A laser-driven target of high-density nuclear polarized hydrogen gas B. Clasie1, C. Crawford1, J. Seely1, W. Xu2, D. Dutta2, and H. Gao1,2 6 0 1Laboratory for Nuclear Science, Massachusetts Institute 0 2 of Technology, Cambridge, MA 02139, USA and n a 2Triangle Universities Nuclear Laboratory, J 5 Duke University, Durham, NC 27708, USA 2 ] h Wereportthebestfigure-of-meritachievedforaninternalnuclearpolarizedhydro- p - gen gas target and a Monte Carlo simulation of spin-exchange optical pumping. The m o dimensionsoftheapparatuswereoptimized usingthesimulation andtheexperimen- t a tal results were in good agreement with the simulation. The best result achieved for . s c this target was 50.5% polarization with 58.2% degree of dissociation of the sample i s y beam exiting the storage cell at a hydrogen flow rate of 1.1 1018 atoms/s. h × p [ The exploitation of polarization observables through the use of polarized beams and po- 1 v larized internal gas targets in storage rings is an increasingly valuable technique in nuclear 2 0 2 and particle physics. Nucleon properties, such as the spin structure functions and the elec- 1 0 tromagnetic form factors, have been measured in recent years with polarization techniques 6 0 utilizing polarized internal targets at DESY (HERMES), NIKHEF and the MIT-Bates Lab- / s c oratory. The spin-dependent asymmetry from the p~ + p~ p + p + φ process has been → i s suggested [1, 2] as a possible probe of the strangeness content of the nucleon. The near y h threshold ~p + p~ Y + Θ+ process could be used to determine the parity of the Θ+ pen- p → : v taquark state [3, 4, 5], if its existence is confirmed. i X The Laser-Driven Target (LDT) is capable of producing nuclear polarized hydrogen and r a deuterium for storage rings. The LDT and the Atomic Beam Source (ABS) (another tech- nique more commonly used) both use storage cells [6] to increase the target thickness, com- paredtoa freegasjet target. However, theLDToffersamorecompact design thantheABS, and can provide a higher Figure of Merit (FOM) [30] as reported in this work. An LDT was first used in nuclear physics experiments [7, 8] in 1997 and 1998 at the Indiana University Cyclotron Facility following earlier work on the laser-driven source and target [9, 10, 11, 12]. 2 A hydrogen LDT project was initiated at MIT in late 1990s with the goal of implementing such a target in the South Hall Ring at the MIT-Bates Linear Accelerator Center for a precision measurement of the proton charge radius [13, 14]. In this paper we report the best FOM result obtained from this target, which benefited from the development of a realistic Monte Carlo (MC) simulation of the target. A LDT is based on the technique of spin-exchange optical pumping. The valence electron of potassium is polarized through optical pumping in a magnetic field of 1 kG using ∼ circularly polarized laser light. Spin exchange collisions then transfer the polarization from potassium to the Hydrogen (H) electron. Finally, the hyperfine interaction during H-H collisions transfers the electron spin to the nucleus [15, 16]. If there are many H-H collisions, the rate of transfer of spin to the nucleus equals the reverse rate, and the system is in Spin Temperature Equilibrium (STE) [17]. The time-constant for STE is approximately given by [17]: 2 1+(B/B ) c τ = , (1) STE n σHHvHH H SE rel where B is the critical magnetic field (507 G for hydrogen), n is the density of atomic c H hydrogen (excluding molecular hydrogen), σHH is the thermally averaged H-H spin exchange SE cross section at the temperature of the spin-exchange cell and vHH is the average relative rel velocity between hydrogen atoms. Laser-driven sources and targets are designed with the dwell time-constant in the spin-exchange cell much greater than the STE time-constant to guarantee that the system is in STE. Moreover, STE has been verified in laser-driven sources and targets [18, 19, 20]. Under STE conditions, the hydrogen nuclear and electron polarizations are equal [18]. The main contributions to depolarization of the alkali and hydrogen in our apparatus come from the flow of atoms into and out of the LDS and depolarization during wall colli- sions [21]. Atoms may also recombine at a surface producing molecules with predominantly zero net nuclear spin. The recombination is characterized by the degree of dissociation, f , α which is the fraction of the hydrogen flux in the sample beam exiting the storage cell that is in atomic form. Drifilm coatings areemployed to limit the recombination and depolarization effects from wall collisions [22]. The depolarization from radiation trapping [23, 24] can be limited by optical pumping in a large magnetic field in the kG range [17]; however, the rate of transfer of spin to the nucleus by the hyperfine interaction is reduced. Therefore, the 3 FIG. 1: Laser Driven Target setup. Note that, for clarity, the polarimeter arm, storage cell, ◦ dissociator, and potassium ampoule are shown rotated by 90 from their actual positions (in the actualsetup,thepolarimeterarmandampoulewouldcomeoutofthepage). Anoptionalsecondary beam can be used to measure the alkali density and polarization via a Faraday polarimeter. magnitude of the magnetic field in the spin-exchange cell must be optimized for these two competing effects [17, 21, 25]. Figure 1 is a schematic view of the MIT LDT. Hydrogen gas flows successively into different sections of a piece of pyrex glassware (which consists of a dissociator tube, a spin- exchange cell and a transport tube) and an aluminum storage cell. The molecular gas is dissociated into atoms by an RF discharge in the dissociator tube. In the spin-exchange cell the hydrogen gas (now a mixture of atoms and molecules) is mixed with the potassium vapor produced in a side-arm by heating a potassium ampoule. The results from two spin- exchange cells, “Original” and “Large-1”, are reported herein. To minimize the number of wall collisions, the Original spin-exchange cell design was spherical with an inner diameter of 4.8 cm. Large-1 was a cylindrical cell optimized by the MC simulation described below. The entire volume contained by the spin-exchange cell, transport tube and storage cell must ◦ be heated to 200–250 C to prevent the alkali-metal vapor from condensing on the walls, which would degrade the drifilm coating. The potassium number density is typically 0.3% compared to H. The standard storage cell is an open ended aluminum cylinder coated with 4 drifilm. Thecellis40cminlength, and1.25cmindiameterwithtwosamplingholesallowing the target gas to be monitored by an atomic polarimeter. One hole is centered and the other one is 15 mm downstream. Both are positioned at right angles to the entrance hole of the storage cell, which ensures that the atoms monitored by the atomic polarimeter undergo wall collisions in the storage cell before escaping the cell. A MC simulation determined that atoms that exit the center (off-center) sampling hole experience, on average, 1370 (1370) wall collisions of which 135 (155) wall collisions are in the storage cell. The laser used is a Titanium-Sapphire laser (Ti:Sapph) pumped with a 20 W Argon ion laser. The laser beam passes through an Electro-Optic Modulator (EOM, not shown), an expanding lens, and a quarter-wave plate before arriving at the spin-exchange cell via a periscope with two polarization-preserving mirrors. The EOM broadens the relatively narrow linewidth of the Ti:Sapph laser to provide a better match to the potassium Doppler absorption profile with a FWHM of 1.0 GHz. In addition, two sampling beams are split off from the pump beam for monitoring the laser spectrum and wavelength. Gasexiting thesampling holeofthestoragecelliscollimatedthroughaseries ofapertures which also serve as conductance limiters between sub-chambers of the polarimeter. A per- manent sextupole magnet focuses one electronic spin state of the atomic beam and defocuses the other. The optimal focal length was determined by an atomic beam simulation. The beam is then sampled by a Quadrupole Mass Analyzer (QMA) which alternately measures both the atomic and molecular intensities. The QMA is shielded from the holding field by two layers of µ-metal. The small signal at 1 m from the storage cell is enhanced using a ∼ chopper along with a lock-in amplifier. The background pressure is reduced to 10−9 Torr by differentially pumping the two sub-chambers with ion pumps and also a NEG pump in the second (QMA) chamber. The background can be measured by blocking the beam with a shutter or moving/rotating the polarimeter away from the sampling hole. The degree of dissociation of the sample beam exiting the storage cell is given by the change in the molecular signal (after subtracting the background) when the RF discharge is turned on and off. The electron polarization of the atomic hydrogen species, P , is given by e the change in the atomic signal when the laser is turned on and off by opening or closing a laser shutter (after subtracting the background). This measurement also indicates the hydrogen nuclear polarization, as the system is designed to be in STE. The mean dwell time for atomic hydrogen in the Original spin-exchange cell and transport tube has been 5 HERMES IUCF MIT LDT (ABS) (LDT) Original Large-1 Gas H D H D H H F 6.57 5.15 100 72 110 110 t 11 [10.5] 50 50 150 150 f 0.48 0.48 0.56 0.58 α ∼ ∼ P 0.45 0.45 0.37 0.50 e ∼ ∼ p 0.78 0.85 0.145 0.102 [0.175] [0.247] z h i F p 2 4.0 3.8 2.1 0.75 3.4 6.7 z ×h i t p 2 6.7 7.6 1.1 0.52 4.6 9.2 z ×h i TABLE I: FOM results from the HERMES ABS [26, 27, 28], IUCF LDT [20], and the MIT LDT. The units are as follows; the flow, F (1016 atoms/s); the thickness, t (1013 atoms/cm2); the FOM, F p 2 (1016 atoms/s); and, the FOM, t p 2 (1013 atoms/cm2). All LDT results for f are z z α ×h i ×h i under operating conditions, with the potassium ampoule heated. calculated by a MC simulation, to be 8.8 ms. For a field of 100 mT and an atomic hydrogen density of 1.0 1014 atoms/cm3 the time-constant for STE given by Equation 1 is 0.052 ms. × The mean dwell time is therefore larger than the STE time constant by a factor of approx- imately 170. The Erlangen hydrogen LDS was verified to be in STE by directly measuring the nuclear polarization [18] in conditions where the mean dwell time was larger than the STE time-constant by a factor of 300, and the system was expected to remain in STE at half that ratio. Results from the IUCF and MIT LDTs are summarized in Table I along with results from the HERMES ABS. The FOM is given as flow p 2 and thickness p 2, where p is the z z z ×h i ×h i h i density averaged nuclear vector polarization. For the MIT LDT, f P α e p = . (2) z h i f +√2(1 f ) α α − For the IUCF target, p , was determined from a scattering experiment [7, 20]. The results z h i for the flow and target thickness of the HERMES ABS are based on Refs. [26, 27, 28], and are the best published ABS results that use a storage cell. 6 FIG. 2: Results achieved by the MIT LDT. The FOM is given as flow p 2 where p is the z z ×h i h i density averaged H nuclear vector polarization assuming the system is in STE. The best results achieved by the MIT LDT in the Original configuration are shown in Fig. 2 together with the overall errors which are dominated by the systematic errors. The combined systematic uncertainty in the FOM is estimated to be 8.4%, which is dominated by the non-linearity in the QMA response (less than 3%), hydrogen flow control (4%), and 3% in the density averaged target polarization. The measurements were repeated several times for this cell geometry under various conditions, including recoating the surface, with reproducible results. A detailed MC simulation of optical pumping and spin-exchange collisions for our target was developed and used to extract the recombination and depolarization coefficients, and to provide a new cell design to improve the target performance. The simulation techniques developed for the LDT are also applicable to the design of the ABS, particularly at future facilities where constraints may cause significant recombination and/or spin-exchange. The recombination coefficient, γ (n ), is the probability for a hydrogen atom to recombine at a r H wall collision and is a function ofn near the surface. As n varies throughout the simulated H H volume, γ changes with position on the surfaces. r In the simulation, a hydrogen atom moves ballistically between wall collisions in the spin-exchange cell, transport tube and storage cell. A new velocity, both magnitude and 7 direction, is randomly generated after each wall collision, according to a Maxwellian and a cosΘ distribution, respectively, where Θ is the polar angle measured with respect to the normal to the surface. At high temperatures, which are experienced in an LDT, the recombination coefficient, γ , is given by [29] r γ (n ) = C n , (3) r H H H where C is a constant. After the hydrogen atom exited either through a sampling hole H or the ends of the storage cell, another hydrogen atom was generated at the top of the spin-exchange cell. The MC was used to determine n throughout the apparatus. As n depends on the H H average probability that atoms have not recombined at a given point, and this probability depends on n through Equation 3, the simulation was iterated and n recalculated after H H each iteration until the degree of dissociation of atoms exiting the storage cell sampling hole and n converged. H Although the hydrogen atoms were transported separately, H-H and H-K spin-exchange collisions were treated by allowing the hydrogen atoms to interact with the average hydrogen electron and nuclear polarization and potassium electron polarization. The apparatus was divided into a 3-dimensional 2 2 2 mm3 grid. Initial values of the average H and K × × polarizations were assigned at every point on the grid. After a hydrogen atom exited the apparatus in the simulation, the average polarizations were updated, and the simulation was iterated until convergence. A hydrogen atom can be depolarized during a wall collision with the probability given by the depolarization coefficient, γ . The MC results were fit to the p experimental results for the Original configuration, shown in Table I, by varying C and γ , H p which were determined to be 3.33 10−18 cm3 and 0.00355 respectively. Further discussion × of the MC simulation will be reported in a forthcoming paper. A cylindrical spin-exchange cell with a much larger diameter was constructed based on the MC studies and the practical constraints of our target chamber. The calculated mean dwell time divided by the STE time constant was 280. This design, labeled Large-1 in Table I, has a spin-exchange cell volume 6.8 times larger than that of the Original design. The best result obtained for this cell using the EOM was P = 50.5% and f = 58.2% at a e α flow rate of 1.1 1018 atoms/s. These results arein goodagreement with the MC simulation, × which predicted P = 57% and f = 51% at the same flow rate. e α 8 While in the Original configuration, drifilm coatings were found to last in excess of 100 hours under operating conditions. The polarization result for the Large-1 cell was stable at 50% polarization for about 12 hours but with rather rapid deterioration of the dissociation fraction. This observation may have been due to uneven heating of the spin-exchange cell and the transport tube. For the Large-1 geometry, there was only a 1 cm gap for the hot air to circulate around the glass due to the constraint of the existing target chamber. One can overcome this constraint with the design of a new target chamber. One may argue that it is probably not completely justified to compare the performance of the HERMES ABS target and the IUCF LDT with the FOM of the LDT obtained in our polarized target lab due to the difference in the storage cell conductances. A detailed study shows that minimal modifications are needed for the installation of this target in the MIT-Bates storage ring. A more realistic comparison which takes into account correction factors due to the target geometry, temperature and molecules still shows that our target with the Large-1 cell geometry has (33 11)% higher figure of merit than that of the ± HERMES hydrogen target. These results represent an even larger improvement compared to the previous best FOM from an LDT, which was obtained at IUCF. 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