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Numerical simulations are inescapable steps in spin dynamics studies and in the design of polarized beam accelerators and optical components. An integral part of the Summer 2021 USPAS Spin Class teachings, under the form of a 2-week miniworkshop, this chapter is also an initiation to the field, “hands on”: in a first Section, numerical simulation exercises are proposed which cover many of the theoretical aspects of hadron and electron spin dynamics addressed during the lectures, including resonant depolarization; preservation methods such as harmonic orbit correction, tune jump, the use of an ac dipole, or snakes; the effect of synchrotron radiation; spin diffusion and its suppression; spin matching. A second Section is dedicated to detailed solutions of these simulation exercises and includes tight comparisons of numerical outcomes and theoretical expectations from the lectures.

Small perturbative fields in a synchrotron influence both the spin and orbital motion of a stored beam. Their effect on the beam polarization consists of two contributions, a direct kick and an effect of the ring lattice due to orbit perturbation. Spin response function is an analytic technique to account for both contributions. We develop such a technique for the spin-transparent synchrotrons where the design spin motion is degenerate. Several perspective applications are illustrated or discussed. In particular, we consider the questions of the influence of lattice imperfections on the spin dynamics and spin manipulation during an experiment. The presented results are of a direct relevance to NICA (JINR), RHIC (BNL), EIC (BNL) and other existing and future colliders when they arranged with polarization control in the spin-transparent mode.

The Jefferson Lab Electron Ion Collider (JLEIC) is a proposed new machine for a nuclear physics research. As proposed, it will deliver between 15 and 65 GeV center of mass energy collisions between electrons and nuclei. It uses the existing CEBAF accelerator as a full energy injector to deliver 3-10 GeV electrons into a new electron collider ring. An all new ion accelerator and collider complex will deliver up to 100 GeV protons, or 40 GeV/nucleon ions. The machine will have luminosity goals of above 10 33 cm -2 sec -1 in the whole energy range. The two collider rings use a unique figure eight layout to deliver a high degree of polarization in both beams. The machine will ultimately include room for two interaction regions. The crossing angle in the primary interaction region will be 50 mrad. This paper will describe the requirements and preliminary designs for both the ion and electron beam transport systems in the most complex 32 m region around the interaction point. The beam transport system includes three separate cryostats housing over 37 superconducting magnets operating at 4.5 K. The design of these cryostats must be closely integrated with the elements of the JLEIC detector.

We consider the capability of flexible spin-transparent polarization control and manipulation in conventional synchrotrons at integer spin resonances by means of spin navigators. The latter are designed as a couple of small solenoids separated by a constant beam bend. We formulate the requirements to the navigator design considering the criteria for stability of the spin motion in the presence of synchrotron energy oscillations. We propose the design of a novel spin-flipping system free of resonant beam depolarization based on such a spin navigator. We discuss the possibilities of testing spin-flipping systems at an integer spin resonance with protons in the Nuclotron ring at JINR in Dubna, Russia, and with deuterons in the RHIC rings at BNL in Upton, New York. The results are relevant to the existing and future facilities where the spin transparency mode can be applied for polarization control.

We present a concept for control of the ion polarization, called a transparent spin method. The spin transparency is achieved by designing such a synchrotron structure that the net spin rotation angle in one particle turn is zero. The polarization direction of any ions including deuterons can be efficiently controlled using weak quasistatic fields. These fields allow for dynamic adjustment of the polarization direction during an experiment. The main features of the transparent spin method are illustrated in a figure-eight collider. The results are relevant to the electron-ion collider considered in the U.S., the nuclotron-based ion collider facility constructed in Russia, and a polarized electron-ion collider planned in China.

We present a review of the possibilities to conduct experiments of high efficiency in the nuclear and high energy physics with spin-polarized beams in a collider complex, configuration of which includes Siberian snakes or figure-8 collider ring. Special attention is given to the recently elicited advantageous possibility to conduct high precision experiments in a regime of the spin transparency (ST) when the design global spin tune is close to zero. In this regime, the polarization control is realized by use of spin navigators (SN), which are compact special insertions of magnets dedicated to a high flexibility spin manipulation including frequent spin flips.

A new polarization control mode called a Spin Transparency (ST) mode is currently being actively developed for new rings. The ST mode is an intrinsic feature of figure-8 rings such as the JLEIC at Jefferson Lab. A racetrack collider can be converted to the ST mode by inserting two identical Siberian snakes into its opposite straights as at NICA, JINR. The ST mode allows one to develop a completely new approach to the measurement of the EDMs of both protons and deuterons. The idea of the method is to use the significant enhancement of the EDM signal by the interaction of the EDM with arc magnets, which has an interference effect. A unique feature of this technique is the conceptual capability of measuring the EDM signal in the whole energy range of a ring without introducing additional electric fields using only its magnetic fields. We describe an experimental setup and provide estimates of the limiting EDM values that can be measured at the JLEIC and NICA colliders.

International audience; Geometry tagging is an experimental technique for selecting event samples where one can, on a statistical basis, control the geometry of the collision in order to make more incisive physics measurements. Several physics measurements at the EIC would benefit significantly from the use of this technique, including studies of gluon anti-shadowing, studies of parton propagation, attenuation and hadronization in the nucleus, and ultimately the search for parton saturation. The JLEIC full-acceptance detector, with full acceptance to forward-going neutrons, protons and nuclear fragments and a high data-taking rate is ideally suited to such geometry tagging. We improve, tune, and apply existing modeling codes, BeAGLE, Sartre, and GEMC, and detector descriptions to study this physics.

The Jefferson Lab Electron Ion Collider (JLEIC) is designed to provide collisions of electron and ion beams with high luminosity and high polarization to reach new frontier in exploration of nuclear structure. The luminosity, exceeding 1033 cm−2s−1 in a broad range of the center-of-mass (CM) energy and maximum luminosity above 1034 cm−2s−1, is achieved by high-rate collisions of short small-emittance low-charge bunches with proper cooling of the ion beam and synchrotron radiation damping of the electron beam. The polarization of light ion species (p, d, 3He) and electron can be easily preserved, manipulated and maintained by taking advantage of the unique figure-8 shape rings. With a growing physics interest, polarized positron-ion collisions are considered to be carried out in the JLEIC to offer an additional probe to study the substructure of nucleons and nuclei. However, the creation of polarized positrons with sufficient intensity is particularly challenging. We propose a dedicated scheme to generate ...

Solenoid Siberian snakes have successfully maintained polarization in particle rings below 1 GeV, but never in multi-GeV rings, because the spin rotation by a solenoid is inversely proportional to the beam momentum. High energy rings, such as Brookhaven's 255 GeV Relativistic Heavy Ion Collider (RHIC), use only odd multiples of pairs of transverse B-field Siberian snakes directly opposite each other. When it became impractical to use a pair of Siberian Snakes in Fermilab's $120\text{ }\text{ }\mathrm{GeV}/\mathrm{c}$ Main Injector, we searched for a new type of single Siberian snake that could overcome all depolarizing resonances in the $8.9--120\text{ }\text{ }\mathrm{GeV}/\mathrm{c}$ range. We found that a snake made of one 4-twist helix and 2 dipoles could maintain the polarization. This snake design could solve the long-standing problem of significant polarization loss during acceleration of polarized protons from a few GeV to tens of GeV, such as in the AGS, before injecting them into multi-hundred GeV rings, such as RHIC.

This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them, and it benefited from inputs from the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the U.S., established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier., Comment: The Second Edition, 164 pages

High beam polarization is essential to the scientific productivity of a collider. Polarized 3He ions are an essential part of the nuclear physics programs at existing and future ion-ion and electron-ion colliders such as BNL's RHIC and eRHIC and JLab's ELIC. Ion sources with performance exceeding that achieved today are a key requirement for the development of these next generation high-luminosity high-polarization colliders. The development of high-intensity high-brightness arc-discharge ion sources at the Budker Institute of Nuclear Physics (BINP) has opened up an opportunity for realization of a new type of a polarized 3He− ion source. This report discusses a polarized 3He− ion source based on the large difference of extra-electron auto-detachment lifetimes of the different 3He− ion hyperfine states. The highest momentum state of 5/2 has the largest lifetime of τ ∼ 350 µs while the lower momentum states have lifetimes of τ ~ 10 µs. By producing 3He− ion beam composed of only the |5/2, ±5/2> hyperfine states and then quenching one of the states by an RF resonant field, 3He− beam polarization of 90% can be achieved. Such a method of polarized 3He− production has been considered before; however, due to low intensities of the He+ ion sources existing at that time, it was not possible to produce any interesting intensity of polarized 3He− ions. The high-brightness arc-discharge ion source developed at BINP can produce a high-brightness 3He+ beam with an intensity of up to 2 A allowing for selection of up to ∼1-4 mA of 3He− ions with ∼90% polarization. The high gas efficiency of an arc-discharge source is important due to the high cost of 3He gas. Some features of such a PIS as well as prototype designs are considered. An integrated 3He− ion source design providing high beam polarization could be prepared using existing BNL equipment with incorporation of new designs of the 1) arc discharge plasma generator, 2) extraction system, 3) charge exchange jet, and 4) magnetic separation system.

We present a new symmetry-based concept for an achromatic low-beta collider interaction region design. A specially-designed symmetric Chromaticity Compensation Block (CCB) induces an angle spread in the passing beam such that it cancels the chromatic kick of the final focusing quadrupoles. Two such CCBs placed symmetrically around an interaction point allow simultaneous compensation of the 1st-order chromaticities and chromatic beam smear at the IP without inducing significant 2nd-order aberrations to the particle trajectory. We first develop an analytic description of this approach and explicitly formulate 2nd-order aberration compensation conditions at the interaction point. The concept is next applied to develop an interaction region design for the ion collider ring of an electron-ion collider. We numerically evaluate performance of the design in terms of momentum acceptance and dynamic aperture. The advantages of the new concept are illustrated by comparing it to the conventional distributed-sextupole chromaticity compensation scheme., 12 pages, 17 figures, to be submitted to Phys. Rev. ST Accel. Beams

Recirculating Linear Accelerators (RLA's) provide a compact and efficient way of accelerating particle beams to medium and high energies by reusing the same linac for multiple passes. In the conventional scheme, after each pass, the different energy beams coming out of the linac are separated and directed into appropriate arcs for recirculation, with each pass requiring a separate fixed-energy arc. In this paper we present a concept of an RLA return arc based on linear combined-function magnets, in which two and potentially more consecutive passes with very different energies are transported through the same string of magnets. By adjusting the dipole and quadrupole components of the constituting linear combined-function magnets, the arc is designed to be achromatic and to have zero initial and final reference orbit offsets for all transported beam energies. We demonstrate the concept by developing a design for a droplet-shaped return arc for a dog-bone RLA capable of transporting two beam passes with momenta different by a factor of two. We present the results of tracking simulations of the two passes and lay out the path to end-to-end design and simulation of a complete dog-bone RLA.

Neutrino Factories (NF) and Muon Colliders (MC) require rapid acceleration of shortlived muons to multi-GeV and TeV energies. A Recirculating Linear Accelerator (RLA) that uses superconducting RF structures can provide exceptionally fast and economical acceleration to the extent that the focusing range of the RLA quadrupoles allows each muon to pass several times through each high-gradient cavity. A new concept of rapidly changing the strength of the RLA focusing quadrupoles as the muons gain energy is being developed to increase the number of passes that each muon will make in the RF cavities, leading to greater cost effectiveness. We discuss the optics and technical requirements for RLA designs, using RF cavities capable of simultaneous acceleration of both μ+ and μ− species. The design will include the optics for the multi-pass linac and droplet-shaped return arcs.

We used an rf solenoid to study the widths of rf spin resonances with both bunched and unbunched beams of 1.85 GeV/c polarized deuterons stored in the COSY synchrotron. With the unbunched beam at different fixed rf-solenoid frequencies, we observed only partial depolarization near the resonance. However, the bunched beam's polarization was almost fully flipped; moreover, its resonance was much narrower. We then used Chao's recent equations to explain this behavior and to calculate the polarization's dependence on various rf-solenoid and beam parameters. Our data and calculations indicate that a bunched deuteron beam's polarization can behave as if the beam has zero momentum spread.

The Chao matrix formalism allows analytic calculations of a beam's polarization behavior inside a spin resonance. We recently tested its prediction of polarization oscillations occurring in a stored beam of polarized particles near a spin resonance. Using a 1.85 GeV/c polarized deuteron beam stored in the COoler SYnchrotron, we swept a new rf solenoid's frequency rather rapidly through 400 Hz during 100 ms, while varying the distance between the sweep's end frequency and the central frequency of an rf-induced spin resonance. Our measurements of the deuteron's polarization near and inside the resonance agree with the Chao formalism's predicted oscillations.

The current design of the Medium-energy Electron-Ion Collider (MEIC) project at Jefferson lab features a single 8 GeV/c figure-8 booster based on super-ferric magnets. Reducing the circumference of the booster by switching to a racetrack design may improve its performance by limiting the space charge effect and lower its cost. We consider problems of preserving proton and deuteron polarizations in a superconducting racetrack booster. We show that using magnets based on hollow high-current NbTi composite superconducting cable similar to those designed at JINR for the Nuclotron guarantees preservation of the ion polarization in a racetrack booster up to 8 GeV/c. The booster operation cycle would be a few seconds that would improve the operating efficiency of the MEIC ion complex.

We present a complete scheme for managing the polarization of ion beams in Jefferson Lab’s proposed Medium-energy Electron-Ion Collider (MEIC). It provides preservation of the ion polarization during all stages of beam acceleration and polarization control in the collider’s experimental straights. We discuss characteristic features of the spin motion in accelerators with Siberian snakes and in accelerators of figure-8 shape. We propose 3D spin rotators for polarization control in the MEIC ion collider ring. We provide polarization calculations in the collider with the 3D rotator for deuteron and proton beams. The main polarization control features of the figure-8 design are summarized.

Stored beams of polarized protons, electrons, or deuterons can be spin flipped by sweeping an rf dipole's or solenoid's frequency through an rf spin resonance. Fitting such data to the modified Froissart-Stora equation's spin resonance strength ${\mathcal{E}}_{\mathrm{FS}}$ gave very large deviations from the $^{*}\mathcal{E}_{Bdl}$ obtained from each rf magnet's $\ensuremath{\int}{B}_{rms}dl$. We recently varied an rf dipole's frequency sweep range $\ensuremath{\Delta}f$, and the momentum spread $\ensuremath{\Delta}p/p$ and betatron tune ${\ensuremath{\nu}}_{y}$ of stored $1.85\text{ }\text{ }\mathrm{GeV}/c$ polarized deuterons. We found a sharp constructive interference when ${\ensuremath{\nu}}_{y}$ was near an intrinsic spin resonance. Moreover, over large $\ensuremath{\Delta}f$ and $\ensuremath{\Delta}p/p$ ranges, ${\mathcal{E}}_{\mathrm{FS}}$ was about 7 times smaller than the predicted $^{*}\mathcal{E}_{Bdl}$.

We recently started testing Chao's proposed new matrix formalism for describing the spin dynamics due to a single spin resonance. The Chao formalism is probably the first fundamental improvement of the Froissart-Stora equation in that it allows analytic calculations of the beam polarization's behavior inside a resonance. We tested the Chao formalism using a $1.85\text{ }\text{ }\mathrm{GeV}/c$ polarized deuteron beam stored in COSY, by sweeping an rf dipole's frequency through 200 Hz, while varying the distance from the sweep's end frequency to an rf-induced spin resonance's central frequency. Since the Froissart-Stora equation itself can make no prediction inside a resonance, we compared our experimental data with the predictions of the Chao formalism and those of an empirical two-fluid model based on the Froissart-Stora equation. The data strongly favor the Chao formalism.

We recently analyzed all available data on spin-flipping stored beams of polarized protons, electrons, and deuterons. Fitting the modified Froissart-Stora equation to the measured polarization data after crossing an rf-induced spin resonance, we found 10 ‐20-fold deviations from the depolarizing resonance strength equations used for many years. The polarization was typically manipulated by linearly sweeping the frequency of an rf dipole or rf solenoid through an rf-induced spin resonance; spin-flip efficiencies of up to 99:9% were obtained. The Lorentz invariance of an rf dipole’s transverse R Bdl and the weak energy dependence of its spin resonance strength E together imply that even a small rf dipole should allow efficient spin flipping in 100 GeV or even TeV storage rings; thus, it is important to understand these large deviations. Therefore, we recently studied the resonance strength deviations experimentally by varying the size and vertical betatron tune of a 2:1 GeV=c polarized proton beam stored in COSY. We found no dependence of E on beam size, but we did find almost 100-fold enhancements when the rf spin resonance was near an intrinsic spin resonance.

We propose a scheme of preserving the proton and deuteron beam polarizations during acceleration and storage in the proposed electron-ion collider at Jefferson Lab. This scheme allows one to provide both the longitudinal and transverse polarization orientations of the proton and deuteron beams at the interaction points of the figure-8 ion collider ring. We discuss questions of matching the polarization direction at all stages of the beam transport including the pre-booster, large booster and ion collider ring.

It seems inappropriate to publish a theoretical Comment [1] about an experimental Article [2] without mentioning in the Comment the theoretical paper [3] referenced in the Article; this paper [3] derived the equation that Ref. [1] claims is incorrect. The authors of [1] now claim to have corrected the errors in their calculations that our collaboration found in their earlier-submitted version of the Comment; we did not check their new Comment for errors. The factor of 2 disagreement in the equations for the depolarizing resonance strength, between the paper [3] referenced in the Article and the paper [4] supported by the Comment, has no effect on any result in the published experimental Article [2]. We included the below two statements in our two more recent articles [5,6] to stress this disagreement: (Ref. [24] in [5]) ‘‘There is a factor of 2 disagreement between the two references [3,4] for Eq. (4). This disagreement has no effect on our results, since the exact conditions of the Froissart-Stora equation [Eq. (3)] are not satisfied for several reasons.’’ (Ref. [20] in [6]) ‘‘There is a factor of 2 disagreement between the two references [3,4] for Eq. (6); this disagreement has no effect on our results.’’ One may now consider these statements as Errata or Addenda to Ref. [2]. However, the experimental SPIN@COSY collaboration declines to offer any opinion on which factor of 2 is correct.

We recently studied the spin manipulation of $1.85\text{ }\text{ }\mathrm{GeV}/c$ vertically polarized deuterons stored in the COSY cooler synchrotron. We adiabatically swept an rf dipole's frequency through an rf-induced spin resonance and observed its effect on the deuterons' vector and tensor polarizations. After optimizing the resonance crossing rate and maximizing the rf dipole's voltage, we measured spin-flip efficiencies of $97\ifmmode\pm\else\textpm\fi{}1%$ and $98.5\ifmmode\pm\else\textpm\fi{}0.3%$ in two separate runs. We also confirmed at higher energy the striking behavior of the spin-1 tensor polarization recently found at IUCF.

We recently stored a 1.85 GeV/c vertically polarized deuteron beam in the COSY Ring in Julich; we then spin‐flipped it by ramping a new air‐core rf dipole’s frequency through an rf‐induced spin resonance to manipulate the polarization direction of the deuteron beam. We first experimentally determined the resonance’s frequency and set the dipole’s rf voltage to its maximum; then we varied its frequency ramp time and frequency range. We used the EDDA detector to measure the vector and tensor polarization asymmetries. We have not yet extracted the deuteron’s tensor polarization spin‐flip parameters from the measured data, since our short run did not provide adequate tensor analyzing‐power data at 1.85 GeV/c. However, with a 100 Hz frequency ramp and our longest ramp time of 400 s, the deuterons’ vector polarization spin‐flip efficiency was 48±1%.

We recently used a new ferrite rf dipole to study spin flipping of a $2.1\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}/c$ vertically polarized proton beam stored in the COSY Cooler Synchrotron in J\"ulich, Germany. We swept the rf dipole's frequency through an rf-induced spin resonance to flip the beam's polarization direction. After determining the resonance's frequency, we varied the frequency range, frequency ramp time, and number of flips. At the rf dipole's maximum strength and optimum frequency range and ramp time, we measured a spin-flip efficiency of $99.92\ifmmode\pm\else\textpm\fi{}0.04%$. This result, along with a similar $0.49\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V}/c$ IUCF result, indicates that, due to the Lorentz invariance of an rf dipole's transverse $\ensuremath{\int}Bdl$ and the weak energy dependence of its spin-resonance strength, an only 35% stronger rf dipole should allow efficient spin flipping in the 100 GeV BNL RHIC Collider or even the 7 TeV CERN Large Hadron Collider.

Progress on the Michigan ultra‐cold proton‐spin‐polarized atomic‐hydrogen Jet target is presented. We describe the present status of the Jet and some beam test results.

The time dependence of the vector and tensor polarization of a 270 MeV stored deuteron beam was measured near a depolarizing resonance, which was induced by an oscillating, longitudinal magnetic field. The distance to the resonance was varied by changing the oscillation frequency. The measured ratio of the polarization lifetimes is tau(vector)/tau(tensor)=1.9+/-0.2. Assuming that the effect of the resonance is to induce transitions between magnetic substates m(I), we find that the transition rate between neighboring states (+1 and 0 or -1 and 0) is four times higher than between the states with m(I)=+1 and -1.

We recently studied spin flipping of a 270 MeV vertically polarized deuteron beam stored in the Indiana University Cyclotron Facility Cooler Ring. We adiabatically swept an rf solenoid’s frequency through an rf-induced spin resonance and observed its effect on the deuterons’ vector and tensor polarizations. After optimizing the resonance crossing rate and maximizing the solenoid’s voltage, we measured a vector spin-flip efficiency of 94:2% � 0:3%. We also found striking behavior of the spin-1 tensor polarization.

We recently studied the spin‐flipping efficiency of an rf‐dipole magnet using a 120‐MeV horizontally polarized proton beam stored in the Indiana University Cyclotron Facility Cooler Ring, which contained a full Siberian snake. We flipped the spin by ramping the rf dipole’s frequency through an rf‐induced depolarizing resonance. By adiabatically turning on the rf dipole, we minimized the beam loss, while preserving almost all of the beam’s polarization. After optimizing the frequency ramp parameters, we used up to 400 multiple spin flips to measure a spin‐flip efficiency of 99.93 ± 0.02%. This result indicates that spin flipping should be possible in very‐high‐energy polarized storage rings, where Siberian snakes are certainly needed and only dipole rf‐flipper magnets are practical.

We recently studied the spin flipping of a 270 MeV vertically polarized deuteron beam stored in the IUCF Cooler Ring. We swept an rf solenoid’s frequency through an rf‐induced spin resonance and observed the effect on the beam’s vector and tensor polarizations. After optimizing the resonance crossing rate and setting the solenoid’s voltage to its maximum value, we obtained a spin‐flip efficiency of about 94 ± 1% for the vector polarization; we also observed a partial spin‐flip of the tensor polarization. We then used the rf‐induced resonance to measure the vector and tensor polarizations’ lifetimes at different distances from the resonance; the polarization lifetime ratio τvector/τtensor was about 1.9 ± 0.4.

Progress on the Michigan ultra‐cold proton‐spin‐polarized atomic hydrogen Jet target is presented. We describe the present status of the Jet and some beam test results.

We recently studied the spin-flipping efficiency of an rf-dipole magnet using a 120-MeV horizontally polarized proton beam stored in the Indiana University Cyclotron Facility Cooler Ring, which contained a nearly full Siberian snake. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. By adiabatically turning on the rf dipole, we minimized the beam loss. After optimizing the frequency ramp parameters, we used 100 multiple spin flips to measure a spin-flip efficiency of 99.63+/-0.05%. This result indicates that spin flipping should be possible in very-high-energy polarized storage rings, where Siberian snakes are certainly needed and only dipole rf-flipper magnets are practical.

We recently used a prototype rf dipole magnet to study the spin flipping of a 669 MeV horizontally polarized electron beam stored in the presence of a nearly full Siberian snake in the new MIT-Bates storage ring. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin flipping to measure a spin-flip efficiency of $94.5\ifmmode\pm\else\textpm\fi{}2.5%$. The spin-flip efficiency was apparently limited by the field strength in the air-core prototype rf dipole magnet. This unexpectedly high efficiency indicates that very efficient spin flipping of the ring's stored polarized electron beam should be possible using the much stronger ferrite spin flipper, which is now being built by the University of Michigan's Spin Physics Center.

To study spin effects in high energy collisions, we are developing an ultra-cold high-density jet target of proton-spin-polarized hydrogen atoms. The target uses a 12 Tesla magnetic field and a 0.3 K separation cell coated with superfluid helium-4 to produce a slow monochromatic electron-spin-polarized atomic hydrogen beam, which is then focused by a superconducting sextupole into the interaction region. In recent tests, we studied a polarized beam of hydrogen atoms focused by the superconducting sextupole into a compression tube detector, which measured the polarized atoms’ intensity. The Jet produced, at the detector, a spin-polarized atomic hydrogen beam with a measured intensity of about 2.8⋅1015 H s−1 and a FWHM area of less than 0.13 cm2. This intensity corresponds to a free jet density of about 1⋅1012 H cm−3 with a proton polarization of about 50%. When the transition RF unit is installed, we expect a proton polarization higher than 90%.

We recently used a vertical-field rf-dipole magnet to study the spin-flipping of a 120 MeV horizontally polarized proton beam stored in the presence of a nearly-full Siberian snake in the IUCF Cooler Ring. The spin was flipped by ramping the rf-dipole’s frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin-flips to measure a maximum spin-flip efficiency of 86.5±0.5% in April 2000, and 92.5±0.5% in June 2000. The spin-flip efficiency was apparently limited by the maximum achievable current in the rf-dipole. This result indicates that spin-flipping a stored polarized proton beam should be possible in high energy rings such as RHIC (and perhaps HERA in the future), where Siberian snakes are utilized and the dipole rf-flipper-magnets should be quite practical. During the June 2000 run, a new faster technique of locating the rf depolarizing resonance frequency was developed.

We recently used an rf dipole magnet to study the spin flipping of a 120 MeV horizontally polarized proton beam stored in the presence of a nearly full Siberian snake in the Indiana University Cyclotron Facility Cooler Ring. We flipped the spin by ramping the rf dipole's frequency through an rf-induced depolarizing resonance. After optimizing the frequency ramp parameters, we used multiple spin flips to measure a spin-flip efficiency of $86.5\ifmmode\pm\else\textpm\fi{}0.5%$. The spin-flip efficiency was apparently limited by the field strength in the rf dipole. This result indicates that spin flipping a stored polarized proton beam should be possible in high energy rings such as the Brookhaven Relativistic Heavy Ion Collider and HERA where Siberian snakes are certainly needed and only dipole rf-flipper magnets are practical.