[J. Res. Natl. Inst. Stand. Technol. 106 Compressing Spin … · 2001. 9. 9. · Compressing...

Volume 106, Number 4, July–August 2001Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 106, 709–729 (2001)]

Compressing Spin-Polarized 3He With aModified Diaphragm Pump

Volume 106 Number 4 July–August 2001

T. R. Gentile, D. R. Rich, andA. K. Thompson

National Institute of Standards andTechnology,Gaithersburg, MD 20899-8461

W. M. Snow

Indiana University,Bloomington, IN 47408

and G. L. Jones

Hamilton College,Clinton, NY 13323

[email protected]@[email protected]

Nuclear spin-polarized 3He gas at pressureson the order of 100 kPa (1 bar) are re-quired for several applications, such as neu-tron spin filters and magnetic resonanceimaging. The metastability-exchange opti-cal pumping (MEOP) method for polar-izing 3He gas can rapidly produce highlypolarized gas, but the best results are ob-tained at much lower pressure (� 0.1 kPa).We describe a compact compression ap-paratus for polarized gas that is based on amodified commercial diaphragm pump.The gas is polarized by MEOP at a typicalpressure of 0.25 kPa (2.5 mbar), andcompressed into a storage cell at a typicalpressure of 100 kPa. In the storage cell,we have obtained 20 % to 35 % 3He polar-

ization using pure 3He gas and 35 % to50 % 3He polarization using 3He-4He mix-tures. By maintaining the storage cell atliquid nitrogen temperature during com-pression, the density has been increasedby a factor of four.

Key words: 3He; helium; metastability-exchange; MRI; neutron; optical pumping;polarization; spin filter.

Accepted: June 6, 2001

Available online: http://www.nist.gov/jres

1. Introduction

Several applications of nuclear spin-polarized 3He gassuch as neutron polarizers [1-5], polarized gas magneticresonance imaging (MRI) [6,7], and polarized targets[8] require gas pressures on the order of 100 kPa (1 bar).Two optical pumping methods have been employed toproduce polarized gas for these applications: spin-ex-change optical pumping (SEOP), [9-12] in which thegas is polarized directly at high pressure, and metastabil-ity-exchange optical pumping (MEOP) [13-15], inwhich the gas is polarized at low pressure (� 0.1 kPa)and then compressed. Compression of polarized 3He,produced by MEOP using a helium lamp, was firstdemonstrated thirty years ago using a Toepler pump

[16]. Following the development of the arc lamppumped Nd:LMA laser [17,18], further development ofthis approach was pursued at the University of Mainz inthe early 1990’s [19]. Soon therafter, the Mainz groupdeveloped a two-stage piston compressor for polarized3He [20], which has subsequently been applied to elec-tron scattering experiments, neutron polarizers and po-larized gas MRI [21]. This apparatus can compress po-larized 3He gas to pressures of several hundred kPa at arate of 50 kPa�L/h while maintaining a polarization of55 % [2]. These impressive results have motivated us todevelop an apparatus of similar design [3]. However,these apparatus are large and complex, so in parallel we

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are pursuing a compact and simple apparatus for polar-ized gas compression, which is the subject of this paper.The compact compression apparatus is based on modifi-cation of a commercial diaphragm pump. Some descrip-tion of this apparatus and the first applications to neu-tron spin filters and polarized gas MRI have recentlybeen reported [1,22,23]. In this paper, we present adetailed description of the apparatus, techniques to opti-mize its performance and increase its capability, andupdated results. We expect that it is only the first step inthe direction of compact compression methods.

The two optical pumping methods, spin-exchangeand metastability-exchange, each have their respectiveattributes and difficulties. We are pursuing both meth-ods for the emerging fields of 3He-based neutron spinfilters and polarized gas MRI. The attributes of spin-ex-change include simplicity, small size, and compatibilitywith continuous, long term operation, while the diffi-culties include an inherently slow polarized 3He produc-tion rate and optical pumping-related constraints on thecell pressure. The physics of the metastability-exchangemethod allows for rapid production of highly polarizedgas at low pressure, but the user is burdened with thetask of preserving the polarization during compression.The present compression devices are large and complex,which has limited the number of groups employing thismethod and effectively prohibited the installation ofsuch devices directly onto neutron beam lines or intoother in situ arrangements. The continuing motivationfor the work begun in this paper is to develop a compact,simple, and reliable compression apparatus.

In the metastability-exchange method, electronic po-larization is produced by optical pumping of metastablehelium atoms, and the polarization is rapidly transferredto the nucleus of the metastable atom via the hyperfineinteraction. The electronic excitation in the metastableatom is transferred to a ground state atom during acollision, while the nuclear polarization is unperturbed.Hence the collision results in a nuclear spin-polarizedground state atom, and the newly excited metastableatom is then repolarized by laser light.

As shown in Fig. 1 the apparatus can be divided intothree stages: optical pumping of low pressure gas(0.1 kPa to 0.3 kPa), compression, and storage of thehigh pressure gas (100 kPa). The apparatus is immersedin a uniform magnetic field produced by two 82 cm IDholding field coils in the Helmholtz configuration.Metastable atoms are produced by a weak electrodelessradio-frequency (rf) discharge, and optically pumped bylight at a wavelength of 1083 nm. The gas can either beaccumulated in the storage cell (“fill mode”), or a con-stant pressure can be maintained in the storage cell bycontinuously leaking gas back to the optical pumpingcell (“recirculation mode”). In the optical pumping cell,

Fig. 1. Conceptual diagram of the apparatus. The notation is dis-cussed in Sec. 2.

the polarization is determined from analysis of the circu-lar polarization of 668 nm wavelength light emitted fromthe discharge. In the storage cell, NMR (nuclear mag-netic resonance) provides a signal that is proportional tothe magnetization. An absolute measure of the storagecell polarization is obtained by optically pumping gas atlow pressure in the storage cell and calibrating the NMRsystem against optical polarimetry.

The paper is organized as follows: In Sec. 2 wepresent the basic principles that influence the achievablepolarization of the compressed gas. In Sec. 3 we presenttwo schemes for optimizing the optical pumping effi-ciency in a compact system. The details of the apparatusare described in Sec. 4 and the results in Sec. 5. In Sec.6 we summarize the status of this work and discuss theoutlook for future development.

2. Principles

In this section we discuss the basic principles thatinfluence the achievable polarization of the compressedgas. In the analysis that follows, we consider the steady-state case of continuous recirculation of the polarizedgas. The achievable gas polarization in the storage cell(StC), Pstc, is given by

Pstc = Popc fc fr (1)

where Popc is the gas polarization in the optical pumpingcell (OPC), fc is the fraction of Popc preserved in transit

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from the OPC to the StC, and fr is the fraction of Pstcmaintained given the finite relaxation time in the StC. fris given by

fr =1

1 + (tstc/�stc)(2)

where tstc is the mean residence time in the storage celland �stc is the relaxation time of the polarization in thestorage cell. fr is usually close to one and therefore is nota major consideration in the achievable value of Pstc. Asdiscussed further in Sec. 5.1, fc decreases with increas-ing time in the compressor. Typically we operate at asufficiently high throughput to obtain fc ≈ 0.75.

For a single optical pumping cell, Popc is given by

Popc =P0

1 + (� /topc)(3)

where P0 is the achievable optical pumping cell polar-ization for zero throughput, � is the effective opticalpumping time constant [14] and topc is the mean resi-dence time in the optical pumping cell. (In the interestof simplicity we have not included the known depen-dence of � on Popc [14,24], but we will revisit this issuein the discussion of results in Sec. 5.) In principle Popccould be optimized by simply increasing the time in theoptical pumping cell (topc), but the increased polariza-tion loss in the compressor (fc) with decreased through-put precludes this simple solution. Optimal operation isa balance between maximizing Popc (low flow) and max-imizing fc (high flow), hence it is desirable to maintainhigh values of Popc at relatively high throughput. For themost part, the inherently rapid optical pumping rate ofthe metastable method with current laser technology[14] fulfills this requirement. We have developed twoschemes to maximize the efficiency of the opticalpumping while preserving the compact spirit of theapparatus: 1) series optical pumping cells with a diffu-sion restriction, and 2) polarization preserving recircula-tion (PPR). In scheme (1), the gas passes sequentiallythrough two optical pumping cells, the first OPC serv-ing as a “pre-polarizer” for the second OPC. The twocells are separated by a diffusion restriction, whichyields a higher value for the polarization in the secondoptical pumping cell, Popc2, than would be obtained withfree exchange between the two cells. In scheme (2), thepolarization of the gas is preserved during recirculationfrom the StC back to the OPC. These schemes arediscussed in detail in Sec. 3, but we note that they arenot critical to the basic operation of this apparatus.

For pure 3He gas, the most important factor that influ-ences the value of P0 in this apparatus is the OPC pres-sure. The optimum pressure for optical pumping of pure3He is about 0.05 kPa [14], whereas in this apparatus we

obtain a typical OPC pressure of 0.25 kPa. In this rangeof pressure, we obtain higher values of the 3He polariza-tion by optically pumping mixtures of 3He and 4He [13].For such mixtures (which are suitable for neutron spinfilters because 4He is transparent to neutrons), the rela-tively high OPC pressure is less significant an issue thanfor pure 3He.

Because of the limited time in the OPC, the optimumdischarge intensity and frequency is determined by abalance between maximizing P0 and minimizing � . Atour typical OPC pressure, the highest value of P0 wouldbe obtained with a weak, low frequency (0.1 MHz to1 MHz) discharge, whereas the smallest value of �would be obtained with a strong, high frequency(�10 MHz) discharge [13,14]. For 3He-4He gas mix-tures with 3He concentrations of 25 % to 50 %, we haveobtained values of P0 between 0.8 and 0.6 for sealedcells filled to a total pressure of 0.21 kPa. The achiev-able value of P0 depends primarily on the dischargeintensity, but also on the discharge frequency and 3Heconcentration. Because minimizing � is important inthis apparatus, we use a high discharge frequency(13.6 MHz) and a fairly strong discharge. For operationof the apparatus with 3He-4He gas mixtures, typicalvalues of P0, Popc, and Pstc are 0.55 to 0.65, 0.45 to 0.65,and 0.30 to 0.50, respectively. For pure 3He gas, thecorresponding typical values are 0.40 to 0.50, 0.25 to0.45, and 0.20 to 0.35, respectively. More detailed infor-mation is provided in Sec. 5.

Here we summarize the notation used in this paper:

• Popc = polarization in a single optical pumping cell• fc = fraction of polarization preserved in transit from

the OPC to the StC• fr = fraction of Pstc maintained given the finite relax-

ation time in the StC• Pstc = polarization in the storage cell• P0 = polarization in a single OPC for zero throughput• � = effective optical pumping time constant in a single

optical pumping cell• �1 (�2) = effective optical pumping time constant in

OPC1 (OPC2)• topc (tstc) = residence time in a single optical pumping

cell (storage cell)• topc1 (topc2) = residence times in OPC1, OPC2• �stc = relaxation time in the storage cell• Popc1 (Popc2) = polarization in OPC1 (OPC2)• f P0 (P0) = polarization in OPC1 (OPC2) for zero

throughput• popc1 (popc2) = pressure in OPC1 (OPC2)• pstc = pressure in the storage cell• Q = throughput (kPa�L/s)• F = volume flow rate at the outlet of the second stage

of the compressor (cm3/s)

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3. Optical Pumping Schemes

3.1 Series Optical Pumping Cells with DiffusionRestriction

Because the 3He gas is optically thin, the simplestapproach to increasing the optical pumping efficiency isto make the cell longer, which increases the residencetime in the OPC without a proportional increase in � .(For larger cell diameter the increases in residence timeand � have been observed to be comparable, yielding aminimal increase in efficiency [14].) However, employ-ing a longer cell also increases the length of the uniformmagnetic field required to prevent relaxation due to fieldgradients [25]. Given the small size of the diaphragmcompressor, we preferred a scheme that would keep theentire apparatus compact. One option is use two adja-cent optical pumping cells that are connected by a tube,which yields a doubling of the optical path length whilethe physical length of each cell is unchanged. The over-all efficiency of such a two-cell arrangement is im-proved if one adds a diffusion restriction between thetwo cells because the gas entering the second cell hasbeen pre-polarized in the first cell. An equilibrium po-larization is established in the first optical pumping cell,and a new equilibrium is established in the second cell.The polarization in the second cell is given by

Popc2 =Popc1 +P0 �Popc1

1+ (�2/topc2)=P0

1 + (�1/topc1)+ (f�2/topc2)[1 + (�1/topc1)][1+ (�2/topc2)]

(4)

where P0 (f P0) is the achievable optical pumping cellpolarization for zero throughput in OPC2 (OPC1), �2(�1) is the effective optical pumping time constant inOPC2 (OPC1), and topc2 (topc1) is the residence time inOPC2 (OPC1). We have used different parameters foreach cell because the pressure, laser power, and dis-charge intensity obtained in OPC1 may differ from thatobtained in OPC2. Popc1 is given by Eq. (3) for theparameters relevant to OPC1. For illustration, we as-sume that the parameters are the same in each cell, ie.,f = 1, � = �1 = �2 and topc = topc1 = topc2. Fig. 2 shows thevariation of Popc2 with the ratio � /topc, as determinedfrom Eq. (4), and compares it to two other cases: 1) Popcdetermined from Eq. (3), which corresponds to a singlecell, and 2) Popc determined from Eq. (3) with � un-changed and topc doubled, which corresponds to the bestpossible case of a two-cell arrangement with no diffu-sion restriction. The two-cell arrangement with a diffu-sion restriction yields the best results.

Realizing such a diffusion restriction without increas-ing popc1 excessively is possible because the diffusionrate increases with the square of the connecting tubediameter while the viscous flow conductance increases

Fig. 2. The variation of Popc2 with the ratio � /topc, for three cases: 1)determined from Eq. (4) for f = 1, � = �1 = �2 and topc = topc1 = topc2,which corresponds to a two-cell arrangement with a diffusion restric-tion (solid line); 2) Popc determined from Eq. (3), which correspondsto a single cell (dashed line); and 3) Popc determined from Eq. (3) with� unchanged and topc doubled, which corresponds to the best possiblecase of a two-cell arrangement with no diffusion restriction (dottedline).

as the fourth power of the diameter. The diffusion timebetween two cells of volume V connected by a capillaryof diameter d and length L (in cm) is given by Td =4LV /�d 2D [26], where D = 190/p is the diffusion coef-ficient in cm3/s for 3He at a pressure p in kPa [27-30].The pressure drop between the two cells is given by�p = Q /C , where Q is the throughput and C =1400pavd 4/L is the viscous flow conductance in L/s forthe average pressure pav in kPa, and the tube diameterand length in cm [31]. Typical values in the apparatusare V = 440 cm3, d = 0.30 cm, L ≈ 40 cm, and pav =0.36 kPa at a throughput of Q = 0.015 kPa�L/s, whichyields Td = 470 s, �p = 0.15 kPa, and topc = 10 s. (Inpractice, we observe �p = 0.2 kPa.) Hence the averageresidence time in the cell is nearly 50 times shorter thanthe diffusion time. The resulting value of 0.46 kPa forpopc1 has been found to be acceptable for optical pump-ing of mixtures and could be decreased for opticalpumping of pure 3He. The diffusion restriction does notaffect the pressure in OPC2.

3.2 Polarization Preserving Recirculation

For recirculation mode, preserving the polarization inits return from the storage cell to the optical pumpingcells allows the achievable OPC polarization to poten-tially increase in each recirculation cycle. For a singleoptical pumping cell, the value of Popc after polarizationpreserving recirculation (PPR) and a second pass of

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optical pumping can be determined using Eq. (4) byreplacing Popc1 with Pstc. The calculation can be iteratedfor more passes through the OPC, and extended to in-clude a two-cell arrangement. The variation of Popc2 with� /topc is shown in Fig. 3 for one, two, and three passesthrough a two-cell arrangement with a diffusion restric-tion, where we have assumed that fc = 0.8. It can be seenthat two passes are sufficient to obtain most of thepossible improvement.

Fig. 3. The variation of Popc with � /topc for one (dashed line), two(dotted line), and three (solid line) passes through a two-cell arrange-ment with a diffusion restriction, assuming polarization preservingrecirculation (see Sec. 3.2) and fc = 0.8.

4. Apparatus

A detailed diagram of the compression apparatus isshown in Fig. 4. The gas is polarized in two 20 cm longoptical pumping cells (OPC1, 4.7 cm ID and OPC2,5.9 cm ID) connected by a diffusion-restricting capil-lary Cop (see Sec. 3.1), passes through the two-stagediaphragm compressor, and is delivered to a storage cell(StC). The part of the apparatus maintained in a uniformmagnetic field, shown in the photograph in Fig. 5, fitsinto a cube about 35 cm on a side. The storage cell islocated at the center of the holding field coils. The celldewar (not shown in photograph) is simply a styrofoamcontainer, allowing the cell to be maintained at liquidnitrogen temperature during compression. To allowspace for the storage cell dewar and the NMR pickupcoil, OPC2 is located 13 cm to the side of the axis of theholding field coils, and OPC1 is parallel to OPC2 andimmediately above it. Gas purity is maintained by agetter (G) and liquid nitrogen traps (LN). The through-put is controlled by a gas regulator, glass capillaries

Fig. 4. Schematic diagram of the compression apparatus, includingthe 3He (or 3He-4He mixture) gas cylinder, pressure regulator, glassstopcock valves (Voc, Vcs, Vs, Vsg, Vppr, Vmo, V1-V5), getter (G), meteringvalve (MV), flow restricting capillary (Cf), PPR flow-restricting cap-illary (Cppr), optical pumping cells (OPC1 and OPC2), diffusion re-striction between the OPCs (Cop), liquid nitrogen traps (LN), themodified two-stage diaphragm compressor, a capacitance manometerto measure the optical pumping cell pressure (PL), a strain gaugesensor to measure the storage cell pressure (PH), the storage cell(StC), glass O-ring connections to permit detachment of the StC (D),storage cell diffusion-restricting capillaries (Cd), and the cell dewar(optional). The system is evacuated by connections to a turbomolecularpump (HV).

(Cf, Cppr), and a metering valve (MV). We discuss thevarious aspects of the apparatus in detail.

4.1 Gas Handling

Connections within the gas recirculation loop areconstructed almost entirely of Pyrex glass. 6 mm IDtubing is used to obtain high conductance in the lowpressure section and 2 mm ID tubing is used to mini-mize volume in the high pressure section. Gas flow iscontrolled using glass stopcock valves, lubricated witha low vapor pressure, bakeable grease [32].1 (However,we have yet to bake the recirculation loop.) Glassflanges with Viton O-rings are used to connect glass

1 Certain commercial equipment, instruments, or materials are identi-fied in this paper to foster understanding. Such identification does notimply recommendation or endorsement by the National Institute ofStandards and Technology, nor does it imply that the materials orequipment identified are necessarily the best available for the pur-pose.

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Fig. 5. Photograph of the section of the apparatus (about 35 cm on a side) that is immersed in the holding magnetic field.The storage cell is located above the compressor, near the centers of the holding field coils and NMR drive coils. The twoOPCs are on the left, and the small dewar for the liquid nitrogen traps are just below the OPCs. The getter (covered withaluminum foil) and metering valve are in the foreground.

tubing to the aluminum compressor head. The entireloop is evacuated by connections to a turbomolecularpump (HV), and gas is introduced from a storage bottlethrough the regulator. Since we typically admit gas tothe recirculation loop at subatmospheric pressure, ahigh purity absolute pressure regulator with a deliverypressure range of 0 kPa to 200 kPa is used. The storagebottles contain either pure 3He or premixed 3He-4He gasmixtures. The connections from the glass recirculationloop to the stainless steel high vacuum system are madewith standard glass to metal bellows, outside the holdingfield coils.

The pressures in the optical pumping cells, popc1 andpopc2, are measured using a capacitance manometer(PL). popc1 (popc2) is measured with V1 (V2) open and V2(V1) closed; both valves are closed during optical pump-ing because the capacitance manometer is magnetic andlocated outside the holding field coils. The StC pressurepstc is measured by a non-magnetic, ceramic strain gauge[33] (PH) that was bonded to glass using high vacuumepoxy.

Before operating the apparatus, all valves are openedand the entire system is evacuated with the compressor

running. The typical base pressure measured by a gaugenear the turbomolecular pump is 3 � 10�5 Pa. For oper-ation in fill mode, valves V1, V2, V3, V4, Vsg, and Vppr arethen closed and 3He gas is admitted through valve V5.When the desired pressure in the StC is obtained, valveVcs is closed and the compressor is turned off. In recir-culation mode, valve Vsg is opened and V5 is closed. Toemploy PPR, the getter and metering valve are by-passed, which forfeits both cleaning of the gas by thegetter and the convenience of flow rate adjustment withthe metering valve.

In recirculation mode, pstc is constant and the through-put is determined by the flow-restricting capillary (Cf)and the metering valve. The 0.1 mm diameter, 1.2 cmlong capillary limits the throughput to a maximum of0.05 kPa�L/s at pstc = 100 kPa. For PPR, the throughputis fixed by the combination of two flow-restricting cap-illaries (Cf and Cppr). In fill mode, the throughput iscontrolled by a combination of the regulator deliverypressure and the metering valve. The throughput is mea-sured by closing valve Voc (with V1 and V2 open) andobserving the change in the capacitance manometerreading for a given period of time.

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High gas purity is critical to maintaining a metastablepopulation. Because of the high energy of the metastablestate of 3He (20 eV), impurity atoms are ionized, result-ing in destruction of the metastable. Gas purity in theOPCs is maintained using liquid nitrogen traps and agetter. The liquid nitrogen traps are simply two U-shaped tubes immersed in a 7 cm diameter, wide-mouthliquid nitrogen dewar. The getter is a commercial heatedgas purifier [34], which we operate at a temperature of570 K. Because the getter material is ferromagnetic, thegas is completely depolarized upon return to the opticalpumping cell. (Because of the large surface area ofgetter material, depolarization would be expected evenif the material were not ferromagnetic.) Given this depo-larization, other sources of depolarization are acceptablein the return line, provided that they do not perturb therequired uniformity of the magnetic field. The onlyother magnetic part is a stem in the metering valve,which is located sufficiently far from the polarized gasto avoid depolarization.

We have not studied the importance of the getter togas purity. For PPR, (in which the getter is bypassed,but the liquid nitrogen traps are not) we have found thatfor a short term operation (hours), we do not see degra-dation of the gas purity. For long term operation, itshould be possible to maintain high gas purity by usinga getter line with a small conductance in parallel withthe PPR line.

4.2 Optical Pumping Cell Preparation andElectrical Discharge

The OPCs were initially subject to the proceduresthat are typically used for the preparation of sealed cells:baking overnight at a temperature of 650 K, followed byseveral treatments with a strong rf discharge. When theapparatus is idle, impurities from the recirculation loop,especially the compressor, contaminate the surface ofthe OPCs. This results in low polarization when thedischarge is first ignited, but on a time scale of 10 minto 30 min the discharge cleans the OPCs and the polar-ization increases.

Metastable 3He atoms are produced by a weak elec-trodeless rf discharge that is generated by coupling≈1 W of power from a 13.6 MHz transmitter [35] to thecell using a resonant step-up transformer circuit. Thecircuit consists of a single-turn primary winding, and a10-turn, 2 cm diameter secondary winding in parallelwith a 110 pF, 4 kV, air-spaced variable capacitor [36]and electrodes on the cell. A separate loop of wirelocated near the transformer and connected to an oscil-loscope provides convenient feedback when tuning thecircuit. For small sealed cells, two electrodes encirclethe ends of the cell. For the OPCs, four straight elec-

trodes parallel to the length of the cell are connectedwith alternating polarity. Twin lead antenna cable mini-mizes stray capacitance in the connections to the elec-trodes. An antenna tuner [37] between the rf transmitterand the resonant circuit improves the impedance match-ing, and also provides a means for viewing the forwardand reflected power.

The strong rf discharge required for cell cleaning wasproduced using a similar apparatus as described above,but in this case 100 W of rf power from a high powertransmitter [38] is coupled to the cell by simply sur-rounding the cell with the step-up transformer windings.Due to the larger inductance from the increased diame-ter of the windings, the secondary winding was only afew turns.

4.3 Optical Pumping

The low pressure gas is polarized using an opticalpumping apparatus similar to one that is described indetail elsewhere [14]. Here we review only the basicfeatures, and point out details that are specific to thisapparatus. The metastable atoms are optically pumpedby 1083 nm wavelength light that is produced by aNd:LMA (neodymium-doped lanthanum magnesiumhexaluminate) laser. A Nd:LMA rod [39] was in-stalled in a commercial arc-lamp-pumped Nd:YAG(neodymium-doped yttrium aluminum garnet) laser[40], and two temperature-controlled etalons wereadded to the laser cavity to tune the laser and narrow itsbandwidth. We typically obtain 2 W to 3 W of laser lightwith a 2 GHz bandwidth.

The laser is tuned by maximizing the fluorescencesignal from a 3He (or 4He) discharge cell that is illumi-nated by the weak beam of laser light transmittedthrough the high reflector at the back end of the lasercavity. The fluorescence emitted normal to the laserbeam is detected by a large area photodiode [41]. Atransmission window is created by the combination of a1000 nm long-wave pass filter and the 1100 nm re-sponse cutoff of the silicon photodiode. The laser istuned to the C9 line (2 3S1 F = 3/2 → 2 3P0 F = 1/2) forpure 3He, or to the 4He D0 line (2 3S1 → 2 3P0) for3He-4He mixtures.

To illuminate both OPCs we used the following ar-rangement: The diverging laser beam is circularly polar-ized before its diameter exceeds 2.5 cm, and then isexpanded to a diameter of 6 cm using a telescopeformed by two 7.5 cm diameter lenses with focallengths of 10 cm and 30 cm. As shown in Fig. 6, theexpanded beam traverses OPC2 and is reflected backwith a slight deflection. Another steering mirror sends itthrough OPC1 and then the beam is similarly reflectedback through OPC1. Since OPC1 is smaller in diameter

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Fig. 6. Schematic diagram of the arrangement used to illuminate bothoptical pumping cells. The scheme is described in Secs. 4.3 and 4.7.1.

than OPC2, the telescope is adjusted to produce a slowlyconverging beam. This scheme allows the full power ofthe laser to be incident on OPC2, and can be constructedwithout the use of large area polarizing optics. We usedoptically-sealed windows [42] to minimize distortion ofthe laser beam, but flame-sealed windows are adequate.

The discharge in each cell is controlled by individualrf power supplies, which allows for different dischargeintensities and frequencies. In principle, a stronger dis-charge in OPC1 would improve the two-cell scheme[43], but in practice we find only weak sensitivity to thedischarge strengths. The benefit from the two-cell ar-rangement is tested by extinguishing the discharge inOPC1, optimizing the discharge strength in OPC2, andobserving the change in Popc2.

Because the optical pumping cells are located fairlyfar off the axis of the holding field coils, the relaxationtime in the absence of the discharge is dominated bymagnetic field gradients. For our typical operating pres-sures, we observe relaxation times of 200 s to 400 s.With the discharges on, the typical relaxation time is70 s.

4.4 Compressor

There are several critical requirements on the com-pressor: 1) an inlet pressure on the order of 0.1 kPa atthroughputs comparable to the polarizing rate for themetastable method; 2) sufficiently low leakage and per-meation from the ambient atmosphere and outgassing ofwetted compressor materials (ie., materials the gas con-tacts), 3) construction from non-magnetic materials sothat the uniform magnetic field is not distorted, and 4)wetted materials that do not cause excessive depolariza-tion during the time the gas is in the compressor. For thelast requirement, the part of the compression cycle dur-ing which the surface to volume ratio is maximum islikely to be the most relevant [20].

With the above requirements as a guide, we chose acommercial two-stage diaphragm pump that is suppliedwithout a motor [44]. A DC drive motor is locatedoutside of the holding field coils and connects to thecompressor via a 50 cm long brass shaft (visible on theright in Fig. 5). The gas contacts aluminum, Viton, and

Teflon, which have reasonably low outgassing rates [31].The largest surface areas in the pump are those of thealuminum pump heads and the Teflon-coated neoprenediaphragms. The one-way valves are Viton flaps. Thepumps we assembled would often pass a helium leaktest, and minimal use of high vacuum grease was alwayssufficient to eliminate any small leakage. By closingvalves V1, V2, Voc, and Vcs, and observing the slow risein pressure on the capacitance manometer, the sum ofoutgassing and inward leakage was measured to be2 � 10�4 Pa�L/s (after many days under vacuum). Allmagnetic parts in the drive train were replaced withnon-magnetic parts that were primarily made of Type316 stainless steel [45] and annealed after machining.Type 316 stainless steel is one of most non-magnetic ofthe readily available stainless steels [46]. The wettedmaterials are non-magnetic and were expected to havesufficiently low relaxation rates [16,47]. Given the highsurface to volume ratios present during compressor op-eration, this appears to be the most difficult requirementto satisfy, and is discussed further in Sec. 5.1.

The required modifications were primarily confinedto the drive train of the compressor. The philosophy wasnot to redesign the pump, but instead to replace mag-netic parts as directly as possible with non-magneticequivalents. The modified compressor was assembledfrom new parts that were obtained from either the pumpmanufacturer or other commercial sources, or fabri-cated by the NIST shop. The drive train of the unmodi-fied pump contains a steel shaft, eccentric, and counter-weight; four steel radial ballbearings; three steelretaining rings; assorted steel screws; two aluminumconnecting rods; thin steel spacers; and two steel di-aphragm studs. The diaphragm is molded over the di-aphragm stud, and screws into the connecting rod. Di-aphragm studs were machined at NIST from Type 316stainless steel and annealed to minimize residual mag-netism before being sent to the pump manufacturer forincorporation into finished diaphragms. The shaft, ec-centric, and counterweight were obtained in Type 316stainless steel by special order to the pump manufac-turer. The steel ballbearings were replaced with com-mercially available Type 316 stainless steel bearings,but for the main bearing a direct replacement was notavailable so a special sleeve was fabricated for the clos-est available bearing. For completeness, steel retainingrings were replaced by rings made from beryllium-cop-per. From a mechanical point of view, the most signifi-cant difference between the original pump and the mod-ified pump is the bearings. The Type 316 bearings arenot precision bearings and are much softer than typicalbearing steel, resulting in a sloppier mechanical system.This does not seem to affect the achievable inlet pres-sure, but may affect the lifetime of the pump. Although

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the nominal rotation speed of the unmodified compres-sor is 1700 rpm, we typically operate the modified com-pressor at 800 rpm or less because the small improve-ment in inlet pressure obtained at higher speeds does notjustify the increased stress, wear, and noise.

A magnetic permeability indicator [48] was used totest parts for magnetism. For all parts except the coun-terweight, there was no response at the most sensitivelevel (� = 0.01). The small amount of magnetism ob-served in the counterweight was not expected to be aproblem, and eventually this was confirmed by replacingit with a brass counterweight. Because the diaphragmstuds are very close to the polarized gas, we checked thatthere was no observable change in the relaxation time ofpolarized gas at 0.13 kPa when the stud was located nextto the cell.

Although the specification for the ultimate pressure(defined as the inlet pressure for zero gas flow) of theunmodified commercial compressor was 0.27 kPa, weobtained a typical ultimate pressure of 0.1 kPa, primar-ily by a simple modification of the orientation of the twopump heads: [49] The heads are normally oriented withthe line between the inlet and outlet ports on each stageparallel to the motor-driven shaft. The ultimate pressureis substantially reduced if instead the heads are orientedso that the ports are in the plane normal to the shaft, andthat the rotating shaft encounters the ports in the orderthat follows the gas flow, ie.: stage 1 inlet, stage 1 outlet,stage 2 inlet, stage 2 outlet. For the five modified pumpswe have constructed, the ultimate pressures range be-tween 0.08 kPa and 0.12 kPa.

The ultimate pressure increases linearly with the out-let pressure, except at the lowest outlet pressures. Forour typical throughputs the inlet pressure is elevated.For the particular pump used for the work in this paper,the inlet pressure in kPa is approximately given by0.013 + 0.67pstc + 13Q , where pstc is the StC (outlet)pressure in MPa, and Q is the throughput in units ofkPa�L/s. In practice, the inlet pressure is typically be-tween 0.1 kPa and 0.3 kPa, as discussed in Sec. 5.

The pressure between the two stages is typically2.7 kPa at an outlet pressure of 100 kPa and is alsoproportional to the outlet pressure. However, it has littleelevation at our typical throughputs because both stageshave the same volume displacement, and the volume ofgas entering the second stage is reduced by the compres-sion ratio of the first stage.

We have limited data on the long term performance ofthe modified compressors. The first one was used forthree years without significant difficulties, but the usewas intermittent and the total operation time was on theorder of 100 h, often at low speed. Once additionalcompressors were constructed, this compressor was op-erated continuously at somewhat higher speed for about

one week until it failed due to a broken connecting rod.During operation a fine metallic powder was producedfrom the drive train, and upon being dismantled evi-dence for significant bearing wear was observed. Basedon our limited experience to date, we consider the com-pressors suitable for intermittent use to fill cells withpolarized gas, while reliability for long term continuousoperation has not been addressed.

4.5 Storage Cells

For testing the apparatus, the storage cell need onlyhave a sufficiently long relaxation time such that fr isnear unity. For pstc = 100 kPa and a flow rate of0.012 kPa�L/s, the average residence time in a 40 cm3

cell is only 0.1 h, so the typical relaxation time of a fewhours obtained with Pyrex glass is adequate. For largercells and applications, longer relaxation times are re-quired. We have obtained relaxation times between 27 hand 72 h for cells constructed from aluminosilicateglasses (Corning 1720 [50] and GE180 [51]), which areknown to yield long relaxation times because of theirlower helium permeability [52]. Each cell was preparedby baking overnight at 650 K, with the compressorsealed off so as to obtain a typical base pressure of4 � 10�6 Pa. Some discharge cleaning was performed,primarily to insure reasonably high polarization for thelow pressure polarization measurement scheme de-scribed in Sec. 4.7.

Other requirements are imposed on the storage cellsby the particular application for the polarized gas. Wehave developed cells for neutron spin filters and polar-ized gas MRI. Neutrons can be polarized (or analyzed)using polarized 3He because of the large spin depen-dence of the 3He absorption cross section. The largenon-equilibrium 3He polarization produced by opticalpumping allows for MRI of lungs and other body cavi-ties. For both of these applications it is often convenientto detach the cell, for transport to a neutron beam lineor MRI scanner. As shown in Figs. 4 and 5, a storagecell is equipped with glass valves (Vs) and O-ring com-pression fittings (D), permitting the cell to be valved offand detached from the compression apparatus. To insurethat the relaxation time of the storage cell is not compro-mised because of the glass valves, the valves are con-nected to the cell through glass capillaries (Cd). At first,we chose the dimensions of the capillary to insure thatthe relaxation time due to diffusion through the capillarywas always much greater than the cell relaxation time,assuming the worst case of complete depolarization ofthe 3He at the valve. In practice we have found that thisrequirement can be relaxed. For example, we have mea-sured a relaxation time of 70 h in a 400 cm3 cell inwhich the diffusion time to the valve is only 3.3 h (5 cm

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long, 0.175 cm diameter capillary, cell pressure of36 kPa). We have yet to see any additional relaxationfrom the valves, which would impart a pressure depen-dence to the storage cell relaxation time due to thepressure dependence of the diffusion time. The absenceof any pressure dependence in the relaxation time forour typical range of storage cell pressures (35 kPa to100 kPa) also indicates that relaxation due to magneticfield gradients [25] is negligible. Based on direct mea-surement of the relaxation time for a 7.2 cm ID, 10 cmlong cell at pressures in the 0.1 kPa range, we estimateseveral thousand hours for the relaxation time due tomagnetic field gradients.

Different construction techniques have been used forneutron spin filter cells as compared to cells for polar-ized gas MRI. The primary additional issue for the neu-tron application is the strong absorption of neutrons by10B (absorption cross section of 3800 b at a neutronwavelength of 0.18 nm). Flat windows are also desirableso that the thickness of 3He is uniform across the neu-tron beam. Corning 1720 glass contains 5 % B2O3 [53],and natural abundance boron contains 20 % 10B. Toavoid attenuation of the neutron beam, optical qualitywindows were constructed from a special batch of Corn-ing 1720 glass [50] that was manufactured using B2O3with an isotopic composition of 99.62 % 11B [54]. For aneutron beam with a 10 % spread in wavelength wemeasured the absorption through a cell with two 4.1 mmthick windows to be 0.80, 0.79, and 0.66 at wavelengthsof 0.5 nm, 1.0 nm, and 2.0 nm, respectively. The corre-sponding transmissions that are expected, assuming lossfrom the small amount of 10B in this glass only, areestimated to be 0.93, 0.87, and 0.75. (The absorptiondue to the 10B increases linearly with increasing neutronwavelength because of the wavelength dependence ofthe cross section.) The additional observed loss of about10 % is consistent with typical neutron scattering fromglasses. Spin filter cells identified as “Mercury” (4.4 cmID, 10 cm length), “Neptune” (7.2 cm ID, 10 cmlength), and “Saturn” (9.5 cm ID, 15 cm length) wereeach constructed using optical seals of such windows toa cylindrical body of normal Corning 1720. The relax-ation times for these three cells just after preparationwere 37 h, 72 h, and 50 h, respectively. Results withthese cells are discussed further below.

GE180 glass is boron-free, but is only commerciallyavailable in narrow diameter tubing. It is possible toattach windows of GE180 glass to a body of Corning1720. We have constructed two such 5.9 cm diametercells, one with flame-sealed rounded windows and an-other with optically sealed windows, and obtained relax-ation times of 27 h and 25 h, respectively. We have testedone 40 cm3 cell constructed entirely of GE180 glass andobtained a relaxation time of only 6 h. Although this

value was unexpectedly low, we do not draw any generalconclusions about GE180 cells from this one test.

For application to polarized gas MRI, 250 cm3 cellsare filled to 100 kPa while being maintained at 77 K (seeSec. 4.6), resulting in a pressure of 400 kPa at 300 K. Toaccommodate this pressure we use a rounded-end con-struction, and threaded glass valves rather than stopcockvalves. Our first cell for this application was constructedfrom Corning 7052 glass [23], and only yielded a initialrelaxation time of 15 h, which subsequently declined to7 h. A cell from normal Corning 1720 was then con-structed and yielded a relaxation time of 33 h.

A few comments will put our cell relaxation times incontext. The surfaces of cells for spin-exchange opticalpumping are inherently modified by the presence ofrubidium, whereas the surfaces of storage cells formetastability-exchange may be bare glass, or deliber-ately coated with metal. Relaxation times over 200 h,limited by magnetic dipolar spin relaxation, have beenobtained in cells for spin-exchange optical pumping[52,55,56]. It has been shown that the relaxation time ofa metal-coated glass cell can be substantially longerthan would be obtained with uncoated glass [57], so therubidium plays an important role in the relaxation timesfor spin-exchange cells. Other evidence for this state-ment includes 1) a relaxation time of over 250 h ob-tained with a spin-exchange cell made from Corning7056 glass [55], as compared to 10 h for uncoated 7056cells [16], and 2) a relaxation time of 176 h obtainedwith a Cs-coated quartz cell [2], as compared to �1 hfor uncoated quartz cells [52]. Since our cells are un-coated, the most appropriate comparison is with otheruncoated cells. Uncoated cells for metastability-ex-change may be either sealed low pressure cells or refill-able cells for use with a compression apparatus. Bettercontrol of impurities is possible for sealed cells. Directmeasurement of relaxation times for sealed, uncoatedlow pressure cells include values between 5 h and 56 h[16,52,57]. Values as high as 140 h, potentially limitedby magnetic field gradients, have been observed for thetransverse relaxation time T2 in sealed low pressure cells[58]. Prior to the work in this paper, the only resultswith refillable cells have been from the Mainz and ILLgroups. Most of their work has been with coated cells[2,57], but a relaxation time of 75 h was reported for acell made from iron-free Supremax glass [2,59], and30 h for cells made from Corning 1720 [60].

Given this context, the observed range of 25 h to70 h for the relaxation times of our storage cells seemsreasonable; indeed it is encouraging that these valuescan be maintained in the less than pristine environmentof the diaphragm compressor. As for the stability ofthese relaxation times, we do see variations, but notnecessarily with any clear pattern. Variations sometimes

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occur when the gas is recirculated, or if it is evacuatedand then refilled. We presume that these variations aredue to changes in impurities on the surface of the cell.If a cell exhibits a drop in relaxation time, recirculatingthe gas will sometimes help. We have the greatestamount of data with the cell Mercury: In the first fewmonths of use, we observed relaxation times between27 h and 37 h. After sitting on the shelf for about a year,a capillary on Mercury was accidentally broken. Afterbeing repaired, it was reinstalled on the apparatus; weakdischarging was done to permit a new calibration (seeSec. 4.7), but it was not baked. The relaxation time wasmeasured to be 29 h, within the range of the earliermeasurements. However, in the course of subsequentexperiments, the relaxation time dropped to 16 h for noclear reason, and did not recover after baking. Aftercleaning with a weak discharge, the relaxation time didrecover to 26 h, and has remained between 26 h and32 h thereafter. For our other cells, we have less history:the relaxation time of the cell Neptune (Saturn) hasvaried between 40 h and 72 h (32 h and 66 h).

4.6 Storage Cell Cooling

Cryogenic methods have been used to increase thedensity of polarized 3He gas [61,62]. We have employeda liquid nitrogen bath to roughly quadruple the densityof the gas for the same storage cell pressure, and thusobtain correspondingly higher pressure when the cell isreturned to room temperature. Using this method, weobtained a room temperature pressure of 400 kPa,which was convenient for gas delivery in a polarized gasMRI demonstration [23]. Alternatively, operation atlower storage cell pressure for a given density permitshigher values of Pstc because of the increase in fc (seeSec. 5). This approach was used for tests of a neutronspin filter [1]. Our space constraints led us to constructcustom size containers from solid blocks of styrofoam.Unfortunately, the particular styrofoam that was avail-able was found to be porous, so we coated the inside ofthese containers with an epoxy with good cryogenicproperties [63].

A potential problem in employing this approach is theeffect of cooling on the relaxation time of the cell. ForPyrex, the competing effects of decreased permeationand increased sticking time lead to a maximum in therelaxation time at 125 K, and at 77 K values comparableto those obtained at room temperature can be obtained[52]. For aluminosilicate cells, the sticking time domi-nates, so the relaxation time generally decreases withdecreasing temperature. Nevertheless, the relaxationtimes for aluminosilicate cells are generally highenough that the decrease does not adversely affect theachievable polarization for a cell at liquid nitrogen tem-

perature. For example, we have observed a decreasefrom �stc = 30 h at 300 K to �stc = 15 h at 77 K in the cellMercury. This result is given as an example, not as adefinitive statement for aluminosilicate cells in general.

We have experienced one unresolved difficulty withthis cooling approach. Even after the cell has warmed toroom temperature, the relaxation time does not return toits room temperature value. The drop in relaxation timeis not irreversible, and often the original room tempera-ture value can be recovered by simply recirculating thegas. We presume that this drop in relaxation time is dueto impurities that are weakly bound to the cell walls.These results make it unclear what fraction of the ob-served decrease in relaxation time upon cooling is trulydue to temperature dependence. Some improvement inthe recovery of the relaxation time has been obtained byusing a liquid nitrogen trap between the compressor andthe storage cell (not shown in Fig. 4).

4.7 Polarization Measurement

The polarization in the OPCs is determined by mea-suring the degree of circular polarization of the 668 nmlight emitted by the discharge [64,65]. The polarizationin the StC is determined by NMR measurements, whichare calibrated by optically pumping low-pressure gas inthe StC directly and recording both the optical andNMR signals. This method eliminates the need forpainstaking water-based calibrations. Although muchsmaller than the signal from compressed gas, the signalfrom low pressure gas is still typically 30 times largerthan a water signal at our typical magnetic field of2.6 mT. NMR is also used to determine cell relaxationtimes.

4.7.1 Optical Polarimetry

For accurate polarimetry using the 668 nm emissionline a dichroic mirror that reflects laser light but doesnot reflect 668 nm light is used at the back of OPC2 (seeFig. 6). For OPC1, an ordinary mirror is used at theback, and a long-wave pass filter is located in front sothat the polarimeter only views OPC2. The goal of bothwavelength selection schemes is to reduce the smallprobability of viewing 668 nm wavelength light thatmay have had its polarization altered upon reflection.When measuring the polarization in OPC1 is desired,the filter is moved behind OPC1 and another filter islocated in front of OPC2.

Employing the optical method requires knowledge ofthe pressure-dependent ratio of the nuclear polarizationto the polarization of the light, which varies between 7and 13 in the pressure range between 0.05 kPa and0.5 kPa. Two calibrations of this ratio, one linked to

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NMR measurements of a water sample [66] and anotherlinked to measurements of pump light absorption [67],each have typical relative standard uncertainties of2.5 % and agree within those uncertainties. Typicalsources of uncertainty in the application of this methodare described in these two calibrations. An additionalsystematic error relevant to a flowing system would arisefrom a pressure drop between the OPCs and the capac-itance manometer. From the calculated conductance ofthe relevant tubing, we estimate the pressure could behigher in OPC2 by no more than 0.03 kPa (at a through-put of 0.015 kPa�L/s) which would result in no morethan a 3 % underestimate in the measurement of Popc2.Overall we estimate that the total relative standard un-certainty in our routine optical polarimetry is 4 %.

Calibration of the ratio for mixtures are less accurateand less extensive. For a mixture of 25 % 3He and 75 %4He the ratio has been found to scale with the inverse ofthe percentage of 3He, with a relative uncertainty of 5 %to 10 % [13]. This result is expected to be generallyapplicable because only the emission from 3He is polar-ized. The vendor’s specified relative uncertainty of 5 %in the percentage of 3He also contributes to the totalrelative standard uncertainty in the calibration of theoptical method for mixtures. Better knowledge of thegas mixture can be obtained by gas analysis, but themixtures purchased were cost-effective for routine use.In addition, the uncertainty in application of the methodto mixtures is increased because of the decreased size ofthe optical signal. Overall we estimate that the totalrelative standard uncertainty in our routine optical polar-imetry for mixtures is 8 %.

4.7.2 NMR Polarimetry

Free induction decay (FID) [68,69] is used to measurethe polarization of the compressed gas in the storagecell. In this method, the magnetization is tipped awayfrom the quantization axis by applying a short pulse ofradiation at the Larmor frequency (85 kHz for our typi-cal operating field of 2.6 mT). After this pulse, thetransverse component of magnetization freely precessesaround the quantization axis at the Larmor frequencywhile decaying in magnitude. The time scale of thedecay, T2, is related to dephasing of the individual nu-clear spins due to inhomogeneity in the static magneticfield. The initial size of the signal is proportional to themagnetization. The free precession is detected with aresonant pickup coil, connected to a dual-phase lock-inamplifier. By calibrating the response of the pickup coilusing optical polarimetry at a known low pressure, andmeasuring the pressure in the storage cell, the storagecell polarization is determined. Figure 7 shows an FIDsignal from 45 % polarized gas produced by direct opti-

cal pumping of pure 3He at a pressure of 0.13 kPa,which we will refer to as the calibration FID signal.Figure 8 shows an FID signal from a compressed gasmixture (33 % 3He, 67 % 4He) at a pressure of 100 kPa.Whereas a fully destructive �/2 rad tip angle was usedfor the calibration FID signal, a tip angle of 0.070 radwas used for the compressed gas. Accounting for thedifferent pressures and tip angles, and the mixture ratiofor the compressed gas, leads to Pstc = 0.51 for the datain Fig. 8. Although performing the optical calibration ofthe NMR system with the same mixture ratio as thecompressed gas cancels out inaccuracy in the knowl-edge of the mixture ratio, we used pure 3He for thecalibration FID signal because it yields both a largerFID signal and a larger optical signal.

The initial tip angle of the magnetization is controlledby the amplitude of the rf pulse applied to the NMRdrive coils. The rf amplitude required for a �/2 tip angleis determined by two methods: 1) by observing com-plete loss of the optical signal from low pressure gasafter the rf pulse, 2) by observing complete loss of theFID signal from compressed gas after the rf pulse. In thelow pressure case, the discharge is extinguished duringNMR, and reignited after the rf pulse to measure theremaining optical signal. In the compressed gas case, asecond �/2 tip is performed to measure the remainingNMR signal. Both measurements are typically per-formed, allowing a double check on the tip angle. Avariation on the NMR test is to determine the requiredamplitude for a � pulse by minimizing the remainingsignal after such a pulse.

Fig. 7. Free induction decay NMR signal from the cell Neptune, usinga fully destructive � /2 rad tip angle. The cell was filled to a pressureof 0.13 kPa of pure 3He and polarized to 45 % by direct opticalpumping. The first few data points are low because of the 3 ms lock-intime constant. The solid line shows a fit to an exponential decay fortimes greater than 0.016 s.

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Fig. 8. Free induction decay NMR signal from the cell Neptune, usinga tip angle of 0.070 rad. Using the compression apparatus, the cell wasfilled to a pressure of 100 kPa of a gas mixture (33 % 3He, 67 % 4He).The first point is low because of the 0.3 ms lock-in time constant. Theshape of the FID is not exponential, but instead is given by the Fouriertransform of the spectral distribution of Larmor frequencies in thecell. Comparing to the data in Fig. 7, and accounting for the mixtureratio for the compressed gas and the different pressures and tip anglesleads to Pstc = 0.51.

By using relatively small tip angles, the polarization ismonitored with minimal loss of polarization. The re-quired amplitude is determined by attenuation relative tothe value needed for a �/2 tip, and is also checked byperforming a sequence of several small tips and measur-ing the remaining polarization. For a tip angle of0.17 rad, the signal height (as compared to a �/2 tip) isreduced by a factor of sin(0.17) = 0.169, but the fractionof the initial polarization remaining after the tip iscos(0.17) = 0.986.

The temporal behavior of the FID is not important aslong it does not affect the measurement of the initial sizeof the signal. For the compressed gas, the shape of theFID is given by the Fourier transform of the spectraldistribution of Larmor frequencies in the cell. Since wedo not generally know the functional form of the shapeof the FID, the initial size of the signal is not extractedby a fitting procedure, but rather is determined directlyfrom the first data points of the FID (ignoring the pointsthat are initially low because of the lock-in time con-stant). If T2 is too short, determining the initial sizebecomes more difficult because shorter lock-in timeconstants are required. T2 is quite sensitive to magneticfield inhomogeneity, so we found that it is important tolocate the storage cell close to the center of the holdingfield coils. T2 typically ranged between 100 ms for smallcells down to 20 ms for large cells. For the relatively

large signals from compressed gas, we could use corre-sponding lock-in time constants between 3 ms and0.3 ms. For the low pressure gas, the long mean freepath allows for “motional narrowing” [70], which leadsto an exponential shape for the calibration FID signal, asshown in Fig. 7. Hence for the calibration FID signal, wedetermined the initial size of the signal from a fit of theFID data to an exponential decay. Motional narrowingalso leads to an increase in T2 because of averaging ofthe gradient, which is convenient because longer lock-intime constants are desirable when measuring the smallersignal from low pressure gas. Although this increase wasobserved for small cells, resulting in T2 ≈ 1 s, the in-crease was less pronounced for larger cells. We attributethis effect to diffusion of gas on the time scale of theFID. The gas near the edge of a large cell, where thegradient may be larger, may only contribute a smallamount to the pickup coil signal for the compressed gas,while diffusion at low pressure results in a larger rangeof gradients sampled by the gas contributing to thepickup coil signal.

For a sufficiently large magnetization and a pickupcoil with a high quality factor, FID can be influenced byradiation damping [68,71] ie. the effect on the magne-tization from the currents induced in the pickup coil.These currents always act upon the magnetization so asto drive it towards the lower energy nuclear magneticsubstate. If the nuclei are initially in the lower (higher)energy state and the magnetization is tipped by an angleless than �/2, the currents generated in the pickup coilshorten (lengthen) T2 and result in a value for the re-maining longitudinal magnetization that is larger(smaller) than the cosine of the tip angle. Whereas in thelower energy case T2 is simply shortened, in the higherenergy case the shape of the FID can be dramaticallymodified because the transverse magnetization can in-crease during the free precession. Here we are con-cerned with the possible effect of radiation damping onFID measurements, in particular on the determinationof Pstc, but also on the measurement of cell relaxationtimes. In general, the initial size of the FID signal isunchanged. However, the effect on the remaining mag-netization can influence the determination of the re-quired amplitude for a �/2 tip by the method discussedabove. In this case, the alternative method of determin-ing the amplitude for a � tip proves to be less sensitiveto radiation damping (see Appendix A). To keep radia-tion damping effects small, we deliberately decreasedthe quality factor of the pickup coil from 120 to 30 byadding two 1.3 k� resistors to the pickup coil circuit. Inaddition we optically pumped to the lower energy state.More discussion of the effects of radiation damping canbe found in the Appendix.

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A tip angle of �/2 is obtained from a 5 ms long, 6 Vpeak amplitude signal applied to a square Helmholtzpair, 23.8 cm on a side. Each coil has 11 turns of0.41 mm diameter wire, and the magnitude of theimpedance was measured to be 60 �. Since theimpedance is dominated by the inductive reactance,these data yield 0.22 mH for the inductance, close to thecalculated value of 0.23 mH [72]. The separation of thetwo coils is close to 0.5445 times the length of one of thesides, which is the ideal separation for a squareHelmholtz pair [73,74]. The drive coil is energized us-ing a reed relay with specified operate and bounce timesof 0.62 ms and 0.40 ms, respectively.

The square pickup coil has 400 turns of 0.20 mmdiameter wire and is 6.6 cm on a side, and 0.50 cm ona side of the wire cross section. Since the NMR signalis directly proportional to frequency, we aimed for aresonant frequency near 100 kHz, the maximum refer-ence frequency for the lock-in amplifier. Stray capaci-tance was minimized by using a preamplifier that waslocated only 60 cm from the pickup coil (the primaryreason it was not even closer was due to its magnetichousing). The connection to the preamplifier was 30 cmof RG58 coaxial cable and 25 cm of RG62 coaxialcable. RG62 has lower capacitance than RG58, but isslightly magnetic, so it was not used in close proximityto the cell. Based on a calculated value of 22 mH for theinductance of the pickup coil and the measured resonantfrequency of 85 kHz, the total capacitance is estimatedto be 160 pF. To prevent overloading the preamplifierfrom pickup of the drive coil pulse, the inputs are keptshorted by a reed relay until 1 ms after the drive coilpulse ends. The relay, as well as protection diodes andthe aforementioned resistors are located in a small boxjust before the preamplifier.

The scatter in the data in Figs. 7 and 8 is due toelectrical noise on the pickup coil signal. To improve theaccuracy of the calibration against optical polarimetry,several measurements of the relatively small calibrationFID signal are averaged. The signal to noise ratio de-pends on the size of the cell, the distance between thecell and the pickup coil (which is larger when the celldewar is used), the polarization and gas pressure, and thenoise level on the particular day that the calibration FIDsignals are obtained. For the data discussed in this pa-per, we estimate the typical relative standard uncertaintyin determining the initial size of the calibration FIDsignal to be 5 %. The total relative standard uncertaintyin measurements of Pstc is estimated to be 9 %, whichincludes additional contributions from the optical polar-imetry itself (4 %, see Sec. 4.7.1), the initial size of theFID signal from the compressed gas (3 %), the ratios ofthe tip angles and gas pressures for the two FID signals

(3 % each), and the mixture ratio (5 % for compressionof mixtures).

5. Results

5.1 Polarization Preservation During Compression

For this apparatus, the fraction of polarization pre-served during compression is clearly the most importantparameter to characterize. Recirculation mode is conve-nient for such tests because the optical pumping cellpressure and polarization, the storage cell pressure andpolarization, and the throughput can be measured underequilibrium conditions. We find that fc increases withthe volume flow rate at the outlet of the second stage ofthe compressor, F (F = Q /pstc). This is reasonable be-cause the time the gas spends in the second stage of thecompressor is inversely proportional to the volume flowrate. The volume flow rate is the slowest at the outlet ofthe second stage because for a given throughput, thevolume flow rate at any point is inversely proportional tothe pressure at that point. Figure 9 shows the variationof fc with F . Although values of fc approaching 0.9 areobserved at high volume flow rates, values of 0.6 to 0.8are more typical. The volume flow rate is optimized bytrading off the increase in fc against the decrease in Popc.Experimentally F is determined by measuring the ratioof the throughput to the storage cell pressure. The valueof fc was determined from the measured values of Pstcand Popc2, and corrected slightly by the value of fr. Thesedata were acquired using a 40 cm3 Pyrex cell, with arelaxation time of 2.7 h. The value of fr varied between0.94 and 1, so the correction was small.

Fig. 9. The variation of fc with F . The data are shown by solid circles,along with a fit to Eq. (5).

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The identification of the second stage of the compres-sor as the likely source of the decrease in fc deservesfurther comment. The pressure at other points in thecompressor also depends on both the storage cell pres-sure and the throughput (see Sec. 4.4), so one mightspeculate that the behavior of fc is related to changes inthe time spent at these other locations. For example, thegas moves rapidly at low pressure, but is much moresensitive to magnetic field gradients. However, we havenot seen any clear correlation with the optical pumpingcell pressure, which would be an indicator of a gradientissue. As for the pressure between the stages, it is almostindependent of throughput, and fc most definitely is not.Further evidence to support the claim that the secondstage is the dominant source of relaxation during com-pression was obtained by reconfiguring the apparatus sothat the polarization could be measured in a buffer cellbetween the stages. For values of F at the lower end ofthe data shown in Fig. 9, the polarization between thetwo stages was still 90 % of Popc2.

We attempted to decrease the relaxation in the secondstage by controlling the transfer of gas from the firststage to the second stage. A pneumatic, non-magneticvalve was installed on the inlet port of the second stage.The idea was to build up pressure in the buffer cell andperiodically open the valve so that the released gaswould travel through the second stage more quickly.(The optical pumping cell pressure would also varyproportionally with the buffer cell pressure.) For rea-sons that are not completely understood, any improve-ment in fc was minor, at best. The lack of improvementmay be due to increased relaxation of the gas residing inthe second stage of the compressor while the valve isclosed.

We do not fully understand the relaxation observedduring compression, but speculate that it is due to thelarge surface to volume ratio in the compressor head.The total surface area of the Teflon-coated diaphragmand aluminum head plate is S = 60 cm2, and the volumeof the compressor head varies between 10 cm3 and es-sentially 0 cm3. At our typical flow rates, the gas spendsmany compression cycles in the head. Although theexact details of the volume as a function of time are notknown, assuming a simple sinusoidal dependence leadsto �c = ( Va)/(S 1/2), where �c is the relaxation time inthe compressor head, Va is the average volume of thehead, is the relaxation time for S /Va = 1 cm�1, and

is the compression ratio. Using this result, fc is given by

fc =1

1 + [(2S )/( F 1/2)]. (5)

Figure 9 shows a fit of the data for fc vs F to this form,with S = 60 cm2 and = 38, and a fitted parameter. A

value of = 360 s/cm was extracted from the fit, wherewe have yet to distinguish between the presumably dif-ferent values for for aluminum and Teflon. There arefew relaxation time measurements in the literature, andwe have not measured the relaxation times for the Tefloncoated diaphragm or the aluminum head. Potentiallyrelevant relaxation time values from the literature in-clude: 14 min for Viton and 10 h for aluminum (surfaceto volume ratio near 1 cm�1) [47] and 24 min for “utilitysheet aluminum” and 17 h for spectrographically purealuminum (surface to volume ratio of 0.08 cm�1) [16].(We considered Viton to be relevant only because itmight be similar to Teflon.) Hence a value of 360 s fora surface to volume ratio of 1 cm�1 seems somewhatshort, but without doing our own controlled measure-ments for the particular Teflon and aluminum used inthe compressor, not much can be concluded. In this caseit would be appropriate to test the materials as used, incontrast with the stringent cleaning procedures used inprevious studies [16]. We found that coating the Teflondiaphragm with aluminum had no discernable effect onfc, which either indicates that the Teflon does not domi-nate the relaxation, or that the hypothesis that the behav-ior of fc is related to relaxation on materials in thecompressor head is invalid. Based on the work to date,we do not have a definitive understanding of the relax-ation, but based on the analysis above the value for thatis required to explain the behavior is not unreasonable.

Whereas fc is fixed for operation in recirculationmode, it varies during operation in fill mode. In general,a higher polarization is obtained when filling a cell to agiven storage cell pressure as compared to recirculatinggas at the same storage cell pressure. This is expectedbecause for a given throughput, pstc rises linearly fromzero to the value that it ultimately has for recirculationmode, hence the average value of F (hence fc) is higher.Alternatively, if the throughput is varied during the fillso as to keep a constant value for F , the conditions areimproved for the optical pumping because the averagevalue of topc is larger. In either case, the average value ofP0 is higher because the average optical pumping cellpressure is lower.

5.2 Optical Pumping Cell Polarization

Given the need for high volume flow rates in order topreserve the polarization during compression, efficientoptical pumping is desirable. In this section we providea sample comparison of the values of optical pumpingcell polarization that we obtain with gas flow (Popc1 andPopc2), as compared to the values without flow (P0).

To compare the measured value of Popc2 during com-pressor operation to the expected value based on Eq. (4)requires determination of the mean residence times topc1

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and topc2, and the four optical pumping parameters P0, f ,�1, and �2. The residence times were determined byshuttering the laser light and measuring the resultantexponential decline in polarization as the polarized gaswas replaced by unpolarized gas. The residence timesobtained were consistent with those determined fromthroughput and pressure measurements. A small correc-tion (10 %) is applied to account for the relaxation in thedischarge. The optical pumping parameters cannot bemeasured by simply stopping the gas flow because thepressures in the OPCs change when this is done. Insteadwe measured the rise in polarization when the laserilluminated each OPC, which were maintained at thepressure and discharge intensity used during compres-sion. For example, for pstc = 80 kPa and Q = 0.015kPa�L/s, the values of popc1 and popc2 are 0.47 kPa and0.27 kPa, respectively, and we measured f P0 = 0.50,P0 = 0.61, �1 = 5.2 s, and �2 = 5.1 s (33 % 3He, 67 % 4Hemixture). For this throughput, topc1 and topc2 are 11.0 sand 9.9 s, respectively. For optical pumping of OPC2 orOPC1 only, Eq. (3) yields Popc2 = 0.40 and Popc1 = 0.34,slightly lower than the observed values of 0.44 and 0.36.For the diffusion-restricted double cell case, Eq. (4)yields Popc2 = 0.52, whereas 0.53 was observed.

Fitting the rise in polarization with an exponential isonly an approximation that yields some kind of averagetime constant. We also used a numerical calculation toinclude the known non-exponential behavior of metasta-bility-exchange optical pumping, which has been char-acterized as a dependence of the effective time constant� on the equilibrium polarization in the cell [14]. Weincorporated a linear decline in � with increasing polar-ization [14] into the numerical calculation. The valuesof the optical pumping parameters in the numericalcalculation were adjusted to reproduce the results of thestatic optical pumping tests. These parameters were thenused in a numerical calculation that included gas flow.For optical pumping of OPC2 or OPC1 only, the numer-ical calculation yielded Popc2 = 0.39 or Popc1 = 0.33, andfor the diffusion-restricted double cell case, Popc2 = 0.50was obtained. As expected, these values are lower thanthose obtained from Eq. (3) and Eq. (4) above, whichincreases the discrepancy between the calculated andmeasured results for optical pumping with gas flow.

Obtaining slightly higher polarization than the calcu-lated result was surprising. We checked the measuredvalues of the optical pumping parameters for OPC2 byoptically pumping a sealed cell of the same dimensions,and obtained similar values. (This test also indicates thatimpurities do not significantly affect the achievable po-larization in the OPCs, at least for our relatively strongdischarge intensities.) As a further test, we also mea-sured the time constants for the rise in the polarizationof the flowing gas upon illuminating each cell, denoted

by �2f and �1f. �2 was determined using the relationship�2

�1 = �2f�1 � topc2�1 , and similarly for �1. For reasons thatare not understood, �2 determined from these flowinggas measurements was half of the value determinedfrom the static measurements, while better agreementwas found for �1. These results would reduce the dis-crepancy discussed above, but we do not have an expla-nation for the apparent difference in the time constantsextracted from static and flowing measurements. Henceit is unclear whether we can claim accurate modelling ofthe optical pumping, and it appears that the achievablepolarization with gas flow is higher than one mightexpect from our modelling. Nevertheless, the diffusionrestricted double cell arrangement clearly yields highervalues for Popc2, and there is reasonable agreement in therelative improvement as compared to the simple singlecell.

By employing PPR, the value of Popc2 was increasedto 0.58. The value of the polarization of the returninggas can be determined by shuttering the laser light to theOPCs and waiting long enough for the gas in the OPCsto be replaced by gas returning from the storage cell.The optical pumping cell polarization slowly drops asthe freshly polarized gas exits, and then stabilizes at thevalue for the polarization of the returning gas. Typicallywe find that Popc2 increases to about 85 % of Pstc.

5.3 Results for Applications

In this section we present our current results for twoapplications: cold neutron spin filters and polarized gasMRI. We focus here on the capability of the compressorto produce polarized gas for these applications, ratherthan the applications themselves.

For a neutron spin filter operating in a given range ofneutron energies, the product of storage cell pressureand cell length is chosen based on a trade-off betweenhigh neutron polarization (or analyzing power) and hightransmission. For cold neutrons, a desirable product istypically 400 kPa�cm. As discussed above, we obtainthe highest 3He polarization by using 3He-4He mixturesand minimizing the storage cell pressure. Although us-ing pure 3He would result in the lowest storage cellpressure, the increase in the achievable optical pumpingcell polarization using mixtures proves to be more im-portant. The combination of these two requirementsmakes long cells preferable, but for practical consider-ations we have limited the cell length to a maximum of15 cm. Using the cell Neptune (10 cm long), we haveobtained Pstc = 0.33 for a mixture of 50 % 3He and 50 %4He continuously recirculated at pstc = 80 kPa. Other op-erating parameters for this test were: popc2 = 0.26 kPa,Q = 0.016 kPa�L/s, Popc2 = 0.45, and fc = 0.74. UsingPPR, Popc2 increased to 0.49 and Pstc to 0.37, and in fillmode we obtained Pstc = 0.45.

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If the cell length were increased to 15 cm, a mixtureof 33 % 3He and 66 % 4He could be used for the samevalue of pstc. For this mixture ratio and almost the samevalues for popc2, Q , and fc, we obtained Pstc = 0.40 andPopc2 = 0.54. For PPR, Popc2 increased to 0.58 and Pstc to0.43. Filling a cell to 100 kPa yielded Pstc = 0.52. Threehours after this particular fill of Neptune, Pstc was deter-mined to be 0.48 by neutron transmission methods [1],which is consistent with the relaxation time of the cell.

For polarized gas MRI it is desirable to either maxi-mize the total magnetization, or to obtain a given mag-netization for the least amount of 3He consumed. De-pending on the future of this field, it may also provedesirable to produce polarized 3He rapidly. In our previ-ously reported application to polarized gas MRI, weproduced 100 kPa�L of 15 % polarized 3He gas in 3 h.The 250 cm3 cell was filled to a pressure of 100 kPa atliquid nitrogen temperature, yielding a room tempera-ture pressure of 400 kPa. We now consider 3He-4Hemixtures to be the most efficient approach to applyingthis apparatus for polarized gas MRI. Use of a 50 % 3Heand 50 % 4He mixture should yield Pstc ≈ 0.44, ie. aneffective overall gas polarization of 0.22. If an adequatesignal to noise can be obtained with a lower magnetiza-tion, the fraction of 3He can be decreased.

6. Conclusion

We have described an apparatus that demonstratesthat highly polarized 3He gas, produced at a typicalpressure of 0.25 kPa by metastability-exchange opticalpumping, can be compressed to a pressure of 100 kPausing a compact, simple, inexpensive apparatus that isbased on a modified commercial diaphragm pump. Fortypical operating conditions, the apparatus can preserveabout 75 % of the polarization produced by opticalpumping at low pressure. The loss of polarization duringcompression decreases with increasing volume flowrate, necessitating flow rates comparable to the opticalpumping rate. To obtain the highest polarization of thelow pressure gas in a compact system operated at suchflow rates, we have exploited two schemes: 1) a two-cellarrangement with a diffusion restriction, and 2) polar-ization preserving recirculation. These techniques allowus to obtain 85 % to 95 % of the achievable opticalpumping cell polarization in the absence of gas flow(P0), but the discharge intensity required for rapid opti-cal pumping limits P0. For typical operating conditions,the optical pumping cell pressure of 0.25 kPa is higherthan optimum for pure 3He gas, and limits the achievablepolarization. This issue is mitigated, but not completelyeliminated, by the use of 3He-4He mixtures; despiteoperation at higher overall pressure and flow rate, the

best results are obtained with mixtures. In general “fillmode” yields better results than “recirculation mode”.All of these issues yield an apparatus for which theperformance is strongly dependent on the required stor-age cell pressure of polarized 3He but is fairly indepen-dent of the size, shape, and relaxation time of the storagecell. Presently we have obtained as high as 52 % 3Hepolarization for a storage cell filled to 100 kPa of amixture containing 33 % 3He and 67 % 4He.

The apparatus is presently being applied for neutronspin filters. Given that we can obtain acceptable 3Hepolarization for a cold neutron spin filter, the key issuenow is longer relaxation time cells. The relaxation timesfor our present cells are more than adequate for a contin-uously recirculated spin filter, but it is currently moreconvenient to fill cells and transport them to the neutronbeam line. We have recently obtained a 200 h relaxationtime using Rb-coated GE180 glass [78], and in a firsttest this long lifetime was not significantly degradedafter cycling to liquid nitrogen temperature.

For polarized gas MRI applications, a liquid nitrogencooling bath provides a convenient method for increas-ing the final cell pressure. Based on our tests, we expectthat the apparatus can produce 100 kPa�L of 20 % polar-ized 3He gas in 2 hours using optical pumping of eitherpure 3He gas or a 3He-4He mixture. Higher productionrates are clearly possible at the expense of the finalpolarization.

The ultimate goal is to realize the full potential of theMEOP method with a compact device. The key issue isreducing the polarization loss in the compressor, not justfor the obvious reasons but also because of the impacton the utility of polarization preserving recirculation. Iflossless compression is combined with PPR, the poten-tial increase in polarization from each pass through theoptical pumping cells would not be diminished by re-covering the loss in each previous pass through the com-pressor. Hence the asymptotic approach to P0 can bedistributed over several passes through the recirculationloop, rather than being required to occur in a single pass.This would decrease the need for large optical pumpingcells and strong discharge intensities. In addition, thisscheme would be more tolerant of higher flow rates,thus increasing the chance that the presumed losslesscompression can actually be attained. Assuming that gaspurity does not limit P0, lossless compression combinedwith PPR should allow storage cell polarizations ap-proaching those obtained for weak discharges in sealedcells (0.7 � 0.8). For the more realistic case of smallpolarization losses and optical pumping cell polarizationslightly less than the sealed cell ideal, Pstc = 0.6 � 0.7should be attainable. Currently, our capability to realizethe full benefits of the PPR scheme is limited by loss ofpolarization in compression.

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Even if PPR is not employed, reduced polarizationloss would still allow operation at lower flow rates, thusdecreasing the optical pumping cell pressure. The resi-dence time in an optical pumping cell of the same vol-ume is increased only slightly because the decrease inOPC pressure offsets the lower flow rate. As an exam-ple, let us assume that fc = 0.95 could be obtained atF = 0.08 cm3/s, which leads to Q = 0.008 kPa�L/s forpstc = 100 kPa, and thus popc = 0.18 kPa. Under theseoptical pumping conditions we have observedPopc2 = 0.64, hence a storage cell polarization of 0.61could be obtained for the presumed value of 0.95 for fc.With some sacrifice in compactness, larger opticalpumping cells should allow OPC polarization approach-ing 70 % in a single pass. For the model presented inSec. 5.1, such low loss would require an order of magni-tude reduction in the term S /( 1/2), which indicatesthat the key parameters are the surface area of the com-pressor head, the relaxation properties of the compres-sor materials, and the compression ratio. For the secondstage of the compressor, the displacement volume couldbe significantly reduced without substantially degradingthe performance of the compressor. Hence it should bepossible to decrease the surface area of the compressorhead, although this would require a different compressoror new construction for the present one. As for thesource of relaxation, our measurements to date do notclearly identify the next step. Indeed, the ineffectivenessof coating the Teflon diaphragm with aluminum sug-gests that a flow-rate dependent fraction of the gas willbe depolarized almost regardless of the material for thediaphragm coating. The relaxation may be an inherentproperty of the compression method that would be diffi-cult to surmount, but further investigation is requiredbefore this conclusion can be drawn. Finally, an increasein the compression ratio could be attempted, but a sub-stantial increase is unlikely for this type of compressor.Realizing nearly lossless compression may require analternative approach such as peristaltic compression[75], but detailed results for this method are needed.

Our results are also limited by the relatively highoptical pumping cell pressure, especially for pure 3He. Ifthe polarization loss could be reduced, a third stage ofcompression could substantially reduce the ultimatepressure. Reducing the elevation of pressure with flowrequires increased pumping speed, which could be ob-tained by using two heads in parallel.

The performance of this apparatus is not significantlylimited by laser power, but improving the results willrequire optimizing every aspect of the system. Althoughhigher power than we have obtained has been reportedfor arc-lamp pumped Nd:LMA lasers [14], we havefound that the attainable performance is variable andseems to be linked to the quality of each laser rod.

Yb-doped fiber lasers [76,77] promise to provide higherpower in a smaller, more compact system.

7. Appendix A. Radiation Damping inFree Induction Decay

For large magnetization and high quality factorpickup coils, radiation damping may affect free induc-tion decay signals. Although these effects can beavoided, it is useful to be aware of the expected changesin the FID, which depend on the initial energy state ofthe nuclei, the strength of the damping, and the size ofthe initial tip angle. We begin by reproducing the solu-tions for free induction decay in the presence of radia-tion damping that are presented by Bloom [71]. In thatwork, the FID in the absence of radiation damping isassumed to be a simple exponential, and longitudinalrelaxation is neglected. The initial tip of the magnetiza-tion is assumed to be instantaneous, ie. the effect ofradiation damping during a finite rf pulse is not consid-ered. For a initial magnetization M (0) and initial tipangle � (0), the transverse magnetization MT(t ) is givenby

MT(t ) = M (0)�� sech[(t � tm)/� ] (6)and the longitudinal magnetization for t = �, Mz(�), isgiven by

Mz(�) = M (0)��1� � 1T2� (7)where �� is the radiation damping relaxation time forT2 = �, T2 is the transverse relaxation time for �� = �, �is determined by

�� 2

= ��T2�2

+ 2��T2�cos� (0) + 1 (8)and tm is determined by

exp(2tm/� ) =1 � [(� /T2) + (� /��)cos� (0)]1 + [(� /T2) + (� /��)cos� (0)]

. (9)

�� is given by [2�Qf M (0)]�1, where Q is the qualityfactor of the pickup coil and f is the filling factor. Asexpected, �� is smaller, hence radiation damping effectsare larger, for large values of Q , f , or M (0). Figure 10shows MT(t )/M (0) determined from Eq. (6) for five tipangles, where we have assumed T2 = 1 s and �� = 0.9 s.The nuclei are presumed to be in the lower energy statebefore the tip. (A tip of � (0) from the lower energy state

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Fig. 10. MT(t )/M (0) determined from

[J. Res. Natl. Inst. Stand. Technol. 106 Compressing Spin … · 2001. 9. 9. · Compressing...

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Transcript of [J. Res. Natl. Inst. Stand. Technol. 106 Compressing Spin … · 2001. 9. 9. · Compressing...