- Email: [email protected]
Larmor labeling by time-gradient magnetic fields
ARTICLE IN PRESS
Physica B 397 (2007) 108–111 www.elsevier.com/locate/physb
Larmor labeling by time-gradient magnetic fields Alexander Ioffea,, Victor Bodnarchukb, Klaus Bussmannb, Robert Mu¨llerb a
Ju¨lich Centre for Neutron Science—Outstation Garching, Forschungszentrum Ju¨lich GmbH, Lichtenbergstr. 1, 85747 Garching, Germany b Forschungszentrum Ju¨lich GmbH, Institut fu¨r Festko¨rperforschung (IFF)—Scattering Methods, 52425 Ju¨lich, Germany
Abstract The Larmor labeling of neutrons, due to the Larmor precession of neutron spin in a magnetic field, opens the unique possibility for the development of neutron spin-echo (NSE) based on neutron scattering techniques, featuring an extremely high energy (momentum) resolution. Here, we present the experimental proof of a new method of the Larmor labeling using time-gradient magnetic fields. r 2007 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 68.35.Ct; 68.47.Mn Keywords: Neutron spin echo; Larmor labeling; High-resolution neutron spectroscopy; High-resolution neutron reflectometry
1. Introduction Because of the Larmor precession of the neutron spin in a magnetic field, the spatial position of the neutron spin vector becomes a unique marker (the Larmor clock) that angular position—the phase j of Larmor precession—is proportional to the propagation time t of every neutron in a magnetic field j ¼ oL t, where oL ¼ gnB is the Larmor frequency (gn—the neutron gyromagnetic ratio). This phenomenon of the so-called Larmor labeling of neutrons underlie the well-known neutron spin-echo (NSE) technique that enables precise measurements of energy (momentum) transfer without a precise knowledge of initial and final energies (momentum) themselves [1]; such high resolution is not feasible at all with conventional neutron scattering techniques, because the required neutron beam monochromatization (collimation) will result in intolerable intensity losses. There are three known NSE techniques—generic NSE [1], neutron-resonance spin echo (NRSE) [2] and rotatingmagnetic field [3] ones. Here, we will show results of first experiments aiming to prove the feasibility of a new NSE technique based upon the use of time-gradient magnetic fields [4].
2. Propagation through a pair of spin turners with timegradient magnetic fields Let us consider a neutron beam polarized in z-direction propagating through two subsequent magnetic field areas, A and B, that we will call spin turners (Fig. 1a). The magnetic fields of both spin turners, separated by a field_ free area of length L, are linearly time-dependent, BðtÞ ¼ Bt (tX0) but oppositely directed, thus providing opposite senses of the Larmor precession of the neutron spin. If neutrons enter the spin turner A at time tA, then the Larmor precession phase (angle) acquired in the result of the propagation across the magnetic field is Z
tA þt
jA ðtA ; tÞ ¼ g tA
E-mail address: [email protected] (A. Ioffe). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.02.051
(1)
where t ¼ a/v (v is the neutron velocity). Neutrons approach the spin turner B after the time-of-flight T ¼ L/v, so that the phase they acquire in the result of the propagation across magnetic field in the spin turner B is Z
tA þTþt
jA ðtA ; tÞ ¼ g Corresponding author. Tel.: +49 2461 613826; fax: +49 2461 612610.
2
_ dt ¼ gBt _ A t þ gB_ t , Bt 2
tA
2
_ dt ¼ gBðt _ A þ TÞt gB_ t . Bt 2 (2)
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
z
109
ST Y
A
B
B=0
B(t)
X
D
B(t) a
P
a
B2 S
Coil 1
L
y
A
B1
R1
R2 Coil 2
B(t) B
Fig. 2. Layout of the experiment. ST are 3-D spin turners, sandwiching the zero-field chamber S.
BT
A
t tA
T
Fig. 1. (a) Two subsequent spin turners with time-gradient magnetic field and (b) the geometrical representation of the Larmor phase acquired due to the propagation through them.
Thus, the total phase of the neutron spin precession (or the total spin precession angle) is _ F ¼ jA ðtA ; tÞ þ jB ðtA ; tÞ ¼ gBTt ¼ gB_
La , vv
(3)
and does not depend on the neutron arrival time tA at the first spin turner but depends on the neutron velocity only. This effect can be easily understood from Fig. 1b: the Larmor precession phase in a field A (B) is given by the dashed area of the corresponding trapezoid, when the phase difference is given by the cross-dashed rectangular, _ whose area is equal to gBTt and is constant for any tA. The polarization Pz of the outgoing beam is La _ Pz ðvÞ ¼ cosðgBTtÞ ¼ cos gB_ , (4) vv and depends only on the neutron velocity v. Indeed, the velocity of each neutron is coded by its spin precession angle in the spin turners that is a linear function of the propagation time between two spin turners A and B. 3. Experiment The experimental proof of this principle of the Larmor labeling was carried out at 3-D neutron polarimeter LAP–ND at the FRJ-2 reactor of the Research Center Ju¨lich [5]. Two solenoid coils of rectangular cross-section are placed inside the zero-field chamber made of a double layer of m-metal (see Fig. 2) and supplied by the current of
opposite directions. The monochromatic neutron beam with wavelength l ¼ 5.6 A˚ (Dl/l ¼ 1.5%) is polarized and analyzed by transmission neutron polarizers (made of FeCo supermirrors sputtered on thin Si substrates (Neutron Optics Berlin, GmbH) magnetized along axis OZ. Nonadiabatic input/output of the polarized neutron beam in/ out of the zero-field chamber is provided by a pair of coupling coils. Two 3-D spin turners sandwiching the zerofield chamber allow to put the neutron spin vector in any desirable direction and thus, to carry out measurements of the neutron beam polarization for X, Y and Z directions. Both coils must provide the same magnitude of the _ Though the coils are driven by magnetic field gradient B. the same linear current, the magnitude of the magnetic fields created in each of coils can be different because of natural deviations in their winding density and thicknesses, nevertheless. Therefore, the first step is to equalize the magnitude of the magnetic field by corresponding current corrections. As a magnetometer we use the neutron polarimeter itself: the coils are supplied with the DC current whose value defines the spin direction of outgoing neutrons. To provide the maximum sensitivity in the accuracy of magnetic field measurements, the spin direction of the incoming neutrons is set to be along the axis OX— this condition corresponds to the maximum sensitivity (of about 0.31) of the analyzer when the neutron spin direction is perpendicular to its magnetization direction. Then quite large DC current is applied to coils 1 and 2, so that the neutron spin undergoes a number of multiple, however opposite sense, rotations in the coils’ fields. If the values of the field integrals for these coils are different, the clockwise and counter clockwise rotations are not compensating each other and a deviation of the neutron spin direction from OX is observed. The resistance of the resistor R2 is adjusted to nullify this deviation: indeed, the field integrals for coils 1 and 2 are equalized. To minimize the depolarization effect of stray magnetic fields produced by the coils themselves, their magnetic flux was partially closed by C-shaped flux closing coils: this
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
measure was sufficient to keep the final polarization on the level of 95% from the incident polarization P0. The time diagram of the experiment is shown in Fig. 3. Coils are supplied with a current creating triangular pulses of magnetic field. These pulses are synchronized with pulses gating the detector channel: only neutrons arriving at the detector during the time Tg are counted. Changing the time shift Dt between gating pulses and triangular pulses one can select neutrons that arrive at coil 1 at different time with respect to the start of the magnetic field pulse and thus ‘‘see’’ different parts of the time-dependent magnetic field. If DtA[0, T/2t], i.e. neutrons see the linear rising slope of _ the magnetic field with B40 and should acquire the _ constant phase jþ ¼ gBtT (see Eq. (1) (note that we use a monochromatic neutron beam). If DtA[T/2, Tt], then neutrons see the linear descending slope of magnetic field _ with Bo0 and should acquire the constant phase _ j ¼ gBTt. However, according to Eq. (4) the beam polarization is an even function of the phase, so that _ Pz ðjþ Þ ¼ Pz ðj Þ ¼ cosðgBTtÞ.
2 T pulse
this dependence can be written as 4Bmax Pz ¼ P0 cos g Tt . T pulse
(6)
Triangular magnetic field pulses in the coils
Tg
Δt
Coil 1
Tpulse
Coil 2
−1 120
140
160
180 b, deg
200
220
240
Fig. 4. Dependence of the neutron beam polarization on the phase shift b ¼ 360 Dt=T pulse between gating and magnetic field pulses. Dashed line indicates the plateau where the neutron beam polarization is conserved.
2500 2000 1500 1000 500 0 −2
0
2
4
6
8
10
12
14
16
Voltage, V Fig. 5. The dependence of Pz on the peak value of the applied triangular voltage pulse shows the sinusoidal dependence as it is predicted by Eq. (6).
,
Bmax
Pz P0
(5)
Such neutron spin evolution is effectively a spin turn that is the same for each neutron in the beam, i.e. the polarization is conserved: P/P0 ¼ 1. However, if neutrons see the top of the triangular pulse, then the phase relations between jA and jB (Eq. (3)) do not hold anymore and the neutron beam practically should be fully depolarized: P/P0E0. The result of the corresponding experiment is shown in Fig. 4: there is a plateau of the expected width of about 701 (Tpulse ¼ 1 ms, Tg ¼ 0.15 ms), where Pz does not depend on the neutron arrival time as it is predicted by Eq. (2). The magnitude of Pz measured in such an experiment should in turn depend on the value of the field integral, i.e. _ This dependence is given on the magnetic field gradient B. by Eq. (4): since for the triangular pulse B_ ¼ 2Bmax
0
Intensity/ 106 monitor counts
110
Detector gate pulses
Detector
Fig. 3. Time diagram of the experiment.
Noting that Bmax is defined by the maximal voltage Vmax of the applied triangular pulses, one can conclude that Pz should be a sinusoidal function of Vmax. The plot of experimental dependence Pz ¼ f(Vmax) (Fig. 5) underlines the clear proof of this prediction as well. Finally, we turn to the demonstration of wavelength (or velocity) encoding in such arrangement. For this purposes the dependence of neutron polarization Pz as the function of distance L (cf. Eq. (4)) between the coils is measured. The result of the measurements plotted as the function of the neutron propagation time T ¼ L/v between the coils is shown in Fig. 6 (please recall that the experiment is carried out with monochromatic neutron beam with l ¼ 5.6 A˚). This result clearly demonstrates the expected modulation as predicted by Eq. (4): the polarization of neutron beam depends on the neutron propagation time. However, the changes in the neutron propagation time T ¼ L/v can also
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
requires only one field. This drastically simplifies the design of spin turning coils and opens easy ways for realizing rather long coils to be used at high tilt angles required by the phonon-focusing NSE method [7,8] and also for the realization of shaped coils, e.g. cylindrical coils required for the wide angle NSE spectroscopy with the simultaneous data acquisition in broad Q-range.
1.0
0.5 Pz / P0
111
0.0
4. Conclusions
−0.5
−1.0 40
60
80 100 120 Time-of-flight, μs
140
160
Fig. 6. Dependence of the neutron polarization Pz on the time-of-flight between coils.
be caused by the different neutron velocities for a fixed distance L between the coils, so that we can conclude that the combination of two subsequent time-gradient magnetic fields act as a neutron velocity (or wavelength) encoder. Because an NSE spectrometer can also be considered as two successive neutron velocity encoders [6], the convolution of their transmission functions defines the response (called the NSE signal) of the NSE spectrometer to the change of the neutron velocity caused by inelastic (quasielastic) scattering on the sample. Indeed, the sequence of two time-gradient magnetic field encoders sandwiching a sample will represent a new kind of the NSE spectrometer [4]. One should also note a kind of analogy between such NSE spectrometer and the neutron resonance spin echo spectrometer NRSE spectrometer built upon RF flippers [3]: both of them are requiring the field-free space between RF-flippers (spin turners). Certainly, the effect of depolarizing neutrons that we see as the change of the magnetic field gradient, i.e. around the vertices of the triangular signal, requires gating of the detector signal and imposes limitations on the maximum frequency of the magnetic field. However, in contrast to the RF flipper, whose operation requires a superposition of the constant magnetic field and the oscillating magnetic field, the operation of the suggested time-gradient field spin turners
We have experimentally demonstrated a new type of neutron velocity (wavelength) encoding that opens a possibility for a new kind of NSE technique—the timegradient magnetic field NSE. The main advantage of this technique is the simplicity of spin turners, so that practically no limits are imposed on their shape and size. This paves the way for the realization of rather long coils for the high tilt angles required for the phonon-focusing NSE method, cylindrical coils required for the wide angle NSE spectroscopy with a simultaneous data acquisition in broad Q-range, etc. Acknowledgments It is our pleasure to thank Th. Bru¨ckel for useful discussions.The project has been partially supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures, contract no. HII3-CT-2003-505925. References [1] F. Mezei, Z. Phyzik 255 (1972) 146. [2] R. Ga¨hler, R. Golub, J. Phys. C3-229 (1984) 45; R. Golub, R. Ga¨hler, Phys. Lett. A 123 (1987) 43. [3] A. Ioffe, Physica B 335 (2003) 169. [4] A. Ioffe, Nucl. Instr. and Meth., submitted. [5] A. Ioffe, K. Bussmann, L. Dohmen, L. Axelrod, G. Gordeev, TH. Bru¨ckel, Physica B 350 (2003) E815. [6] A. Ioffe, Nucl. Instr. and Meth. A 529 (2004) 39. [7] F. Mezei, Neutron spin echo and polarized neutrons, in: Neutron Inelastic Scattering 1977, IAEA, Vienna, 1978, pp. 125–134. [8] T. Keller, R. Golub, F. Mezei, R. Ga¨hler, Physica B 241–243 (1997) 101.
Physica B 397 (2007) 108–111 www.elsevier.com/locate/physb
Larmor labeling by time-gradient magnetic fields Alexander Ioffea,, Victor Bodnarchukb, Klaus Bussmannb, Robert Mu¨llerb a
Ju¨lich Centre for Neutron Science—Outstation Garching, Forschungszentrum Ju¨lich GmbH, Lichtenbergstr. 1, 85747 Garching, Germany b Forschungszentrum Ju¨lich GmbH, Institut fu¨r Festko¨rperforschung (IFF)—Scattering Methods, 52425 Ju¨lich, Germany
Abstract The Larmor labeling of neutrons, due to the Larmor precession of neutron spin in a magnetic field, opens the unique possibility for the development of neutron spin-echo (NSE) based on neutron scattering techniques, featuring an extremely high energy (momentum) resolution. Here, we present the experimental proof of a new method of the Larmor labeling using time-gradient magnetic fields. r 2007 Elsevier B.V. All rights reserved. PACS: 61.12.Ha; 68.35.Ct; 68.47.Mn Keywords: Neutron spin echo; Larmor labeling; High-resolution neutron spectroscopy; High-resolution neutron reflectometry
1. Introduction Because of the Larmor precession of the neutron spin in a magnetic field, the spatial position of the neutron spin vector becomes a unique marker (the Larmor clock) that angular position—the phase j of Larmor precession—is proportional to the propagation time t of every neutron in a magnetic field j ¼ oL t, where oL ¼ gnB is the Larmor frequency (gn—the neutron gyromagnetic ratio). This phenomenon of the so-called Larmor labeling of neutrons underlie the well-known neutron spin-echo (NSE) technique that enables precise measurements of energy (momentum) transfer without a precise knowledge of initial and final energies (momentum) themselves [1]; such high resolution is not feasible at all with conventional neutron scattering techniques, because the required neutron beam monochromatization (collimation) will result in intolerable intensity losses. There are three known NSE techniques—generic NSE [1], neutron-resonance spin echo (NRSE) [2] and rotatingmagnetic field [3] ones. Here, we will show results of first experiments aiming to prove the feasibility of a new NSE technique based upon the use of time-gradient magnetic fields [4].
2. Propagation through a pair of spin turners with timegradient magnetic fields Let us consider a neutron beam polarized in z-direction propagating through two subsequent magnetic field areas, A and B, that we will call spin turners (Fig. 1a). The magnetic fields of both spin turners, separated by a field_ free area of length L, are linearly time-dependent, BðtÞ ¼ Bt (tX0) but oppositely directed, thus providing opposite senses of the Larmor precession of the neutron spin. If neutrons enter the spin turner A at time tA, then the Larmor precession phase (angle) acquired in the result of the propagation across the magnetic field is Z
tA þt
jA ðtA ; tÞ ¼ g tA
E-mail address: [email protected] (A. Ioffe). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.02.051
(1)
where t ¼ a/v (v is the neutron velocity). Neutrons approach the spin turner B after the time-of-flight T ¼ L/v, so that the phase they acquire in the result of the propagation across magnetic field in the spin turner B is Z
tA þTþt
jA ðtA ; tÞ ¼ g Corresponding author. Tel.: +49 2461 613826; fax: +49 2461 612610.
2
_ dt ¼ gBt _ A t þ gB_ t , Bt 2
tA
2
_ dt ¼ gBðt _ A þ TÞt gB_ t . Bt 2 (2)
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
z
109
ST Y
A
B
B=0
B(t)
X
D
B(t) a
P
a
B2 S
Coil 1
L
y
A
B1
R1
R2 Coil 2
B(t) B
Fig. 2. Layout of the experiment. ST are 3-D spin turners, sandwiching the zero-field chamber S.
BT
A
t tA
T
Fig. 1. (a) Two subsequent spin turners with time-gradient magnetic field and (b) the geometrical representation of the Larmor phase acquired due to the propagation through them.
Thus, the total phase of the neutron spin precession (or the total spin precession angle) is _ F ¼ jA ðtA ; tÞ þ jB ðtA ; tÞ ¼ gBTt ¼ gB_
La , vv
(3)
and does not depend on the neutron arrival time tA at the first spin turner but depends on the neutron velocity only. This effect can be easily understood from Fig. 1b: the Larmor precession phase in a field A (B) is given by the dashed area of the corresponding trapezoid, when the phase difference is given by the cross-dashed rectangular, _ whose area is equal to gBTt and is constant for any tA. The polarization Pz of the outgoing beam is La _ Pz ðvÞ ¼ cosðgBTtÞ ¼ cos gB_ , (4) vv and depends only on the neutron velocity v. Indeed, the velocity of each neutron is coded by its spin precession angle in the spin turners that is a linear function of the propagation time between two spin turners A and B. 3. Experiment The experimental proof of this principle of the Larmor labeling was carried out at 3-D neutron polarimeter LAP–ND at the FRJ-2 reactor of the Research Center Ju¨lich [5]. Two solenoid coils of rectangular cross-section are placed inside the zero-field chamber made of a double layer of m-metal (see Fig. 2) and supplied by the current of
opposite directions. The monochromatic neutron beam with wavelength l ¼ 5.6 A˚ (Dl/l ¼ 1.5%) is polarized and analyzed by transmission neutron polarizers (made of FeCo supermirrors sputtered on thin Si substrates (Neutron Optics Berlin, GmbH) magnetized along axis OZ. Nonadiabatic input/output of the polarized neutron beam in/ out of the zero-field chamber is provided by a pair of coupling coils. Two 3-D spin turners sandwiching the zerofield chamber allow to put the neutron spin vector in any desirable direction and thus, to carry out measurements of the neutron beam polarization for X, Y and Z directions. Both coils must provide the same magnitude of the _ Though the coils are driven by magnetic field gradient B. the same linear current, the magnitude of the magnetic fields created in each of coils can be different because of natural deviations in their winding density and thicknesses, nevertheless. Therefore, the first step is to equalize the magnitude of the magnetic field by corresponding current corrections. As a magnetometer we use the neutron polarimeter itself: the coils are supplied with the DC current whose value defines the spin direction of outgoing neutrons. To provide the maximum sensitivity in the accuracy of magnetic field measurements, the spin direction of the incoming neutrons is set to be along the axis OX— this condition corresponds to the maximum sensitivity (of about 0.31) of the analyzer when the neutron spin direction is perpendicular to its magnetization direction. Then quite large DC current is applied to coils 1 and 2, so that the neutron spin undergoes a number of multiple, however opposite sense, rotations in the coils’ fields. If the values of the field integrals for these coils are different, the clockwise and counter clockwise rotations are not compensating each other and a deviation of the neutron spin direction from OX is observed. The resistance of the resistor R2 is adjusted to nullify this deviation: indeed, the field integrals for coils 1 and 2 are equalized. To minimize the depolarization effect of stray magnetic fields produced by the coils themselves, their magnetic flux was partially closed by C-shaped flux closing coils: this
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
measure was sufficient to keep the final polarization on the level of 95% from the incident polarization P0. The time diagram of the experiment is shown in Fig. 3. Coils are supplied with a current creating triangular pulses of magnetic field. These pulses are synchronized with pulses gating the detector channel: only neutrons arriving at the detector during the time Tg are counted. Changing the time shift Dt between gating pulses and triangular pulses one can select neutrons that arrive at coil 1 at different time with respect to the start of the magnetic field pulse and thus ‘‘see’’ different parts of the time-dependent magnetic field. If DtA[0, T/2t], i.e. neutrons see the linear rising slope of _ the magnetic field with B40 and should acquire the _ constant phase jþ ¼ gBtT (see Eq. (1) (note that we use a monochromatic neutron beam). If DtA[T/2, Tt], then neutrons see the linear descending slope of magnetic field _ with Bo0 and should acquire the constant phase _ j ¼ gBTt. However, according to Eq. (4) the beam polarization is an even function of the phase, so that _ Pz ðjþ Þ ¼ Pz ðj Þ ¼ cosðgBTtÞ.
2 T pulse
this dependence can be written as 4Bmax Pz ¼ P0 cos g Tt . T pulse
(6)
Triangular magnetic field pulses in the coils
Tg
Δt
Coil 1
Tpulse
Coil 2
−1 120
140
160
180 b, deg
200
220
240
Fig. 4. Dependence of the neutron beam polarization on the phase shift b ¼ 360 Dt=T pulse between gating and magnetic field pulses. Dashed line indicates the plateau where the neutron beam polarization is conserved.
2500 2000 1500 1000 500 0 −2
0
2
4
6
8
10
12
14
16
Voltage, V Fig. 5. The dependence of Pz on the peak value of the applied triangular voltage pulse shows the sinusoidal dependence as it is predicted by Eq. (6).
,
Bmax
Pz P0
(5)
Such neutron spin evolution is effectively a spin turn that is the same for each neutron in the beam, i.e. the polarization is conserved: P/P0 ¼ 1. However, if neutrons see the top of the triangular pulse, then the phase relations between jA and jB (Eq. (3)) do not hold anymore and the neutron beam practically should be fully depolarized: P/P0E0. The result of the corresponding experiment is shown in Fig. 4: there is a plateau of the expected width of about 701 (Tpulse ¼ 1 ms, Tg ¼ 0.15 ms), where Pz does not depend on the neutron arrival time as it is predicted by Eq. (2). The magnitude of Pz measured in such an experiment should in turn depend on the value of the field integral, i.e. _ This dependence is given on the magnetic field gradient B. by Eq. (4): since for the triangular pulse B_ ¼ 2Bmax
0
Intensity/ 106 monitor counts
110
Detector gate pulses
Detector
Fig. 3. Time diagram of the experiment.
Noting that Bmax is defined by the maximal voltage Vmax of the applied triangular pulses, one can conclude that Pz should be a sinusoidal function of Vmax. The plot of experimental dependence Pz ¼ f(Vmax) (Fig. 5) underlines the clear proof of this prediction as well. Finally, we turn to the demonstration of wavelength (or velocity) encoding in such arrangement. For this purposes the dependence of neutron polarization Pz as the function of distance L (cf. Eq. (4)) between the coils is measured. The result of the measurements plotted as the function of the neutron propagation time T ¼ L/v between the coils is shown in Fig. 6 (please recall that the experiment is carried out with monochromatic neutron beam with l ¼ 5.6 A˚). This result clearly demonstrates the expected modulation as predicted by Eq. (4): the polarization of neutron beam depends on the neutron propagation time. However, the changes in the neutron propagation time T ¼ L/v can also
ARTICLE IN PRESS A. Ioffe et al. / Physica B 397 (2007) 108–111
requires only one field. This drastically simplifies the design of spin turning coils and opens easy ways for realizing rather long coils to be used at high tilt angles required by the phonon-focusing NSE method [7,8] and also for the realization of shaped coils, e.g. cylindrical coils required for the wide angle NSE spectroscopy with the simultaneous data acquisition in broad Q-range.
1.0
0.5 Pz / P0
111
0.0
4. Conclusions
−0.5
−1.0 40
60
80 100 120 Time-of-flight, μs
140
160
Fig. 6. Dependence of the neutron polarization Pz on the time-of-flight between coils.
be caused by the different neutron velocities for a fixed distance L between the coils, so that we can conclude that the combination of two subsequent time-gradient magnetic fields act as a neutron velocity (or wavelength) encoder. Because an NSE spectrometer can also be considered as two successive neutron velocity encoders [6], the convolution of their transmission functions defines the response (called the NSE signal) of the NSE spectrometer to the change of the neutron velocity caused by inelastic (quasielastic) scattering on the sample. Indeed, the sequence of two time-gradient magnetic field encoders sandwiching a sample will represent a new kind of the NSE spectrometer [4]. One should also note a kind of analogy between such NSE spectrometer and the neutron resonance spin echo spectrometer NRSE spectrometer built upon RF flippers [3]: both of them are requiring the field-free space between RF-flippers (spin turners). Certainly, the effect of depolarizing neutrons that we see as the change of the magnetic field gradient, i.e. around the vertices of the triangular signal, requires gating of the detector signal and imposes limitations on the maximum frequency of the magnetic field. However, in contrast to the RF flipper, whose operation requires a superposition of the constant magnetic field and the oscillating magnetic field, the operation of the suggested time-gradient field spin turners
We have experimentally demonstrated a new type of neutron velocity (wavelength) encoding that opens a possibility for a new kind of NSE technique—the timegradient magnetic field NSE. The main advantage of this technique is the simplicity of spin turners, so that practically no limits are imposed on their shape and size. This paves the way for the realization of rather long coils for the high tilt angles required for the phonon-focusing NSE method, cylindrical coils required for the wide angle NSE spectroscopy with a simultaneous data acquisition in broad Q-range, etc. Acknowledgments It is our pleasure to thank Th. Bru¨ckel for useful discussions.The project has been partially supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures, contract no. HII3-CT-2003-505925. References [1] F. Mezei, Z. Phyzik 255 (1972) 146. [2] R. Ga¨hler, R. Golub, J. Phys. C3-229 (1984) 45; R. Golub, R. Ga¨hler, Phys. Lett. A 123 (1987) 43. [3] A. Ioffe, Physica B 335 (2003) 169. [4] A. Ioffe, Nucl. Instr. and Meth., submitted. [5] A. Ioffe, K. Bussmann, L. Dohmen, L. Axelrod, G. Gordeev, TH. Bru¨ckel, Physica B 350 (2003) E815. [6] A. Ioffe, Nucl. Instr. and Meth. A 529 (2004) 39. [7] F. Mezei, Neutron spin echo and polarized neutrons, in: Neutron Inelastic Scattering 1977, IAEA, Vienna, 1978, pp. 125–134. [8] T. Keller, R. Golub, F. Mezei, R. Ga¨hler, Physica B 241–243 (1997) 101.