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A compact neutron Ramsey resonance apparatus for polarised neutron radiography
ARTICLE IN PRESS Nuclear Instruments and Methods in Physics Research A 605 (2009) 5–8
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
A compact neutron Ramsey resonance apparatus for polarised neutron radiography F.M. Piegsa a,b,, B. van den Brandt a, P. Hautle a, J.A. Konter a a b
Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland ¨ nchen, D-85748 Garching, Germany Physics Department, Technische Univ. Mu
a r t i c l e in fo
abstract
Available online 5 February 2009
A compact apparatus to perform polarised neutron radiography on macroscopic objects is presented. Its working principle, based on Ramsey’s resonance technique, allows to observe interactions between neutron spins and magnetic fields. Despite its shortness of only 480 mm, the magnetic field homogeneity allows for large beam cross-sections of up to 20 20 mm2. The applied magnetic field at the sample position is variable and can be tuned from about 4 to almost 32 mT without violating the Ramsey resonance condition. The performance of the apparatus is demonstrated in systematic tests, which show a phase stability of 1 degree and a sensitivity of about 7.5 108 Tm. & 2009 Elsevier B.V. All rights reserved.
Keywords: Neutron physics Ramsey resonance technique Neutron radiography
1. Introduction Ramsey’s technique of separated oscillating fields is a method sensitive to spin-dependent interactions of particles with external fields, detected as a spin precession angle j [1,2]. This technique adapted to neutrons can be employed to observe interactions between neutron spins and magnetic or pseudomagnetic fields, i.e. spin-dependent interaction with polarised nuclei [3–5]. A neutron Ramsey apparatus1 consists ideally of a homogeneous steady magnetic field B0 where the spins of a well-collimated and monochromatic polarised neutron beam get non-adiabatically flipped twice by 901 by two superimposed phase-locked fields oscillating perpendicularly to B0 with the angular frequency o (p/ 2-spin flippers). Between the spin-flips the neutron spins precess freely in the plane perpendicular to the steady field and get analysed by a neutron spin filter behind the second p/2-spin flipper. To ensure that the neutron spins precess on average in phase with the oscillating fields the so-called Ramsey resonance condition must be fulfilled, saying that the average steady magnetic field along the neutron flight path between the p/2-spin flippers must be equal to the field at the position of the oscillating fields. This implies that the steady magnetic field does not necessarily need to be homogeneous. Successive scanning of the angular frequency o close to the neutron Larmor frequency o0 ¼ gnB0, where gn is the gyromagnetic ratio of the neutron, results in a sinusoidal intensity oscillation
Corresponding author at: Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland. Tel.: +41 56 310 5395; fax: +41 56 310 3718. E-mail address: fl[email protected] (F.M. Piegsa). 1 A theoretical description of a Ramsey apparatus can be found in Ref. [5,6].
0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.01.161
(Ramsey pattern). Any additional precession angle j of the neutron spins between the p/2-spin flippers can be measured as an equally sized phase shift of the Ramsey pattern modulo 3601. As originally proposed in Ref. [7] the combination of a Ramsey apparatus with a standard neutron radiography setup makes it possible to take two-dimensional images of magnetic and pseudomagnetic fields, e.g. produced by ferromagnetic materials or samples containing polarised nuclear spins (neutron spin phase imaging). The here presented compact Ramsey apparatus was designed to further explore the possibilities of this novel method.
2. The Ramsey apparatus A scheme of the 480 mm long Ramsey apparatus is presented in Figs. 1 and 2. The setup consists of two 4 mm-thick ferromagnetic steel plates (a), which are connected at every corner by four blocks, each assembled from two NdFeB/N35 permanent magnets2 (b) and a sandwiched ferromagnetic steel block (c). Each steel block is wound with a coil of 3 50 windings of 0.7 mm diameter copper wire, which can be used to trim the magnetic field produced by the permanent magnets. This yields a mean magnetic field of about 18 mT, corresponding to a neutron Larmor frequency of about 530 kHz, in the centre of the 100 480 65 mm3 volume. The magnetic field strength in z-direction along the neutron flight path has been measured and is plotted in Fig. 3. It shows a plateau of B0 ¼ (17.9470.04) mT from y ¼ 180 to 300 mm, where the neutron spin precession takes place. Due to the trimming, the field at both ends of the apparatus 2
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Fig. 1. Scheme of the Ramsey apparatus with the monochromatic polarised neutron beam (n) coming from the left. (a) ferromagnetic steel plates (100 480 4 mm3), (b) permanent magnet blocks (15 40 8 mm3), (c) ferromagnetic steel blocks (12 40 49 mm3) wound with copper wire serving as trim coils, (d) neutron polarisation analyser, (e) radio frequency p/2-spin flippers, (f) split pair coil (compensation coil), (g) split pair coil (sample coil), (h) 4 20 mm2 slit for sample positioning and (k) copper tubes with cooling water soldered on copper plates, which are thermally anchored to the steel plates. Drawing is not to scale.
Fig. 3. Plot of the magnetic field strength in z-direction along the neutron flight path in the centre of the volume enclosed by the steel plates. The field was determined for different currents in the sample coil and the compensation coil: Is ¼ Ic ¼ 0 A (filled circles), Is ¼ Ic ¼ 2 A (white circles), Is ¼ Ic ¼ +1 A (filled triangles) and Is ¼ Ic ¼ +3 A (white triangles). The vertical dashed line at y ¼ 260 mm marks the sample site. The two 10 mm-thick p/2-spin flippers can be freely positioned at y ¼ 180–190 mm and y ¼ 290–300 mm, respectively. For the measurement a vector field probe connected to a LakeShore 460 3-channel gaussmeter was used. The magnetic field was scanned in steps of 10 mm.
Fig. 2. Photograph of the Ramsey apparatus.
diverges from the field in the plateau region. But this does not harm the functionality of the Ramsey apparatus, as there the field only serves as a holding field for the neutron polarisation and the magnetisation of the remanent transmission spin analysing device3 (d), respectively. The two radio frequency p/2-spin flippers (e) are 24 10 23 mm3 box-shaped coils, which are wound on a Teflon body with a 20 20 mm2 window for neutrons. Each coil consists of 9 turns of a 0.3 mm diameter bare copper wire with a pitch of 3 mm and produces a linear oscillating field along the x-axis. They are connected in series and form the inductance of a matched resonant circuit for frequencies around 790 kHz. The circuit is driven far off resonance by a signal generator and a 250 W power amplifier at about 550 kHz to profit from the almost flat power absorption spectra of the circuit in the operating frequency range.4 The distance between the p/2-spin flippers can be adjusted between 100 and 120 mm to optimise for the Ramsey resonance condition. To apply magnetic fields on a sample, which differ from the field provided by the permanent magnets, it is necessary to compensate the additional field integral along the neutron flight path by a compensation coil to fulfill the Ramsey condition. The compensation coil (f) and the sample coil (g) are two identical rectangular split pair coils consisting each of 2 150 windings of 0.7 mm diameter copper wire wound on an aluminium body. The cross-sections of the windings have a size of 15 7.5 mm2 and are vertically separated by a 20 mm distance, which allows for a
20 20 mm2 neutron beam window. Each coil produces a magnetic field with a strength5 of about 4.4 mT/A along the z-axis. In the following the convention is used, that a positive (negative) current in the coil strengthens (weakens) the steady field produced by the permanent magnets. During the normal operation of the Ramsey apparatus the polarities of the applied voltages are chosen such that the fields are pointing antiparallel to each other, as presented in Fig. 3. Furthermore, the plot shows that the magnetic field at the position of the p/2-spin flippers stays almost constant, while the sample field can be chosen freely over a large range. Hence, the field at the sample position (h) can be varied from about 4 up to 32 mT. In principle lower or higher fields can be achieved but produce depolarisation at the edges of the neutron beam, as the magnetic field direction inverts due to the stronger field close to the coil windings. On the other hand, a short-time inversion of the magnetic field above the coercivity over the whole sample size can be used to demagnetise ferromagnetic samples. A picture of the Ramsey apparatus is given in Fig. 2 showing the meandering water cooling tubes (k) soldered on copper plates. They stabilise the temperature of the setup to 20 1C and avoid unwanted phase drifts of the neutron spins and the Ramsey patterns due to thermal expansions.
3. Systematic performance tests The performance of the Ramsey apparatus has been tested with the cold polarised neutron reflectometer Narziss at the spallation neutron source SINQ at the Paul Scherrer Institute. The monochromator of the reflectometer provides a neutron beam with a wavelength spectrum which peaks at l0 ¼ 5 A˚ and has a width Dl/l0 of 1.5%. The beam size is restricted by two cadmium diaphragms in front of the apparatus, with rectangular holes of 1 mm width, 5 mm height and a distance of 725 mm between each
3
For a detailed description of the device see Ref. [8]. The forward and reflected power of the amplifier are 125 and 113 W, respectively, which yields an absorbed rf-power of about 12 W for both p/2-spin flippers. 4
5 This field strength was measured in the center of the neutron beam window, with the coils placed between the ferromagnetic steel plates.
ARTICLE IN PRESS F.M. Piegsa et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 5–8
Fig. 4. Scan of the neutron count rate as a function of the p/2-spin flipper frequency, with Is ¼ Ic ¼ 0 A. The envelope of the resonance is plotted as a dashed curve.
Fig. 5. Demonstration of the phase stability of the Ramsey apparatus with Is ¼ Ic ¼ +2 A, which corresponds to a field at the sample position of about 27.5 mT. The mean value of the neutron spin phase angle has been arbitrarily set to 01. The standard deviation (thin horizontal lines) is 71.01, with a mean length of the statistical error bars of the individual measurements of 70.81.
other. The collimation behind the sample only restricts the height of the neutron beam (also 5 mm), but not its width. Fig. 4 shows a typical Ramsey pattern obtained with the setup, by successively scanning the p/2-spin flipper frequency in steps of 1 kHz. Its period Df of about 7 kHz is in agreement with the theoretically expected value [5]. The dip of the envelope of the resonance signal at about 540 kHz is caused by the fringe fields of the p/2-spin flipper coils.6 To reduce measurement time and to achieve a good signal-to-noise ratio the frequency scans are typically restricted to the region close to 560 kHz and to only 11 points (from 555 to 565 kHz). These excerpts of the complete Ramsey pattern are then fitted with a sinusoidal function, from which a phase angle is obtained (neutron spin phase angle). To test the stability of the apparatus we repeatedly performed such Ramsey frequency scans and determined the phase angle, while keeping the magnetic field constant. The result of a longterm measurement over 3.5 h, which is much longer than typical exposure times in neutron imaging, is shown in Fig. 5. This
6 This was confirmed by quantum mechanical simulations of our Ramsey apparatus using time-evolution operators.
7
Fig. 6. Test of reproducibility of the neutron spin phase by simultaneously changing the currents in the sample and the compensation coil every 30 min. One cycle consists of five magnetic field changes at the sample position: 2.5, 11.5, 18.5, 25.5 and 34.5 mT, which correspond to the following mean neutron spin phase angles: 731, 351, 01, 451 and 1321. The mean length of the error bars is approximately 721.
Fig. 7. Neutron counts at a fixed p/2-spin flipper frequency of 560 kHz as a function of the sample coil current. The plotted line describes a sinusoidal fit through the measured points with a period of (227.370.2) mA, which corresponds to an additional neutron spin precession of (1583.871.4)1/A.
delivers a phase stability of about 71.01 for 5 A˚ neutrons. The sensitivity of a Ramsey apparatus can be described as the minimal magnetic field path integral, which is still detectable due to the limited phase stability. In our case this yields a sensitivity of 77.5 108 Tm. Another important property of the apparatus is demonstrated in Fig. 6, which describes how well the initial value of the neutron spin phase angle is reproduced, after the magnetic field at the sample position has been varied. It is checked by periodically changing the current through the sample and the compensation coil, while Ramsey frequency scans are taken continuously. The changes in the coil currents (Is ¼ Ic ¼ 3.5, 1.5, 0, +1.5 and +3.5 A) are clearly visible as jumps in the phase angle. This is due to the fact that the two coils are not perfectly identical and therefore deliver slightly different magnetic fields at equal currents. The effect can in principle be canceled by a corresponding correction of the compensation coil current.7 The
7
Here the correction would have been on the level of about 2%.
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F.M. Piegsa et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 5–8
Fig. 8. Left: absorption image of a coil with 6 windings, a length of about 7 mm and an inner diameter of 3 mm made of 0.8 mm-thick copper wire. Right: Neutron spin phase image of the magnetic field produced by this coil using a current of 3 A. The calibration bar gives the phase shift in degrees. Neutrons with a wavelength of l0 ¼ 6 A˚ and Dl/ l0 ¼ 10% have been used. Both images have a size of about 20 20 mm2, which corresponds to 150 150 pixels of the employed neutron camera [10].
reproducibility over 8 h was in average 731 and is therefore slightly larger than the stability. This is caused by the hysteresis of the two steel plates, which enclose the apparatus at the bottom and the top. Hence, the use of ferromagnetic materials should be reduced as much as possible in future setups. As a test of the functionality the neutron count rate at a fixed p/2-spin flipper frequency is measured for different currents in the sample coil (see Fig. 7). As expected the number of detected neutrons oscillates with the accumulated neutron spin precession due to the additional magnetic field. A broader wavelength spectrum causes a smearing of the Ramsey pattern and therefore leads to a decrease in the signal-to-noise ratio. Therefore the relative width of the wavelength distribution restricts the precession angle to a practical limit of approximately 1801 l0/Dl. Hence, the wavelength l0 and the width of the spectrum have to be chosen correctly in relation to the sample thickness and the expected additional spin precession.
4. Outlook The Ramsey apparatus presented here is optimised to perform polarised neutron radiography, i.e. neutron spin phase imaging. Its compact design makes it easily integratable into existing imaging beam lines. The shortness reduces the sample–detector distance to approximately 20 cm so that sub-millimeter resolution can be achieved without having a sophisticated beam collimation.
An illustration of the capability of the apparatus is presented in Fig. 8 showing an image of the neutron spin phase shift caused by the magnetic field of a small coil. The phase shift of maximum 1651 in the center of the coil agrees well with the expected value of (156715)1 (neglecting the fringe fields), calculated using Eq. (1) in Ref. [7]. Further results and images of ferromagnetic samples using this apparatus taken at the small angle neutron scattering facility SANS-I [9] at the Paul Scherrer Institute will be published shortly. References [1] N. Ramsey, Phys. Rev. 78 (1950) 695. [2] N. Ramsey, Molecular Beams, Oxford University Press, Oxford, 1956. [3] A. Abragam, M. Goldman, Nuclear Magnetism: Order and Disorder, Oxford University Press, Oxford, 1982. [4] H. Gla¨ttli, M. Goldman, Methods of Experimental Physics, vol. 23, part C, Academic Press, New York, 1987, pp. 241–286. [5] F.M. Piegsa, B. van den Brandt, H. Gla¨ttli, P. Hautle, J. Kohlbrecher, J.A. Konter, B.S. Schlimme, O. Zimmer, Nucl. Instr. and Meth. A 589 (2008) 318. [6] R. Golub, R. Ga¨hler, T. Keller, Am. J. Phys. 62 (1994) 779. [7] F.M. Piegsa, B. van den Brandt, P. Hautle, J.A. Konter, Nucl. Instr. and Meth. A 586 (2008) 15. [8] F.M. Piegsa, M. Schneider, Nucl. Instr. and Meth. A 594 (2008) 74. [9] V.K. Aswal, B. van den Brandt, P. Hautle, J. Kohlbrecher, J.A. Konter, A. Michels, F.M. Piegsa, J. Stahn, O. Zimmer, Nucl. Instr. and Meth. A 586 (2008) 86. [10] M.J. Mu¨hlbauer, E. Calzada, B. Schillinger, Nucl. Instr. and Meth. A 542 (2005) 324.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research A journal homepage: www.elsevier.com/locate/nima
A compact neutron Ramsey resonance apparatus for polarised neutron radiography F.M. Piegsa a,b,, B. van den Brandt a, P. Hautle a, J.A. Konter a a b
Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland ¨ nchen, D-85748 Garching, Germany Physics Department, Technische Univ. Mu
a r t i c l e in fo
abstract
Available online 5 February 2009
A compact apparatus to perform polarised neutron radiography on macroscopic objects is presented. Its working principle, based on Ramsey’s resonance technique, allows to observe interactions between neutron spins and magnetic fields. Despite its shortness of only 480 mm, the magnetic field homogeneity allows for large beam cross-sections of up to 20 20 mm2. The applied magnetic field at the sample position is variable and can be tuned from about 4 to almost 32 mT without violating the Ramsey resonance condition. The performance of the apparatus is demonstrated in systematic tests, which show a phase stability of 1 degree and a sensitivity of about 7.5 108 Tm. & 2009 Elsevier B.V. All rights reserved.
Keywords: Neutron physics Ramsey resonance technique Neutron radiography
1. Introduction Ramsey’s technique of separated oscillating fields is a method sensitive to spin-dependent interactions of particles with external fields, detected as a spin precession angle j [1,2]. This technique adapted to neutrons can be employed to observe interactions between neutron spins and magnetic or pseudomagnetic fields, i.e. spin-dependent interaction with polarised nuclei [3–5]. A neutron Ramsey apparatus1 consists ideally of a homogeneous steady magnetic field B0 where the spins of a well-collimated and monochromatic polarised neutron beam get non-adiabatically flipped twice by 901 by two superimposed phase-locked fields oscillating perpendicularly to B0 with the angular frequency o (p/ 2-spin flippers). Between the spin-flips the neutron spins precess freely in the plane perpendicular to the steady field and get analysed by a neutron spin filter behind the second p/2-spin flipper. To ensure that the neutron spins precess on average in phase with the oscillating fields the so-called Ramsey resonance condition must be fulfilled, saying that the average steady magnetic field along the neutron flight path between the p/2-spin flippers must be equal to the field at the position of the oscillating fields. This implies that the steady magnetic field does not necessarily need to be homogeneous. Successive scanning of the angular frequency o close to the neutron Larmor frequency o0 ¼ gnB0, where gn is the gyromagnetic ratio of the neutron, results in a sinusoidal intensity oscillation
Corresponding author at: Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland. Tel.: +41 56 310 5395; fax: +41 56 310 3718. E-mail address: fl[email protected] (F.M. Piegsa). 1 A theoretical description of a Ramsey apparatus can be found in Ref. [5,6].
0168-9002/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2009.01.161
(Ramsey pattern). Any additional precession angle j of the neutron spins between the p/2-spin flippers can be measured as an equally sized phase shift of the Ramsey pattern modulo 3601. As originally proposed in Ref. [7] the combination of a Ramsey apparatus with a standard neutron radiography setup makes it possible to take two-dimensional images of magnetic and pseudomagnetic fields, e.g. produced by ferromagnetic materials or samples containing polarised nuclear spins (neutron spin phase imaging). The here presented compact Ramsey apparatus was designed to further explore the possibilities of this novel method.
2. The Ramsey apparatus A scheme of the 480 mm long Ramsey apparatus is presented in Figs. 1 and 2. The setup consists of two 4 mm-thick ferromagnetic steel plates (a), which are connected at every corner by four blocks, each assembled from two NdFeB/N35 permanent magnets2 (b) and a sandwiched ferromagnetic steel block (c). Each steel block is wound with a coil of 3 50 windings of 0.7 mm diameter copper wire, which can be used to trim the magnetic field produced by the permanent magnets. This yields a mean magnetic field of about 18 mT, corresponding to a neutron Larmor frequency of about 530 kHz, in the centre of the 100 480 65 mm3 volume. The magnetic field strength in z-direction along the neutron flight path has been measured and is plotted in Fig. 3. It shows a plateau of B0 ¼ (17.9470.04) mT from y ¼ 180 to 300 mm, where the neutron spin precession takes place. Due to the trimming, the field at both ends of the apparatus 2
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Fig. 1. Scheme of the Ramsey apparatus with the monochromatic polarised neutron beam (n) coming from the left. (a) ferromagnetic steel plates (100 480 4 mm3), (b) permanent magnet blocks (15 40 8 mm3), (c) ferromagnetic steel blocks (12 40 49 mm3) wound with copper wire serving as trim coils, (d) neutron polarisation analyser, (e) radio frequency p/2-spin flippers, (f) split pair coil (compensation coil), (g) split pair coil (sample coil), (h) 4 20 mm2 slit for sample positioning and (k) copper tubes with cooling water soldered on copper plates, which are thermally anchored to the steel plates. Drawing is not to scale.
Fig. 3. Plot of the magnetic field strength in z-direction along the neutron flight path in the centre of the volume enclosed by the steel plates. The field was determined for different currents in the sample coil and the compensation coil: Is ¼ Ic ¼ 0 A (filled circles), Is ¼ Ic ¼ 2 A (white circles), Is ¼ Ic ¼ +1 A (filled triangles) and Is ¼ Ic ¼ +3 A (white triangles). The vertical dashed line at y ¼ 260 mm marks the sample site. The two 10 mm-thick p/2-spin flippers can be freely positioned at y ¼ 180–190 mm and y ¼ 290–300 mm, respectively. For the measurement a vector field probe connected to a LakeShore 460 3-channel gaussmeter was used. The magnetic field was scanned in steps of 10 mm.
Fig. 2. Photograph of the Ramsey apparatus.
diverges from the field in the plateau region. But this does not harm the functionality of the Ramsey apparatus, as there the field only serves as a holding field for the neutron polarisation and the magnetisation of the remanent transmission spin analysing device3 (d), respectively. The two radio frequency p/2-spin flippers (e) are 24 10 23 mm3 box-shaped coils, which are wound on a Teflon body with a 20 20 mm2 window for neutrons. Each coil consists of 9 turns of a 0.3 mm diameter bare copper wire with a pitch of 3 mm and produces a linear oscillating field along the x-axis. They are connected in series and form the inductance of a matched resonant circuit for frequencies around 790 kHz. The circuit is driven far off resonance by a signal generator and a 250 W power amplifier at about 550 kHz to profit from the almost flat power absorption spectra of the circuit in the operating frequency range.4 The distance between the p/2-spin flippers can be adjusted between 100 and 120 mm to optimise for the Ramsey resonance condition. To apply magnetic fields on a sample, which differ from the field provided by the permanent magnets, it is necessary to compensate the additional field integral along the neutron flight path by a compensation coil to fulfill the Ramsey condition. The compensation coil (f) and the sample coil (g) are two identical rectangular split pair coils consisting each of 2 150 windings of 0.7 mm diameter copper wire wound on an aluminium body. The cross-sections of the windings have a size of 15 7.5 mm2 and are vertically separated by a 20 mm distance, which allows for a
20 20 mm2 neutron beam window. Each coil produces a magnetic field with a strength5 of about 4.4 mT/A along the z-axis. In the following the convention is used, that a positive (negative) current in the coil strengthens (weakens) the steady field produced by the permanent magnets. During the normal operation of the Ramsey apparatus the polarities of the applied voltages are chosen such that the fields are pointing antiparallel to each other, as presented in Fig. 3. Furthermore, the plot shows that the magnetic field at the position of the p/2-spin flippers stays almost constant, while the sample field can be chosen freely over a large range. Hence, the field at the sample position (h) can be varied from about 4 up to 32 mT. In principle lower or higher fields can be achieved but produce depolarisation at the edges of the neutron beam, as the magnetic field direction inverts due to the stronger field close to the coil windings. On the other hand, a short-time inversion of the magnetic field above the coercivity over the whole sample size can be used to demagnetise ferromagnetic samples. A picture of the Ramsey apparatus is given in Fig. 2 showing the meandering water cooling tubes (k) soldered on copper plates. They stabilise the temperature of the setup to 20 1C and avoid unwanted phase drifts of the neutron spins and the Ramsey patterns due to thermal expansions.
3. Systematic performance tests The performance of the Ramsey apparatus has been tested with the cold polarised neutron reflectometer Narziss at the spallation neutron source SINQ at the Paul Scherrer Institute. The monochromator of the reflectometer provides a neutron beam with a wavelength spectrum which peaks at l0 ¼ 5 A˚ and has a width Dl/l0 of 1.5%. The beam size is restricted by two cadmium diaphragms in front of the apparatus, with rectangular holes of 1 mm width, 5 mm height and a distance of 725 mm between each
3
For a detailed description of the device see Ref. [8]. The forward and reflected power of the amplifier are 125 and 113 W, respectively, which yields an absorbed rf-power of about 12 W for both p/2-spin flippers. 4
5 This field strength was measured in the center of the neutron beam window, with the coils placed between the ferromagnetic steel plates.
ARTICLE IN PRESS F.M. Piegsa et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 5–8
Fig. 4. Scan of the neutron count rate as a function of the p/2-spin flipper frequency, with Is ¼ Ic ¼ 0 A. The envelope of the resonance is plotted as a dashed curve.
Fig. 5. Demonstration of the phase stability of the Ramsey apparatus with Is ¼ Ic ¼ +2 A, which corresponds to a field at the sample position of about 27.5 mT. The mean value of the neutron spin phase angle has been arbitrarily set to 01. The standard deviation (thin horizontal lines) is 71.01, with a mean length of the statistical error bars of the individual measurements of 70.81.
other. The collimation behind the sample only restricts the height of the neutron beam (also 5 mm), but not its width. Fig. 4 shows a typical Ramsey pattern obtained with the setup, by successively scanning the p/2-spin flipper frequency in steps of 1 kHz. Its period Df of about 7 kHz is in agreement with the theoretically expected value [5]. The dip of the envelope of the resonance signal at about 540 kHz is caused by the fringe fields of the p/2-spin flipper coils.6 To reduce measurement time and to achieve a good signal-to-noise ratio the frequency scans are typically restricted to the region close to 560 kHz and to only 11 points (from 555 to 565 kHz). These excerpts of the complete Ramsey pattern are then fitted with a sinusoidal function, from which a phase angle is obtained (neutron spin phase angle). To test the stability of the apparatus we repeatedly performed such Ramsey frequency scans and determined the phase angle, while keeping the magnetic field constant. The result of a longterm measurement over 3.5 h, which is much longer than typical exposure times in neutron imaging, is shown in Fig. 5. This
6 This was confirmed by quantum mechanical simulations of our Ramsey apparatus using time-evolution operators.
7
Fig. 6. Test of reproducibility of the neutron spin phase by simultaneously changing the currents in the sample and the compensation coil every 30 min. One cycle consists of five magnetic field changes at the sample position: 2.5, 11.5, 18.5, 25.5 and 34.5 mT, which correspond to the following mean neutron spin phase angles: 731, 351, 01, 451 and 1321. The mean length of the error bars is approximately 721.
Fig. 7. Neutron counts at a fixed p/2-spin flipper frequency of 560 kHz as a function of the sample coil current. The plotted line describes a sinusoidal fit through the measured points with a period of (227.370.2) mA, which corresponds to an additional neutron spin precession of (1583.871.4)1/A.
delivers a phase stability of about 71.01 for 5 A˚ neutrons. The sensitivity of a Ramsey apparatus can be described as the minimal magnetic field path integral, which is still detectable due to the limited phase stability. In our case this yields a sensitivity of 77.5 108 Tm. Another important property of the apparatus is demonstrated in Fig. 6, which describes how well the initial value of the neutron spin phase angle is reproduced, after the magnetic field at the sample position has been varied. It is checked by periodically changing the current through the sample and the compensation coil, while Ramsey frequency scans are taken continuously. The changes in the coil currents (Is ¼ Ic ¼ 3.5, 1.5, 0, +1.5 and +3.5 A) are clearly visible as jumps in the phase angle. This is due to the fact that the two coils are not perfectly identical and therefore deliver slightly different magnetic fields at equal currents. The effect can in principle be canceled by a corresponding correction of the compensation coil current.7 The
7
Here the correction would have been on the level of about 2%.
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F.M. Piegsa et al. / Nuclear Instruments and Methods in Physics Research A 605 (2009) 5–8
Fig. 8. Left: absorption image of a coil with 6 windings, a length of about 7 mm and an inner diameter of 3 mm made of 0.8 mm-thick copper wire. Right: Neutron spin phase image of the magnetic field produced by this coil using a current of 3 A. The calibration bar gives the phase shift in degrees. Neutrons with a wavelength of l0 ¼ 6 A˚ and Dl/ l0 ¼ 10% have been used. Both images have a size of about 20 20 mm2, which corresponds to 150 150 pixels of the employed neutron camera [10].
reproducibility over 8 h was in average 731 and is therefore slightly larger than the stability. This is caused by the hysteresis of the two steel plates, which enclose the apparatus at the bottom and the top. Hence, the use of ferromagnetic materials should be reduced as much as possible in future setups. As a test of the functionality the neutron count rate at a fixed p/2-spin flipper frequency is measured for different currents in the sample coil (see Fig. 7). As expected the number of detected neutrons oscillates with the accumulated neutron spin precession due to the additional magnetic field. A broader wavelength spectrum causes a smearing of the Ramsey pattern and therefore leads to a decrease in the signal-to-noise ratio. Therefore the relative width of the wavelength distribution restricts the precession angle to a practical limit of approximately 1801 l0/Dl. Hence, the wavelength l0 and the width of the spectrum have to be chosen correctly in relation to the sample thickness and the expected additional spin precession.
4. Outlook The Ramsey apparatus presented here is optimised to perform polarised neutron radiography, i.e. neutron spin phase imaging. Its compact design makes it easily integratable into existing imaging beam lines. The shortness reduces the sample–detector distance to approximately 20 cm so that sub-millimeter resolution can be achieved without having a sophisticated beam collimation.
An illustration of the capability of the apparatus is presented in Fig. 8 showing an image of the neutron spin phase shift caused by the magnetic field of a small coil. The phase shift of maximum 1651 in the center of the coil agrees well with the expected value of (156715)1 (neglecting the fringe fields), calculated using Eq. (1) in Ref. [7]. Further results and images of ferromagnetic samples using this apparatus taken at the small angle neutron scattering facility SANS-I [9] at the Paul Scherrer Institute will be published shortly. References [1] N. Ramsey, Phys. Rev. 78 (1950) 695. [2] N. Ramsey, Molecular Beams, Oxford University Press, Oxford, 1956. [3] A. Abragam, M. Goldman, Nuclear Magnetism: Order and Disorder, Oxford University Press, Oxford, 1982. [4] H. Gla¨ttli, M. Goldman, Methods of Experimental Physics, vol. 23, part C, Academic Press, New York, 1987, pp. 241–286. [5] F.M. Piegsa, B. van den Brandt, H. Gla¨ttli, P. Hautle, J. Kohlbrecher, J.A. Konter, B.S. Schlimme, O. Zimmer, Nucl. Instr. and Meth. A 589 (2008) 318. [6] R. Golub, R. Ga¨hler, T. Keller, Am. J. Phys. 62 (1994) 779. [7] F.M. Piegsa, B. van den Brandt, P. Hautle, J.A. Konter, Nucl. Instr. and Meth. A 586 (2008) 15. [8] F.M. Piegsa, M. Schneider, Nucl. Instr. and Meth. A 594 (2008) 74. [9] V.K. Aswal, B. van den Brandt, P. Hautle, J. Kohlbrecher, J.A. Konter, A. Michels, F.M. Piegsa, J. Stahn, O. Zimmer, Nucl. Instr. and Meth. A 586 (2008) 86. [10] M.J. Mu¨hlbauer, E. Calzada, B. Schillinger, Nucl. Instr. and Meth. A 542 (2005) 324.