of overcoming the spin resonances using an AC dipole, and present the results from the 2D and 3D electromagnetic study of the AC Dipole using the OPERA computer code [3].

In polarized proton collision experiments, it is highly advantageous to flip the spin of each bunch of protons during the stores to reduce the systematic errors. Experiments done at energies less than 2 GeV have demonstrated a spin-flip efficiency over 99%. At high energy colliders with Siberian snakes, a single magnet spin flipper does not work because of the large spin tune spread and the generation of multiple, overlapping resonances. A more sophisticated spin flipper, constructed of nine-dipole magnets, was used to flip the spin in the BNL Relativistic Heavy Ion Collider. A special optics choice was also used to make the spin tune spread very small. A 97% spin-flip efficiency was measured at both 24 and 255 GeV. These results show that efficient spin flipping can be achieved at high energies using a nine-magnet spin flipper.

Spin flipper experiments during RHIC Run 17 were performed to study its effectiveness as a method for polarization sign reversal during stores. Numerical simulations are reported here, which were performed in accompaniment of these, and are being pursued with the aim of accurately reproducing the experimental conditions and providing thorough insight in the role of various key parameters participating in the dynamics of the spin flip, such as the sweep rate of the AC dipole, chromatic orbit control at RHIC snakes, RF parameters, possible effects of non-linear spin resonances, mirror resonance, tolerance on flipper magnet parameters , etc. The ultimate goal is for these simulations to serve as a guidance toward perfect flip (Pf/Pi ≈ −1) to allow routine use during physics Runs.

(|Pf/Pi| > 99 %) spin flip efficiency during the nominal physics store running conditions at 255 GeV.

The Relativistic Heavy Ion Collider (RHIC) operation as the polarized proton collider presents unique challenges since both luminosity(L) and spin polarization(P) are important. With longitudinally polarized beams at the experiments, the figure of merit is LP{sup 4}. A lot of upgrades and modifications have been made since last polarized proton operation. A 9 MHz rf system is installed to improve longitudinal match at injection and to increase luminosity. The beam dump was upgraded to increase bunch intensity. A vertical survey of RHIC was performed before the run to get better magnet alignment. The orbit control is also improved this year. Additional efforts are put in to improve source polarization and AGS polarization transfer efficiency. To preserve polarization on the ramp, a new working point is chosen such that the vertical tune is near a third order resonance. The overview of the changes and the operation results are presented in this paper. Siberian snakes are essential tools to preserve polarization when accelerating polarized beams to higher energy. At the same time, the higher order resonances still can cause polarization loss. As seen in RHIC, the betatron tune has to be carefully set and maintained on the ramp and during the store to avoid polarization loss. In addition, the orbit control is also critical to preserve polarization. The higher polarization during this run comes from several improvements over last run. First we have a much better orbit on the ramp. The orbit feedback brings down the vertical rms orbit error to 0.1mm, much better than the 0.5mm last run. With correct BPM offset and vertical realignment, this rms orbit error is indeed small. Second, the jump quads in the AGS improved input polarization for RHIC. Third, the vertical tune was pushed further away from 7/10 snake resonance. The tune feedback maintained the tune at the desired value through the ramp. To calibrate the analyzing power of RHIC polarimeters at any energy above injection, the polarized hydrogen jet target runs for every fill with both beams. Based on the known analyzing power, there is very little polarization loss between injection and 100 GeV. An alternative way is to measure the asymmetry at 100 GeV followed by ramping up to 250 GeV and back down to 100 GeV and then to measure the asymmetry again at 100 GeV. If the asymmetry after the down ramp is similar to the measurement before the up ramp, polarization was also preserved during the ramp to 250 GeV. The analyzing power at storage energy can then be extracted from the asymmetries measured at 100 GeV and 250 GeV. The tune and orbit feedbacks are essential for the down ramp to be possible. The polarized proton operation is still going on. We will push bunch intensity higher until reaching the beam-beam limit. The even higher intensity will have to wait for the electron lenses to compensate the beam-beam effect. To understand the details of spin dynamics in RHIC with two snakes, spin simulation with the real magnet fields have been developed recently. The study will provide guidance for possible polarization loss schemes. Further polarization gain will requires a polarized source upgrade; more careful setup jump quads in the AGS to get full benefit; and control emittance in the whole accelerator chain.

For the RHIC spin flipper to achieve a rotating field, it requires operating five AC dipoles as a pair of closed orbit bumps. One key requirement is to minimize the remnant AC dipole driven betatron oscillation outside of the spin flipper by 50 dB [1]. In the past, due to its inherent sensitivity, a single pickup with a direct-diode detector (3D) [4] and dynamic signal analyzer (DSA) were used to measure bump closure by measuring the remnant oscillations. This however proved to be inadequate, as the betatron phase advance between the AC dipoles is non-zero. A method of combining multiple BPMs into a sensitive measure of bump closure has been developed and was tested during RHIC polarized proton operation in 2013. This technique as well as the experimental results will be presented. INTRODUCTION A spin flipper for RHIC (Relativistic Heavy Ion Collider) has been developed for RHIC spin-physics experiments. It is needed to cancel systematic errors by reversing the spin direction of the two colliding beams multiple times during a store [2]. Figure 1: Spin flipper configuration The spin flipper system consists of four DC dipole magnets (spin rotators) and five AC dipole magnets (see fig. 1). The aim of this configuration is to produce a rotating field. Multiple AC dipoles are needed to localize the driven coherent betatron oscillation inside the spin flipper [1, 3]. While results from the 2012 run did suggest the presence of a rotating field, the polarization lifetime was degraded with the AC dipoles on. This suggested incomplete bump closure and/or incorrect phase between bumps [1] which lead to reinvestigating the method used to close the AC dipole bumps. Operationally the AC dipoles form two bumps that minimize the effect of the AC dipoles outside of the spin flipper. The central AC dipole, #3 in figure 1, is common to both bumps. Both AC-dipole bumps operate at the same frequency, but are phase shifted from each other. The convention used when expressing closure in dB is to make the 0 dB reference the strongest AC dipole. In case of the dual bump, AC dipole #4 is used. BBQ 3D AFE & DSA Up until the 2013 run the closure was only trimmed using the pickup and direct-diode detector (3D) analog front end (AFE) of the RHIC baseband tune meter (BBQ) processed via a DSA. Figure 2: Closed bump DSA beam spectrum (green plot). The red plot is the fitted AC dipole magnet currents. Figure 3: AC dipole #4 alone (solid) and closed bump (dotted) BPM beam spectrum of the most sensitive BPM. The DSA spectrum in figure 2 (green plot) shows that the closure for the AC dipole bumps was 67 dB. However, the spectrum of the most sensitive BPM (fig. 3, dotted plot) shows a closure of only 28 dB. This nearly two order of magnitude difference clearly shows that it’s not possible to determine closure using a single pickup (at a single frequency). The possibility of using a single pickup at multiple frequencies has not yet been fully explored. COMBINING BPM MEASURMENTS Even though discrete Fourier transform (DFT) spectrums, which typically are calculated using the fast Fourier transform (FFT) algorithm, are used here, these ___________________________________________ *Work supported by Brookhaven Science Associates, LLC under contract DE-AC02-98CH10886 with the U.S. Department of Energy and RIKEN, Japan. methods are not strictly DFT/FFT methods. As a matter of fact the BPM magnitude and phase used by software calculations used a sine/cosine fit, which can be thought of as the evaluation of the discrete time Fourier transform (DTFT) or z-transform at a single frequency. Figure 4: BPM spectrums of weakest (blue), strongest (red), average (green), weighted average (black) and vector average (purple) for AC dipole #4 at 90 Apk (76 G·m) for PP at injection (23.8 GeV). Figure 5: BPM spectrums of weakest (blue), strongest (red), average (green), weighted average (black) and vector average (purple) for AC dipole #4 at 117.9 Apk (100 G·m) for PP at store (255 GeV). Figures 4 and 5 show the weakest and strongest BPM spectrums and the spectrums for different methods of combining BPMs for polarized proton beam at injection and store respectively when excited by a single AC dipole (#4). In all cases the response is normalized to place the AC dipole peak at the driven frequency (0.49) at 0 dB. This is done as convenient way to visualize the signal to noise ratio. BPM data was taken with 1024 turn data records. For the 2013 run, 4096 turn records were available and these longer records would improve the signal to noise ratio by 6dB. Also note that the AC dipole excitation is 2 dB stronger for the data taken at store. The weakest BPM responses (blue traces) do change proportionally with the change in energy or magnetic rigidity (~20 dB). The strongest response (red traces) changes less (~12dB), which is just a direct result of the optics also being different. The weakest and strongest responses were also produced by different BPMs. The average response (green trace) is just a simple magnitude average:

The five AC dipole RHIC spin flipper design in the RHIC Blue ring was first tested during the RHIC 2012 polarized proton operation. The advantage of this design is to eliminate the vertical coherent betatron oscillations outside the spin flipper. The closure of each ac dipole vertical bump was measured with orbital response as well as spin. The effect of the rotating field on the spin motion by the spin flipper was also confirmed by measuring the suppressed resonance at Q{sub s} = 1 - Q{sub osc}.

The five AC dipole RHIC spin flipper design in the RHIC Blue ring was first tested during the RHIC 2012 polarized proton operation. The advantage of this design is to eliminate the vertical coherent betatron oscillations outside the spin flipper [1]. The closure of each ac dipole vertical bump was measured with orbital response as well as spin. The effect of the rotating field on the spin motion by the spin flipper was also confirmed by measuring the suppressed resonance at Qs = 1 −Qosc.

The commissioning of the RHIC spin flipper in the RHIC Blue ring during the RHIC polarized proton run in 2009 showed the detrimental effects of global vertical coherent betatron oscillation induced by the 2-AC dipole plus 4-DC dipole configuration [1]. Additional three AC dipoles were added to the RHIC spin flipper in the RHIC Blue ring during the summer of 2010 to eliminate the vertical coherent betatron oscillations outside the spin flipper [2]. This new design is scheduled to be commissioned during the RHIC polarized proton run in 2011. This paper presents the status of the system as well as latest simulation results.