H-jet measures beam polarization at RHIC

The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory is unique. In addition to accelerating heavy ions, it also accelerates spin-polarized protons to high energies and enables the study of collisions between polarized protons with centre-of-mass energies up to 500 GeV.

Collisions between high-energy polarized protons are a powerful way of finding out what is spinning inside, technically known as the “spin structure functions” of the proton. The long-held assumption that the proton’s spin is simply the sum of the spins of the three quarks inside the proton has been laid to rest by experiments at SLAC, CERN and DESY. These have shown that less than 30% of the proton’s spin is accounted for by the spin of the quarks. Besides quarks, the proton (and neutron) contains gluons – the particles that explain the strong force that binds protons and neutrons in the atomic nucleus. Finding out what contribution gluons make to the spin of the proton and neutron is central to our understanding of nuclear matter.

Several large efforts are under way to study this question. The Common Muon and Proton Apparatus for Structure and Spectroscopy (COMPASS) collaboration at CERN and the HERMES collaboration at DESY bombard polarized protons (protons with their spin axes aligned in the same direction) with energetic muons or electrons. However, these experiments use electromagnetic probes, so the gluons are seen only indirectly.

Collisions between polarized energetic protons at RHIC should offer a more direct view of the gluon spin contribution. For this purpose, bunches of polarized protons are loaded into the RHIC accelerator, with the “blue” beam orbiting clockwise and the “yellow” beam orbiting counter-clockwise. (The beams are named after the coloured stripes on the collider’s two rings of magnets.) The two beams meet head-on at several different collision regions of the ring and the resulting secondary particles are observed by four detectors: BRAHMS, PHENIX, PHOBOS and STAR. The polarized protons originate from a special ion source that produces polarized negative hydrogen ions. These then pass in turn through a series of accelerators before being injected into RHIC.

This process is more difficult than it sounds. The polarized protons have a magnetic moment associated with their spin (they act like small compass needles). This raises the likelihood that the spin direction may be lost during the millions of times the protons orbit the ring, on each turn passing through the hundreds of magnets that are needed to deflect and focus the proton beam. Accelerator physicists avoid this depolarization by using spin precessors known as Siberian Snakes, but the question remains: how do we know the exact degree of polarization (the fraction of particles with spin up versus spin down) after the beam has been accelerated to full energy?

Measuring polarization

The polarization of a beam of protons is measured by inserting a thin target (an analyser) into the beam and observing the number of scattered particles at equal angles to the left and the right of the beam. The left:right intensity ratio depends on how much the beam is polarized (the beam polarization, P) and on how sensitive the scattering process is to the spin direction of the beam particles (the analysing power, A). The problem is that at very high energies there are no scattering processes for which the analysing power is known with sufficient accuracy. At lower energies than those achieved at RHIC, for example at the Proton Synchrotron at CERN and the Alternating Gradient Synchrotron at Brookhaven, moderate-angle elastic proton-proton scattering has been used, based on measurements of the analysing power using polarized hydrogen targets. The analysing power was observed to fall with energy, and the effectiveness of this method is exhausted by around 30 GeV.

However, for small scattering angles, the interference of the electromagnetic and strong interactions is expected to provide a significant analysing power for elastic proton-proton (and proton-nucleus) scattering. This analysing power, which is the basis of the RHIC high-energy polarimeters, derives from the same electromagnetic amplitude that generates the proton’s anomalous magnetic moment. Experiment E704 at Fermilab used 200 GeV/c polarized protons from hyperon decay to detect the asymmetry in scattering from a hydrogen target (Akchurin 1993). The largest analysing power, AN, was about 0.04 but the statistical errors were large. A calculation of the analysing power agreed with these measurements, but they are subject to uncertainties in the strong interaction amplitudes. Hence, an accurate calibration of the reaction is required.

The idea for the beam-polarization calibration at RHIC is simple in principle. Let the high-energy beam cross a jet of polarized hydrogen atoms of known nuclear polarization, and measure the left:right ratio in the number of scattered particles; then reverse the sign of the target polarization periodically to cancel asymmetries caused by differences in detector geometry or efficiency in the left and right directions. This gives the target asymmetry ε_tgt = P_tgtA_N. Now measure the corresponding asymmetry but with the polarization of the beam particles reversed, to give ε_beam = P_beamA_N. Since in proton-proton elastic scattering the analysing power AN, which is a measure of the polarization-sensitivity of the scattering process, is the same no matter which proton is polarized, the ratio of beam asymmetry to target asymmetry, ε_beam⁄ε_tgt, multiplied by the known target polarization, P_tgt, gives an absolute measurement of the beam polarization, P_beam.

The trick is to make a jet of known polarization and of sufficient density to achieve reasonable count rates. The Brookhaven polarized-hydrogen jet is produced by an atomic beam source (ABS) in which molecular hydrogen is dissociated by a radio-frequency (RF) discharge, and the resulting atomic hydrogen beam is spin-separated and focused according to electron spin by sets of six-pole magnets (figure 1). The spin of the resulting particles is manipulated by RF transitions, which flip the spin to produce either up or down proton polarization. The principle is not new. Equipment of this type was originally developed for ion sources that produced polarized protons. Work on an ABS for use as an internal target of polarized hydrogen in the Super Proton Synchrotron at CERN was carried out some 30 years ago (Dick et al. 1981 and 1986), but was eventually abandoned because the target density (a few times 1011 H/cm³) was insufficient. To get around the low jet density, most recent experiments with polarized hydrogen gas targets use long “storage cells” into which hydrogen atoms from an ABS are injected (Steffens and Haeberli 2004). These storage cells increase the target thickness by a factor of about 100, but at RHIC the need to know the scattering angle of the very-low-energy recoil protons precludes the use of an extended target.

The polarized atomic hydrogen jet constructed for RHIC has achieved a beam intensity of 1.2 × 1017 H/s, which is the highest intensity recorded to date. At the point of interaction with the RHIC beams, the hydrogen beam profile is nearly gaussian and has a full width at half-maximum of 6.5 mm. The areal density of the hydrogen target is (1.3 ± 0.2) × 10¹² H/cm².

Hydrogen atoms formed by dissociating molecular hydrogen in an RF discharge emerge through a 2 mm-diameter cooled nozzle (optimum temperature 65 K) and enter a set of tapered six-pole magnets that are made of high-flux rare-earth permanent magnets (these have a pole-tip field of 1.5 T and a maximum gradient of 2.5 T/cm). The magnets are divided into sections to improve pumping. They were designed by elaborate optimization using empirical data on dissociator output versus gas flow and temperature, as well as attenuation by gas scattering in the beam-forming region and in the six-pole magnets. The atomic beam diverges in the first set of magnets, passes a long drift space, and converges in the second set of magnets towards the target region.

Near the point where the RHIC beam intersects the atomic hydrogen beam, a “holding field” provides a very uniform vertical magnetic field. The strength of the field (0.12 T) was chosen to avoid depolarization of the atoms by the periodic electromagnetic field that is produced by the beam bunches. Stringent conditions had to be met by the fringe fields of the guide field magnet to assure a slow adiabatic field change between the six-pole field, the RF transitions and the guide field.

The target polarization is reversed periodically by turning on one or other of two RF coils, which induces spin-flips in the hydrogen atoms. A second set of six-pole magnets and RF coils placed after the interaction point serve to measure the proton polarization at the target. The efficiency of the spin-flip transitions is found to be above 99%. In the finite holding field there is a residual coupling of the proton spin to the electron spin, which results in a net proton polarization of 0.96. The largest uncertainty in the target polarization arises from the uncertainty in the measured contamination of the atomic hydrogen beam by molecular hydrogen, which is unpolarized. Taking into account this dilution, the target polarization is P_tgt = 0.924 ± 0.018.

Results at RHIC

With a target of pure hydrogen atoms, proton-proton scattering with low momentum transfer can be uniquely identified by detecting the recoil proton near 90° with respect to the high-energy beam. The Fermilab experiment E704 showed significant spin-dependence in proton-proton scattering for momentum transfer in the range |t| = 0.001-0.03 (GeV/c)². This corresponds to recoil protons of a few hundred kilo-electron-volts to several mega-electron-volts.

Recoils are detected in silicon-strip detectors placed 80 cm from the hydrogen jet (figure 2). Recoil protons from proton-proton elastic scattering are identified by their time-of-flight and energy-angle correlation (figure 3). The figure illustrates the clear identification of protons, with the solid curve showing the predicted relationship between proton energy and time of flight. Events from different detector strips are distinguished by colour, and it is this correlation between scattering angle and energy that demonstrates that the scattering is elastic.

The average of P_tgt(ε_beam/ε_tgt), taken over all energy bins of the recoil detector, determines the beam polarization P_beam. In fact, etgt and ebeam are measured at the same time by loading into the ring bunches of opposite polarization and reversing the target polarization every few minutes. The results of measurements on the blue beam during early 2004 show (ε_beam/ε_tgt) = 0.43 ± 0.02, where the error is purely statistical. Assuming a target polarization of 0.924 ± 0.018, the RHIC beam polarization was 0.392 ± 0.026. For the measurements in 2005, the detectors were displaced along the RHIC beam direction to allow detection of recoils from both blue and yellow beams. Preliminary results indicate that, compared with 2004, the beam polarization has improved by about 15%, which is an important accomplishment. These results can be used to determine the t-dependence of the analysing power A_N = P_tgt/ε_tgt for proton-proton elastic scattering at 100 GeV. The results, which are shown in figure 4, agree closely with calculations based on Coulomb nuclear interference without any hadronic spin-flip.

The polarized hydrogen jet makes it possible to determine the polarization of high-energy protons to an accuracy of a few per cent, without using a model. Theory predicts that the method will be successful over the entire energy range that is accessible by RHIC.

The polarized hydrogen jet does not interfere with the operation of the ring. Despite the small target density and without the use of coincidence detection, it has proved possible to cleanly identify proton-proton elastic events with minimal background.

The major drawback of the polarized hydrogen jet is that the low count rate precludes rapid monitoring of the beam polarization – for example, during beam tuning. For this reason, a proton-carbon (pC) polarimeter is used. This permits relative beam polarization to be measured in less than a minute. The polarized hydrogen jet enables the pC polarimeters to be calibrated to an accuracy better than 6%. Thus the polarized-hydrogen target and the carbon target serve complementary roles.

• The development and operation of the polarized hydrogen jet target was a collaboration between BNL (C-AD, Instrumentation and Physics), ITEP (Moscow), IUCF, Kyoto University, Riken BNL Research Center, University of Wisconsin-Madison and Yale University.