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A compact solenoid 3He neutron spin filter with a fast spin flip capability
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506 www.elsevier.com/locate/nima
A compact solenoid 3He neutron spin filter with a fast spin flip capability Takashi Ino, Suguru Muto Neutron Science Laboratory, KEK, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan Received 22 March 2005; accepted 12 April 2005 Available online 13 June 2005
Abstract We have designed and demonstrated a compact solenoid 3He neutron spin filter with a fast spin flip capability. The He spin is flipped by adiabatic fast passage (AFP) in a short time and with very little polarization loss, which is essential for polarized neuron scattering measurements in cancellation of systematic errors. A solenoid coil and compensation coils provide a uniform magnetic field for the polarized 3He to minimize the longitudinal spin relaxation. This neutron spin filter can be installed rather easily in neutron scattering spectrometers as a neutron polarizer as well as a neutron spin analyzer. We describe the design and the performance of the device tested by AFP-NMR and with a pulsed neutron beam at KEK. r 2005 Elsevier B.V. All rights reserved. 3
PACS: 61.12.q; 75.25.+z; 29.25.Pj; 29.27.Hj Keywords: 3He polarization; Neutron spin filter; Polarized neutron; Neutron scattering; Adiabatic fast passage (AFP); Spallation neutron source
1. Introduction Polarized neutrons provide a powerful tool not only to study magnetism but also for researches on structure and dynamics of materials. Polarized neutrons are essential also in the fields of nuclear and particle physics. Neutrons can be polarized in Corresponding author. Tel.: +81 29 864 5619;
fax: +81 29 864 3202. E-mail address: [email protected] (T. Ino).
various ways. Polarizing crystal monochromators and polarizing supermirrors [1] are probably the most popular neutron polarizers today. The polarized gaseous 3He, however, attracts much attention as a neutron spin filter recently because of its broad energy coverage and large solid angle acceptance. The spin-dependent large neutron capture cross-section of the 3He nucleus enables one to filter out neutrons with certain spin directions from cold to epithermal energy ranges [2]. A large sold angle for divergent scattered
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.04.057
ARTICLE IN PRESS 500
T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
neutrons can be covered with polarized gaseous 3 He as a neutron spin analyzer. Such polarized 3He neutron spin filters (NSF) are of great interest at high flux steady-state and pulsed neutron sources. Particularly at pulsed neutron sources, the 3He NSF is required to be as small as possible because most neutron spectrometers are inside thick concrete radiation shielding and space for the NSF is limited. In addition, polarized neutron scattering instruments often require the neutron spin inversion to cancel out systematic uncertainties, and are equipped with static or radio frequency (RF) magnetic spin flippers [1]. These spin flippers, however, occupy some space and change magnetic fields depending on the neutron spin direction that usually introduces asymmetry for neutrons with opposite spins. On the other hand, small size 3He NSFs, which did not have a fast spin flip capability, were demonstrated by authors [3,4]. To meet both requirements, the compactness and the symmetric spin inversion of neutrons, we designed and demonstrated a compact solenoid 3He NSF with a fast spin flip capability (CSF). In the CSF, the 3He spin, which corresponds to that of neutrons, is inverted by adiabatic fast passage (AFP) [5] with very little polarization loss. The spin flip of 3He nuclei by AFP does not induce magnetic field changes, except when the spin is being reversed, and consequently no asymmetry arises in the spin inversion. In this article, we present the design and the performance of the CSF that can be used in various neutron scattering experiments.
the transverse component of the field gradient. To satisfy this requirement with keeping the size compact, we designed a solenoid coil with a pair of field compensation coils in symmetric positions at both edges of the solenoid. Fig. 1 shows the dimensions of the solenoid coil and the compensation coils. Enameled cupper wire of f 1.07 mm was wound in two layers on a cylindrical bobbin with a diameter of 120 mm and a length of 500 mm. The compensation coils were wound also in two layers with the same wire on the solenoid from both edges. The number of turns of each compensation coil was determined by calculations so that the magnetic field gradient around the solenoid center was minimized as well as all the coils were able to be connected in series and operated with one power supply. Magnetic field calculations for the solenoid coil with and without the compensation coils are illustrated in Figs. 2 and 3 as the transverse field gradient. The calculation for the solenoid coil with the compensation coils shows that the transverse field gradient satisfies o104(/cm) over the cylindrical area with a diameter of 80 mm and a length of 150 mm. A cylindrical 3He cell with an inner diameter of 24 mm and an inside length of 47 mm was placed at the solenoid center. A Helmholtz coil with a diameter of 94 mm was used to provide an RF field for AFP. It was set inside the solenoid coil at the center and positioned perpendicular to the solenoid axis. Each circular coil was wound 20 turns compensation coil (2 layers) solenoid coil (2 layers)
2. Design of the compact solenoid 3He neutron spin filter with a fast spin flip capability An inhomogeneous magnetic field contributes the spin relaxation of polarized gaseous 3He [6–8]. The transverse field gradient as low as qBT =qT 104 ð=cmÞ B0
(1)
is preferred to neglect the longitudinal spin relaxation for the polarized 3He nuclei. Here, B0 is the mean magnitude of the spin holding magnetic field for polarized 3He, and qBT =qT is
120 coil bobbin (t5) 500
Fig. 1. A cross-sectional view of the solenoid coil and the field compensation coils. The diameter of cylindrical bobbin is 120 mm, the length is 500 mm, and the thickness is 5 mm. Enameled cupper wire of f 1.07 mm was wound in two layers on the bobbin as a solenoid coil, and another two layers (37 turns+36 turns) were wound from each edge of the solenoid for compensation of the magnetic field.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
501
50 ∂B T
40
∂T
[/cm]
B0
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0013
0.0012
0.0011
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
10
0.0003
0.0002
20
0.0004
0.0001
R [mm]
30
0 0
20
40
80
60
100
Z [mm]
Fig. 2. The calculation of transverse magnetic field gradient for the solenoid coil without the compensation coils is shown on the radial (R) vs. axial (Z) plain where (R ¼ 0, Z ¼ 0) is the center of the solenoid.
50 0.00015 0.0001
40
0
R [mm]
30 5e-05 20
-0.00035
-0.0003
-0.00025
[/cm]
-0.0002
B0
∂T
-0.0001
∂B T
10
-0.00015
-5e-05
0 0
20
40
60
80
Z [mm] Fig. 3. The calculation of transverse magnetic field gradient for the solenoid coil with the compensation coils.
100
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
502
with f 0.2 mm enameled cupper wire. The impedance of the Helmholtz coil was matched to that of the oscillator output with a matching circuit to maximize the RF emission at the resonance frequency of a pickup coil for AFPNMR. The pickup coil was made with f 0.1 mm wire wound 300 turns on a 38 mm diameter bobbin Y solenoid bobbin (5 mm thick)
Helmholtz coil
R=
60
3He
cell
X
and found to have its resonance frequency at 92.1 kHz without a resonant capacitor. The pickup coil was placed under the 3He cell perpendicularly to both the solenoid and the Helmholtz coil axes. A Larmor precession frequency of 92.1 kHz corresponds to a magnetic field of 2.84 mT for the 3He nucleus, and such field was produced by a current of 1.23 A flowed in the solenoid coil and the compensation coils. See Fig. 4 for a crosssectional view and a schematic drawing of the Helmholtz coil, the 3He cell and the pickup coil showing the arrangement inside the solenoid. The calculation of the static magnetic field generated by the Helmholtz coil is shown in Fig. 5. The actual RF field may differ from the static field calculation because of the presence of conductive materials nearby such as the solenoid coil and the pickup coil. The effect of such perturbations was found to be negligible for AFP as shown in the next section. Fig. 5 shows that the RF field amplitude within a radiuso28 mm, which sufficiently covers our 3He cell, is less than 710% and uniform enough for AFP. The field gradient,
[mm] 50
pickup coil
0.6
0.5
0.7 0.8
40
Helmholtz coil
1.5 1.8
0.9 1.2
1.6 1.9
X [mm]
1 30
20
28 mm
10
1.7 1.4 1.3
1.1 1
3
He cell
0.4
1.1 0 0
10
20 30 Z [mm]
40
50
pickup coil Fig. 4. The arrangement of the Helmholtz coil, the cylindrical 3 He cell, and the pickup coil inside the solenoid bobbin. The solenoid and the cylinder axis of the 3He cell coincide with that of the neutron beam. The cross-sectional view perpendicular to the solenoid axis is shown at the center.
Fig. 5. The calculation of the static magnetic field for the Helmholtz coil. The field amplitude was normalized to unity at the center of the coil (X ¼ 0, Z ¼ 0). The Z-axis corresponds to the solenoid axis, and the X-axis to that of the Helmholtz coil. The variation of field amplitude is less than 710% within the spherical area with a radius of 28 mm.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
3. AFP-NMR test The performance of the CSF was tested with polarized 3He nuclei by AFP-NMR. A sealed 3He cell was prepared [9] and polarized by the spinexchange optical pumping [10,11]. The polarized 3 He cell with a spin relaxation time of 70 h was, then, transported and set in the CSF for the test. The AFP parameters, the magnetic field sweep speed and the RF field magnitude, were studied by observing the depolarization of the 3He in 100 consecutive AFP-NMR measurements. The single measurement sequence consists of (1) turning on the RF field, (2) sweeping the spin-holding magnetic field up and down, and (3) turning off the RF field. Fig. 6 shows such depolarization in 100 continuous NMR measurements with the optimum AFP parameters. Considering a 1% spin relaxation during the period of the measurements, the polarization loss in a single AFP-NMR measurement was found only to be 0.04%. The polarization loss in the AFP 3He spin flip was also studied. A single AFP spin flip was accomplished by (1) turning on the RF field, (2) sweeping the spin-holding magnetic field up, (3) turning off the
AFP NMR Signal [mV]
Polarization loss in one measurement : 0.04%
6.7 AFP NMR Signal [mV]
however, may have contributed additional spin relaxation for the polarized 3He, and the RF field was always turned off except when required.
503
6.6 6.5 Polarization loss in one spin flip: 0.02%
0.0 -6.5 -6.6 -6.7 0
20
40
60
80
100
Flip Number
Fig. 7. Measurements of the 3He polarization loss in the AFP spin flip. The 3He spin was flipped 100 times. The AFP-NMR signal (dots) appeared in the opposite sign in each spin flip. From the exponential fit (solid curves), the polarization loss in a single spin flip was found to be 0.02%.
RF field, and (4) sweeping the spin-holding magnetic field down to the initial amplitude. The NMR measurements are shown in Fig. 7 for the depolarization in 100 spin flips with the same AFP parameters. The polarization loss in a single AFP spin flip was observed 12 of that in a single AFPNMR measurement as was expected. Note that a single AFP spin flip took only 2.5 s.
4. Neutron beam test The transmission T of neutrons with the polarization Pi for 3He with the polarization PHe , the number density r, and the thickness t can be written in the following expression:
6.15
T ¼ esrt ðcosh PHe srt Pi sinh PHe srtÞ
6.10
where s is the spin averaged neutron capture crosssection of the 3He nucleus. The sign between the two terms in Eq. (2) depends on the polarization directions of the initial neutrons and the 3He nuclei. If the initial neutrons are unpolarized (Pi ¼ 0), Eq. (2) is simplified to
6.05 6.00 5.95 5.90 0
20
40 60 Measurement Number 3
80
100
Fig. 6. The polarization loss of the He due to the AFP-NMR measurement. The depolarization was measured to be 5% in a series of AFP-NMR measurements for 100 times. Subtracting a spin relaxation of 1% during the period of the measurements, the polarization loss in a single AFP-NMR measurement was observed to be 0.04%. The dots are the measurements, and the solid curve is an exponential fit.
T ¼ esrt cosh PHe srt
(2)
(3)
and the polarization of the transmitted neutrons becomes P ¼ tanh PHe srt.
(4)
Eq. (4) can be rewritten with the neutron transmissions for unpolarized 3He ðPHe ¼ 0Þ and
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
for polarized 3He T ðPHe Þ as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ 1 ðT ðPHe ¼0Þ =T ðPHe Þ Þ2 .
(5)
From Eq. (2), one can determine the polarization of the initial neutrons by measuring the transmissions through polarized 3He. Taking the ratio of the transmissions with spin-antiparallel to spin-parallel gT , the initial neutron polarization can be presented as Pi ¼
1 gT coth PHe srt. 1 þ gT
(6)
We measured such neutron polarization as a test of the CSF. Two identical CSFs were prepared, one as a neutron polarizer and the other as a neutron spin analyzer. They were set on the H-8 beamline at the pulsed neutron source of KEK (KENS). See Fig. 8 for the experimental apparatus. The polarization of neutrons transmitted through CSF 1 was determined by the transmission ratio for CSF 2 with the 3He spin-flip and nonflip. The two CSFs were placed 70 cm apart from each center, making a gap of 20 cm between them. The solenoid coil with the compensation coils of each CSF was operated at the same current that provided a magnetic field strong enough to hold the neutron spin direction in the gap while causing minimal interference at the 3He cells. A fast scintillator neutron detector, located downstream the beamline, was used to count the transmitted neutrons. By taking the ratio of the neutron counts with the 3He spin-flip and nonflip, the transmission ratio gT was obtained. The measurements of neutrons with spin-antiparallel to 3He and spin-parallel were repeated at short intervals to minimize systematic uncertainties due neutron source (H2O moderator) CSF 2
CSF 1 50 cm collimator
70 cm
3
detector He cell
Fig. 8. The experimental setup of the CSF on the H-8 beamline at KENS. Transmitted neutrons were counted with a fast scintillation neutron detector. The two CSFs were 70 cm apart from each center, making a gap of 20 cm between them. The magnetic field in the gap was strong enough to hold the neutron spin direction but weak enough at each CSF center.
to the polarization loss by the AFP spin flip and the spin relaxation of the polarized 3He. The 3He gas density and thickness rt in the CSF 2 cell had been measured from the neutron transmission for the unpolarized 3He by following T ¼ esrt or PHe ¼ 0 in Eq. (3), where absorption of neutrons in the cell windows had been taken into account by the transmission for an empty cell with the same dimensions. The 3He polarization PHe was monitored by AFP-NMR of CSF 2 that had been calibrated with the neutron transmission in Eq. (3). Both rt and PHe were determined with accuracies better than 1%. Fig. 9 shows measurements of the neutron transmission ratios for the 3He in CSF 2 with spin-antiparallel to spin-parallel. It was evident that the incoming neutrons to CSF 2 had certain polarizations because the transmission ratios were measured to be less than unity. From the ratios, the polarizations of the neutrons were calculated by Eq. (6) and plotted in Fig. 10 as crosses. The polarizations of the neutrons transmitted through CSF 1 were also measured independently. Displaced CSF 2 from the beamline, the neutron transmissions for CSF 1 with the 3He polarized and unpolarized were measured. Following Eq. (5), the neutron polarizations were evaluated and plotted as circles in Fig. 10. Both measurements, gT and the transmissions for CSF 1, were performed in succession within two hours. The 3 He polarizations in CSF 1 and CSF 2 decreased by 3% during the measurements since the spin relaxation times of the two cells were 70 and 59 h, Neutron Transmission Ratio
504
1.0 0.8 0.6 0.4 0.2 0.0 0.01
2
3
4
5 6 7 8 9
2
0.1 Neutron Energy [eV]
3
4
5 6 7 8 9
1
Fig. 9. Neutron transmission ratios for the 3He in CSF 2 with spin-nonflip to spin-flip. Discrepancies of the ratios from unity verified spin polarization of the initial neutrons.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
Neutron Polarization
1.0
spin flip is
Measurements by CSF 2 spin flip Measurements by CSF 1 transmission
1 dH 0 gH 1 H 1 dt
0.8 0.6 0.4 0.2 0.0 0.01
505
2
3
4
5 6 7 8 9
2
0.1 Neutron Energy [eV]
3
4
5 6 7 8 9
1
Fig. 10. Neutron polarizations measured by the transmission ratios for the 3He in CSF 2 with spin-noflip and spin-flip are shown as crosses. Another independent measurements by the neutron transmissions for CSF 1 are also plotted as circles. Error bars are statistical only.
respectively. The corresponding neutron polarizations changed by 2–3%, which were less than the statistical uncertainties, among the energies in Fig. 10. The polarizations of neutrons measured from the CSF 1 transmissions agreed well with those measured by gT for CSF 2 as seen in Fig. 10.
(7)
where the spin relaxation time is long enough to be neglected [5]. Here, g is the gyromagnetic ratio of the 3He nucleus, H 1 is a rotational component of the RF magnetic field, and dH 0 =dt is the sweep speed of the spin-holding field. The adiabatic condition can easily be satisfied for increased sweep speed dH 0 =dt with higher RF field H 1 . In our case, however, the polarization loss became larger when dH 0 =dt was increased with H 1 . It was probably limited by our DC power supply for the solenoid and compensation coils. The DC power supply must have become unstable due to the inductance of the CSF solenoid coil when dH 0 =dt was increased. With a proper power supply and control, the spin flipping time will be shortened significantly. We employed a Helmholtz coil for AFP to produce a uniform RF magnetic field that fitted the size of our 3He cells (Fig. 5), but a large uniform field to fit a larger cell can be formed with
5. Conclusions
X [mm]
50
0.7
40
0.8
30
0.9
20 10 0 0
20
40
60
80
100
80
100
Z [mm] 50 0.5
40 Y [mm]
We have designed and successfully demonstrated a compact solenoid 3He neutron spin filter with a fast spin flip capability (CSF). The polarization loss in a single AFP spin flip was 0.02% and negligible small for almost any neutron scattering experiments. A single 3He spin flip took only 2.5 s that minimize time loss during the measurement. The CSF is compact and can easily be installed in neutron spectrometers as a neutron polarizer as well as a neutron spin analyzer. Unlike neutron spin flippers that change static or RF magnetic fields, the CSF does not change the magnetic fields and hence very small systematic uncertainties arise in spin-flip measurements. Or, they can be infinitely reduced by calibrations with AFP-NMR or by repeating the spin flip.
0.7
0.2 0.3 0.4 0.6 0.8 0.9
30 20
1
10 0 0
6. Future improvements A single AFP 3He spin flip took 2.5 s, but it can be shortened. The adiabatic condition in the
20
40
60 Z [mm]
Fig. 11. The calculation of the static magnetic field produced by the four parallel currents (Fig. 12). The magnitude of the field is normalized to unity at the center (X ¼ 0, Y ¼ 0, Z ¼ 0).
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
506
Y positive current
positive 25
solenoid bobbin (5 mm thick)
R=
60
47
X
47
25 negative
negative current
[mm]
Fig. 12. Four linear currents inside the CSF solenoid bobbin. A cross-sectional view of the four linear currents in parallel with the Z-axis (the solenoid axis) is drawn. The four currents are at the same magnitude and arranged at symmetric positions. All the current lengths are 500 mm (Z ¼ 250 to +250 mm).
a different electromagnet configuration. Fig. 11 shows a calculation of such a uniform field generated by four linear currents arranged as in Fig. 12. The field magnitude varies 10% in a cylindrical area with a diameter of 60 mm and a length over 200 mm. In addition to this requirement, the transverse gradient of the 3He spinholding magnetic field limits the maximum size of the 3He cell. As shown in Fig. 3, the transverse field gradient satisfies the condition of Eq. (1) or o104 (/cm) over a cylindrical area with a diameter of 80 mm and a length of 150 mm. Consequently, 3He cells as large as a cylinder with a diameter of 60 mm and a length of 150 mm can be used for the CSF with this modification. We note that the requirement on the field gradient of o104 (/cm) is rather tight for a practical 3He cell with a finite relaxation time, and thus a longer cell will fit the modified CSF. The magnetic field calculations suggest that the size of the CSF can be minimized according to that of a 3He cell. For instance, if one uses a cylindrical 3 He cell with a diameter of 30 mm and a length of
75 mm, the dimensions of the CSF can be reduced to 12—only 25 cm long and 6 cm in diameter. But still, the performance will be the same as the CSF we demonstrated. The CSF was designed to use an already polarized 3He cell, of which polarization gradually decreased with time by the spin relaxation, because it was not equipped with a heater or an oven for the optical-pumping. This was only limited by the temperature tolerances of the materials used in the CSF. Metallic materials were avoided for AFP. Fabricated with high-temperature plastics such as polyimide, polyphenylene sulfide, or polyetheretherketone, the CSF will be able to polarize 3He in-situ, and a stable polarized neutron beam will be possible.
Acknowledgment This work was supported in part by a Grant-inAid for Creative Scientific Research (No. 16GS0417) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References [1] W. Gavin Williams, Polarized Neutrons, Clarendon Press, Oxford, 1988. [2] K.P. Coulter, A.B. McDonald, W. Happer, T.E. Chupp, M.E. Wagshul, Nucl. Inst. and Meth. A 270 (1988) 90. [3] V.R. Skoy, Y. Masuda, S. Muto, T. Ino, G.N. Kim, J. Neutron Res. 13 (2005) 119. [4] G.L. Jones, J. Baker, W.C. Chen, B. Collett, J.A. Cowan, M.F. Dias, T.R. Gentile, C. Hoffmann, T. Koetzle, W.T. Lee, K. Littrell, M. Miller, A. Schultz, W.M. Snow, X. Tong, H. Yan, A. Yue, Physica B 356 (2005) 86. [5] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1961. [6] R.L. Gamblin, T.R. Carver, Phys. Rev. 138 (1965) A946. [7] L.D. Schearer, G.K. Walters, Phys. Rev. 139 (1965) A1398. [8] G.D. Cates, S.R. Schaefer, W. Happer, Phys. Rev. A 37 (1988) 2877. [9] T. Ino, S. Muto, Y. Masuda, G.N. Kim, V.R. Skoy, Physica B 356 (2005) 109. [10] M.A. Bouchiat, T.R. Carver, C.M. Varnum, Phys. Rev. Lett. 5 (1960) 373. [11] T.G. Walker, W. Happer, Rev. Mod. Phys. 69 (1997) 629.
Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506 www.elsevier.com/locate/nima
A compact solenoid 3He neutron spin filter with a fast spin flip capability Takashi Ino, Suguru Muto Neutron Science Laboratory, KEK, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan Received 22 March 2005; accepted 12 April 2005 Available online 13 June 2005
Abstract We have designed and demonstrated a compact solenoid 3He neutron spin filter with a fast spin flip capability. The He spin is flipped by adiabatic fast passage (AFP) in a short time and with very little polarization loss, which is essential for polarized neuron scattering measurements in cancellation of systematic errors. A solenoid coil and compensation coils provide a uniform magnetic field for the polarized 3He to minimize the longitudinal spin relaxation. This neutron spin filter can be installed rather easily in neutron scattering spectrometers as a neutron polarizer as well as a neutron spin analyzer. We describe the design and the performance of the device tested by AFP-NMR and with a pulsed neutron beam at KEK. r 2005 Elsevier B.V. All rights reserved. 3
PACS: 61.12.q; 75.25.+z; 29.25.Pj; 29.27.Hj Keywords: 3He polarization; Neutron spin filter; Polarized neutron; Neutron scattering; Adiabatic fast passage (AFP); Spallation neutron source
1. Introduction Polarized neutrons provide a powerful tool not only to study magnetism but also for researches on structure and dynamics of materials. Polarized neutrons are essential also in the fields of nuclear and particle physics. Neutrons can be polarized in Corresponding author. Tel.: +81 29 864 5619;
fax: +81 29 864 3202. E-mail address: [email protected] (T. Ino).
various ways. Polarizing crystal monochromators and polarizing supermirrors [1] are probably the most popular neutron polarizers today. The polarized gaseous 3He, however, attracts much attention as a neutron spin filter recently because of its broad energy coverage and large solid angle acceptance. The spin-dependent large neutron capture cross-section of the 3He nucleus enables one to filter out neutrons with certain spin directions from cold to epithermal energy ranges [2]. A large sold angle for divergent scattered
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.04.057
ARTICLE IN PRESS 500
T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
neutrons can be covered with polarized gaseous 3 He as a neutron spin analyzer. Such polarized 3He neutron spin filters (NSF) are of great interest at high flux steady-state and pulsed neutron sources. Particularly at pulsed neutron sources, the 3He NSF is required to be as small as possible because most neutron spectrometers are inside thick concrete radiation shielding and space for the NSF is limited. In addition, polarized neutron scattering instruments often require the neutron spin inversion to cancel out systematic uncertainties, and are equipped with static or radio frequency (RF) magnetic spin flippers [1]. These spin flippers, however, occupy some space and change magnetic fields depending on the neutron spin direction that usually introduces asymmetry for neutrons with opposite spins. On the other hand, small size 3He NSFs, which did not have a fast spin flip capability, were demonstrated by authors [3,4]. To meet both requirements, the compactness and the symmetric spin inversion of neutrons, we designed and demonstrated a compact solenoid 3He NSF with a fast spin flip capability (CSF). In the CSF, the 3He spin, which corresponds to that of neutrons, is inverted by adiabatic fast passage (AFP) [5] with very little polarization loss. The spin flip of 3He nuclei by AFP does not induce magnetic field changes, except when the spin is being reversed, and consequently no asymmetry arises in the spin inversion. In this article, we present the design and the performance of the CSF that can be used in various neutron scattering experiments.
the transverse component of the field gradient. To satisfy this requirement with keeping the size compact, we designed a solenoid coil with a pair of field compensation coils in symmetric positions at both edges of the solenoid. Fig. 1 shows the dimensions of the solenoid coil and the compensation coils. Enameled cupper wire of f 1.07 mm was wound in two layers on a cylindrical bobbin with a diameter of 120 mm and a length of 500 mm. The compensation coils were wound also in two layers with the same wire on the solenoid from both edges. The number of turns of each compensation coil was determined by calculations so that the magnetic field gradient around the solenoid center was minimized as well as all the coils were able to be connected in series and operated with one power supply. Magnetic field calculations for the solenoid coil with and without the compensation coils are illustrated in Figs. 2 and 3 as the transverse field gradient. The calculation for the solenoid coil with the compensation coils shows that the transverse field gradient satisfies o104(/cm) over the cylindrical area with a diameter of 80 mm and a length of 150 mm. A cylindrical 3He cell with an inner diameter of 24 mm and an inside length of 47 mm was placed at the solenoid center. A Helmholtz coil with a diameter of 94 mm was used to provide an RF field for AFP. It was set inside the solenoid coil at the center and positioned perpendicular to the solenoid axis. Each circular coil was wound 20 turns compensation coil (2 layers) solenoid coil (2 layers)
2. Design of the compact solenoid 3He neutron spin filter with a fast spin flip capability An inhomogeneous magnetic field contributes the spin relaxation of polarized gaseous 3He [6–8]. The transverse field gradient as low as qBT =qT 104 ð=cmÞ B0
(1)
is preferred to neglect the longitudinal spin relaxation for the polarized 3He nuclei. Here, B0 is the mean magnitude of the spin holding magnetic field for polarized 3He, and qBT =qT is
120 coil bobbin (t5) 500
Fig. 1. A cross-sectional view of the solenoid coil and the field compensation coils. The diameter of cylindrical bobbin is 120 mm, the length is 500 mm, and the thickness is 5 mm. Enameled cupper wire of f 1.07 mm was wound in two layers on the bobbin as a solenoid coil, and another two layers (37 turns+36 turns) were wound from each edge of the solenoid for compensation of the magnetic field.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
501
50 ∂B T
40
∂T
[/cm]
B0
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0013
0.0012
0.0011
0.001
0.0009
0.0008
0.0007
0.0006
0.0005
10
0.0003
0.0002
20
0.0004
0.0001
R [mm]
30
0 0
20
40
80
60
100
Z [mm]
Fig. 2. The calculation of transverse magnetic field gradient for the solenoid coil without the compensation coils is shown on the radial (R) vs. axial (Z) plain where (R ¼ 0, Z ¼ 0) is the center of the solenoid.
50 0.00015 0.0001
40
0
R [mm]
30 5e-05 20
-0.00035
-0.0003
-0.00025
[/cm]
-0.0002
B0
∂T
-0.0001
∂B T
10
-0.00015
-5e-05
0 0
20
40
60
80
Z [mm] Fig. 3. The calculation of transverse magnetic field gradient for the solenoid coil with the compensation coils.
100
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
502
with f 0.2 mm enameled cupper wire. The impedance of the Helmholtz coil was matched to that of the oscillator output with a matching circuit to maximize the RF emission at the resonance frequency of a pickup coil for AFPNMR. The pickup coil was made with f 0.1 mm wire wound 300 turns on a 38 mm diameter bobbin Y solenoid bobbin (5 mm thick)
Helmholtz coil
R=
60
3He
cell
X
and found to have its resonance frequency at 92.1 kHz without a resonant capacitor. The pickup coil was placed under the 3He cell perpendicularly to both the solenoid and the Helmholtz coil axes. A Larmor precession frequency of 92.1 kHz corresponds to a magnetic field of 2.84 mT for the 3He nucleus, and such field was produced by a current of 1.23 A flowed in the solenoid coil and the compensation coils. See Fig. 4 for a crosssectional view and a schematic drawing of the Helmholtz coil, the 3He cell and the pickup coil showing the arrangement inside the solenoid. The calculation of the static magnetic field generated by the Helmholtz coil is shown in Fig. 5. The actual RF field may differ from the static field calculation because of the presence of conductive materials nearby such as the solenoid coil and the pickup coil. The effect of such perturbations was found to be negligible for AFP as shown in the next section. Fig. 5 shows that the RF field amplitude within a radiuso28 mm, which sufficiently covers our 3He cell, is less than 710% and uniform enough for AFP. The field gradient,
[mm] 50
pickup coil
0.6
0.5
0.7 0.8
40
Helmholtz coil
1.5 1.8
0.9 1.2
1.6 1.9
X [mm]
1 30
20
28 mm
10
1.7 1.4 1.3
1.1 1
3
He cell
0.4
1.1 0 0
10
20 30 Z [mm]
40
50
pickup coil Fig. 4. The arrangement of the Helmholtz coil, the cylindrical 3 He cell, and the pickup coil inside the solenoid bobbin. The solenoid and the cylinder axis of the 3He cell coincide with that of the neutron beam. The cross-sectional view perpendicular to the solenoid axis is shown at the center.
Fig. 5. The calculation of the static magnetic field for the Helmholtz coil. The field amplitude was normalized to unity at the center of the coil (X ¼ 0, Z ¼ 0). The Z-axis corresponds to the solenoid axis, and the X-axis to that of the Helmholtz coil. The variation of field amplitude is less than 710% within the spherical area with a radius of 28 mm.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
3. AFP-NMR test The performance of the CSF was tested with polarized 3He nuclei by AFP-NMR. A sealed 3He cell was prepared [9] and polarized by the spinexchange optical pumping [10,11]. The polarized 3 He cell with a spin relaxation time of 70 h was, then, transported and set in the CSF for the test. The AFP parameters, the magnetic field sweep speed and the RF field magnitude, were studied by observing the depolarization of the 3He in 100 consecutive AFP-NMR measurements. The single measurement sequence consists of (1) turning on the RF field, (2) sweeping the spin-holding magnetic field up and down, and (3) turning off the RF field. Fig. 6 shows such depolarization in 100 continuous NMR measurements with the optimum AFP parameters. Considering a 1% spin relaxation during the period of the measurements, the polarization loss in a single AFP-NMR measurement was found only to be 0.04%. The polarization loss in the AFP 3He spin flip was also studied. A single AFP spin flip was accomplished by (1) turning on the RF field, (2) sweeping the spin-holding magnetic field up, (3) turning off the
AFP NMR Signal [mV]
Polarization loss in one measurement : 0.04%
6.7 AFP NMR Signal [mV]
however, may have contributed additional spin relaxation for the polarized 3He, and the RF field was always turned off except when required.
503
6.6 6.5 Polarization loss in one spin flip: 0.02%
0.0 -6.5 -6.6 -6.7 0
20
40
60
80
100
Flip Number
Fig. 7. Measurements of the 3He polarization loss in the AFP spin flip. The 3He spin was flipped 100 times. The AFP-NMR signal (dots) appeared in the opposite sign in each spin flip. From the exponential fit (solid curves), the polarization loss in a single spin flip was found to be 0.02%.
RF field, and (4) sweeping the spin-holding magnetic field down to the initial amplitude. The NMR measurements are shown in Fig. 7 for the depolarization in 100 spin flips with the same AFP parameters. The polarization loss in a single AFP spin flip was observed 12 of that in a single AFPNMR measurement as was expected. Note that a single AFP spin flip took only 2.5 s.
4. Neutron beam test The transmission T of neutrons with the polarization Pi for 3He with the polarization PHe , the number density r, and the thickness t can be written in the following expression:
6.15
T ¼ esrt ðcosh PHe srt Pi sinh PHe srtÞ
6.10
where s is the spin averaged neutron capture crosssection of the 3He nucleus. The sign between the two terms in Eq. (2) depends on the polarization directions of the initial neutrons and the 3He nuclei. If the initial neutrons are unpolarized (Pi ¼ 0), Eq. (2) is simplified to
6.05 6.00 5.95 5.90 0
20
40 60 Measurement Number 3
80
100
Fig. 6. The polarization loss of the He due to the AFP-NMR measurement. The depolarization was measured to be 5% in a series of AFP-NMR measurements for 100 times. Subtracting a spin relaxation of 1% during the period of the measurements, the polarization loss in a single AFP-NMR measurement was observed to be 0.04%. The dots are the measurements, and the solid curve is an exponential fit.
T ¼ esrt cosh PHe srt
(2)
(3)
and the polarization of the transmitted neutrons becomes P ¼ tanh PHe srt.
(4)
Eq. (4) can be rewritten with the neutron transmissions for unpolarized 3He ðPHe ¼ 0Þ and
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
for polarized 3He T ðPHe Þ as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ 1 ðT ðPHe ¼0Þ =T ðPHe Þ Þ2 .
(5)
From Eq. (2), one can determine the polarization of the initial neutrons by measuring the transmissions through polarized 3He. Taking the ratio of the transmissions with spin-antiparallel to spin-parallel gT , the initial neutron polarization can be presented as Pi ¼
1 gT coth PHe srt. 1 þ gT
(6)
We measured such neutron polarization as a test of the CSF. Two identical CSFs were prepared, one as a neutron polarizer and the other as a neutron spin analyzer. They were set on the H-8 beamline at the pulsed neutron source of KEK (KENS). See Fig. 8 for the experimental apparatus. The polarization of neutrons transmitted through CSF 1 was determined by the transmission ratio for CSF 2 with the 3He spin-flip and nonflip. The two CSFs were placed 70 cm apart from each center, making a gap of 20 cm between them. The solenoid coil with the compensation coils of each CSF was operated at the same current that provided a magnetic field strong enough to hold the neutron spin direction in the gap while causing minimal interference at the 3He cells. A fast scintillator neutron detector, located downstream the beamline, was used to count the transmitted neutrons. By taking the ratio of the neutron counts with the 3He spin-flip and nonflip, the transmission ratio gT was obtained. The measurements of neutrons with spin-antiparallel to 3He and spin-parallel were repeated at short intervals to minimize systematic uncertainties due neutron source (H2O moderator) CSF 2
CSF 1 50 cm collimator
70 cm
3
detector He cell
Fig. 8. The experimental setup of the CSF on the H-8 beamline at KENS. Transmitted neutrons were counted with a fast scintillation neutron detector. The two CSFs were 70 cm apart from each center, making a gap of 20 cm between them. The magnetic field in the gap was strong enough to hold the neutron spin direction but weak enough at each CSF center.
to the polarization loss by the AFP spin flip and the spin relaxation of the polarized 3He. The 3He gas density and thickness rt in the CSF 2 cell had been measured from the neutron transmission for the unpolarized 3He by following T ¼ esrt or PHe ¼ 0 in Eq. (3), where absorption of neutrons in the cell windows had been taken into account by the transmission for an empty cell with the same dimensions. The 3He polarization PHe was monitored by AFP-NMR of CSF 2 that had been calibrated with the neutron transmission in Eq. (3). Both rt and PHe were determined with accuracies better than 1%. Fig. 9 shows measurements of the neutron transmission ratios for the 3He in CSF 2 with spin-antiparallel to spin-parallel. It was evident that the incoming neutrons to CSF 2 had certain polarizations because the transmission ratios were measured to be less than unity. From the ratios, the polarizations of the neutrons were calculated by Eq. (6) and plotted in Fig. 10 as crosses. The polarizations of the neutrons transmitted through CSF 1 were also measured independently. Displaced CSF 2 from the beamline, the neutron transmissions for CSF 1 with the 3He polarized and unpolarized were measured. Following Eq. (5), the neutron polarizations were evaluated and plotted as circles in Fig. 10. Both measurements, gT and the transmissions for CSF 1, were performed in succession within two hours. The 3 He polarizations in CSF 1 and CSF 2 decreased by 3% during the measurements since the spin relaxation times of the two cells were 70 and 59 h, Neutron Transmission Ratio
504
1.0 0.8 0.6 0.4 0.2 0.0 0.01
2
3
4
5 6 7 8 9
2
0.1 Neutron Energy [eV]
3
4
5 6 7 8 9
1
Fig. 9. Neutron transmission ratios for the 3He in CSF 2 with spin-nonflip to spin-flip. Discrepancies of the ratios from unity verified spin polarization of the initial neutrons.
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
Neutron Polarization
1.0
spin flip is
Measurements by CSF 2 spin flip Measurements by CSF 1 transmission
1 dH 0 gH 1 H 1 dt
0.8 0.6 0.4 0.2 0.0 0.01
505
2
3
4
5 6 7 8 9
2
0.1 Neutron Energy [eV]
3
4
5 6 7 8 9
1
Fig. 10. Neutron polarizations measured by the transmission ratios for the 3He in CSF 2 with spin-noflip and spin-flip are shown as crosses. Another independent measurements by the neutron transmissions for CSF 1 are also plotted as circles. Error bars are statistical only.
respectively. The corresponding neutron polarizations changed by 2–3%, which were less than the statistical uncertainties, among the energies in Fig. 10. The polarizations of neutrons measured from the CSF 1 transmissions agreed well with those measured by gT for CSF 2 as seen in Fig. 10.
(7)
where the spin relaxation time is long enough to be neglected [5]. Here, g is the gyromagnetic ratio of the 3He nucleus, H 1 is a rotational component of the RF magnetic field, and dH 0 =dt is the sweep speed of the spin-holding field. The adiabatic condition can easily be satisfied for increased sweep speed dH 0 =dt with higher RF field H 1 . In our case, however, the polarization loss became larger when dH 0 =dt was increased with H 1 . It was probably limited by our DC power supply for the solenoid and compensation coils. The DC power supply must have become unstable due to the inductance of the CSF solenoid coil when dH 0 =dt was increased. With a proper power supply and control, the spin flipping time will be shortened significantly. We employed a Helmholtz coil for AFP to produce a uniform RF magnetic field that fitted the size of our 3He cells (Fig. 5), but a large uniform field to fit a larger cell can be formed with
5. Conclusions
X [mm]
50
0.7
40
0.8
30
0.9
20 10 0 0
20
40
60
80
100
80
100
Z [mm] 50 0.5
40 Y [mm]
We have designed and successfully demonstrated a compact solenoid 3He neutron spin filter with a fast spin flip capability (CSF). The polarization loss in a single AFP spin flip was 0.02% and negligible small for almost any neutron scattering experiments. A single 3He spin flip took only 2.5 s that minimize time loss during the measurement. The CSF is compact and can easily be installed in neutron spectrometers as a neutron polarizer as well as a neutron spin analyzer. Unlike neutron spin flippers that change static or RF magnetic fields, the CSF does not change the magnetic fields and hence very small systematic uncertainties arise in spin-flip measurements. Or, they can be infinitely reduced by calibrations with AFP-NMR or by repeating the spin flip.
0.7
0.2 0.3 0.4 0.6 0.8 0.9
30 20
1
10 0 0
6. Future improvements A single AFP 3He spin flip took 2.5 s, but it can be shortened. The adiabatic condition in the
20
40
60 Z [mm]
Fig. 11. The calculation of the static magnetic field produced by the four parallel currents (Fig. 12). The magnitude of the field is normalized to unity at the center (X ¼ 0, Y ¼ 0, Z ¼ 0).
ARTICLE IN PRESS T. Ino, S. Muto / Nuclear Instruments and Methods in Physics Research A 548 (2005) 499–506
506
Y positive current
positive 25
solenoid bobbin (5 mm thick)
R=
60
47
X
47
25 negative
negative current
[mm]
Fig. 12. Four linear currents inside the CSF solenoid bobbin. A cross-sectional view of the four linear currents in parallel with the Z-axis (the solenoid axis) is drawn. The four currents are at the same magnitude and arranged at symmetric positions. All the current lengths are 500 mm (Z ¼ 250 to +250 mm).
a different electromagnet configuration. Fig. 11 shows a calculation of such a uniform field generated by four linear currents arranged as in Fig. 12. The field magnitude varies 10% in a cylindrical area with a diameter of 60 mm and a length over 200 mm. In addition to this requirement, the transverse gradient of the 3He spinholding magnetic field limits the maximum size of the 3He cell. As shown in Fig. 3, the transverse field gradient satisfies the condition of Eq. (1) or o104 (/cm) over a cylindrical area with a diameter of 80 mm and a length of 150 mm. Consequently, 3He cells as large as a cylinder with a diameter of 60 mm and a length of 150 mm can be used for the CSF with this modification. We note that the requirement on the field gradient of o104 (/cm) is rather tight for a practical 3He cell with a finite relaxation time, and thus a longer cell will fit the modified CSF. The magnetic field calculations suggest that the size of the CSF can be minimized according to that of a 3He cell. For instance, if one uses a cylindrical 3 He cell with a diameter of 30 mm and a length of
75 mm, the dimensions of the CSF can be reduced to 12—only 25 cm long and 6 cm in diameter. But still, the performance will be the same as the CSF we demonstrated. The CSF was designed to use an already polarized 3He cell, of which polarization gradually decreased with time by the spin relaxation, because it was not equipped with a heater or an oven for the optical-pumping. This was only limited by the temperature tolerances of the materials used in the CSF. Metallic materials were avoided for AFP. Fabricated with high-temperature plastics such as polyimide, polyphenylene sulfide, or polyetheretherketone, the CSF will be able to polarize 3He in-situ, and a stable polarized neutron beam will be possible.
Acknowledgment This work was supported in part by a Grant-inAid for Creative Scientific Research (No. 16GS0417) from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
References [1] W. Gavin Williams, Polarized Neutrons, Clarendon Press, Oxford, 1988. [2] K.P. Coulter, A.B. McDonald, W. Happer, T.E. Chupp, M.E. Wagshul, Nucl. Inst. and Meth. A 270 (1988) 90. [3] V.R. Skoy, Y. Masuda, S. Muto, T. Ino, G.N. Kim, J. Neutron Res. 13 (2005) 119. [4] G.L. Jones, J. Baker, W.C. Chen, B. Collett, J.A. Cowan, M.F. Dias, T.R. Gentile, C. Hoffmann, T. Koetzle, W.T. Lee, K. Littrell, M. Miller, A. Schultz, W.M. Snow, X. Tong, H. Yan, A. Yue, Physica B 356 (2005) 86. [5] A. Abragam, Principles of Nuclear Magnetism, Oxford University Press, Oxford, 1961. [6] R.L. Gamblin, T.R. Carver, Phys. Rev. 138 (1965) A946. [7] L.D. Schearer, G.K. Walters, Phys. Rev. 139 (1965) A1398. [8] G.D. Cates, S.R. Schaefer, W. Happer, Phys. Rev. A 37 (1988) 2877. [9] T. Ino, S. Muto, Y. Masuda, G.N. Kim, V.R. Skoy, Physica B 356 (2005) 109. [10] M.A. Bouchiat, T.R. Carver, C.M. Varnum, Phys. Rev. Lett. 5 (1960) 373. [11] T.G. Walker, W. Happer, Rev. Mod. Phys. 69 (1997) 629.