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High resolution NRSE spectrometer with 2D-focusing supermirrors
Physica B 406 (2011) 2470–2472
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
High resolution NRSE spectrometer with 2D-focusing supermirrors Masaaki Kitaguchi a,, Masahiro Hino a, Yuji Kawabata a, Seiji Tasaki b, Ryuji Maruyama c, Toru Ebisawa c a b c
Research Reactor Institute, Kyoto University, Kumatori, Sennan, Osaka 590-0494, Japan Department of Nuclear Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan J-PARC Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
a r t i c l e i n f o
a b s t r a c t
Available online 25 November 2010
In the neutron resonance spin echo (NRSE) spectrometer [1] the divergent beam provides the deviation of the flight length, which makes the phase difference between neutron spin states and also decreases the contrast of the spin echo signals. The flight length can be adjusted by using parabolic focusing mirrors [11], which can be fabricated with replica technique. Correction for beam divergence effect in the NRSE spectrometer using 2D-focusing supermirrors will be discussed. & 2010 Elsevier B.V. All rights reserved.
Keywords: Neutron resonance spin echo Beam divergence effect Focusing mirror
1. Introduction Neutron spin echo (NSE) is one of the techniques with the highest energy resolution for quasi-elastic scattering [2]. The difference between incident and scattered neutron velocity is measured as the difference between the spin precession provided by static magnetic fields before and after the sample. The energy resolution is limited by the deviation of the precession due to the inhomogeneity of the magnetic fields and the divergent beam because the precession is proportional to the field integral. Correction of the precession for the ‘‘beam divergence effect’’ is needed in order to keep the neutron intensity by taking the divergent beam. The use of ‘‘Fresnel coils’’ enables the measurements. The beam divergence effect can be successfully corrected with the arrangement of three Fresnel coils in the static magnetic field of NSE. The arrangement of Fresnel coils enable us to perform the measurement with the Fourier time up to 400 ns [3–6]. Neutron resonance spin echo (NRSE) spectrometer, which is a variety of neutron spin echo, contains resonance spin flippers (RSFs) and zero-fields instead of the homogeneous static magnetic fields for spin precession in the conventional NSE [1]. It has the advantage to be constructed in small area and to perform measurements with less sensitivity of magnetic environment. In the case of NRSE, the energy resolution is limited mainly by the effect of the divergent beam. The beam divergence makes the deviation of the relative phase between up- and down-spin components, which is equivalent to spin precession, because the relative phase is proportional to the neutron flight length. Some methods to correct the beam divergence effect for NRSE have been proposed and demonstrated [7–10], however, they could not be applied for high
Corresponding author.
E-mail address: [email protected] (M. Kitaguchi). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.11.062
resolution NRSE spectrometer. Now we discuss on the correction for much higher resolution NRSE by using 2D-focusing mirrors.
2. Correction in NRSE The relative phase between the two spin components is proportional to the neutron flight length and the difference of wavenumber between the components. For the beam with the incident angle of y, the length is changed from L to L=cosy, where L is the distance between the two RSFs. The relative phase becomes
f ¼ DkL=cosy,
ð1Þ
where Dk is the difference of wavenumber between the two spin components, which is made by a RSF. Fresnel coils adjust Dk by magnetic field distribution in order to keep the total phase constant. In NSE, the spin quantization axis is parallel to the direction of the neutron beam. The direction of the correction fields which make the additional field integral is also along to the beam. The magnetic field with the strength depending on the radius and with the direction along the beam can be provided by the Fresnel coil (Fig. 1). However, it is very difficult to arrange the Fresnel coils to be applied for NRSE, because the spin quantization axis is generally transverse to the beam. The vertical magnetic fields in RSFs is required for the welldefined zero-field for high resolution NRSE. The spin quantization axis need to be changed adiabatically from the vertical direction of RSFs into the longitudinal direction of Fresnel coils in zero-field between the RSFs. The magnetic field for the transition of the spin quantization axis makes the vertical asymmetric distribution of the field integral. When neutrons pass through the two transition fields at the entrance and the exit of the weak field between the RSFs, the relative phase is distributed depending on the difference of the field integral (Fig. 2). Although the weak guide field between the RSFs, or
M. Kitaguchi et al. / Physica B 406 (2011) 2470–2472
3. Elliptic focusing mirror in NRSE Now we consider the devices which focus the beam from a RSF to the next RSF. The length of the ray from the focus of the elliptic mirror to the other focus is constant. When the RSFs are set on the two focuses and the neutrons are reflected by the elliptic mirror, the length between the two RSFs is constant (Fig. 3). The relative phase DkL is also constant. This idea using elliptic mirror has already proposed, however, has not been investigated minutely. By using 1-dimensional focusing mirror we reported that the relative phase was corrected according to the paths of reflected neutrons [11]. The large and 2-dimensional elliptic mirror is required to accept larger and 2-dimensional divergent angle of neutrons. It was very difficult to make the base of such neutron mirror, which has both smooth surface and precise shape. Nowadays we can fabricate the ‘‘supermirror sheet’’ (established by M. Hino, patent pending). Neutron multilayer supermirror is fabricated by ion beam sputtering method on a silicon wafer and covered by a flexible sheet. The multilayer glued on the sheet tightly is peeled from the silicon wafer. The multilayer on the sheet can be bent and re-shape freely. The correction method using large elliptic mirrors can be discussed as a feasible idea now. We performed Monte-Carlo simulation of the setup of the NRSE with elliptic mirrors. The width and length of the elliptic mirror was 100 and 1000 mm. The major and minor dimension of the ellipse was 1250 and 65.4 mm, respectively. This means the precession region of 2.5 m. The incident angle at the center of the mirror was 31. The supermirror was assumed to reflect all neutrons. The effective frequency of the RFSs was 0.8 MHz and the neutron wavelength was 2 nm. Therefore we got NRSE with the fourier time of 400 ns. The pinholes with the diameter of 5 mm was put on the focuses (Fig. 4). The path length through the two pinholes and reflected by the mirror was calculated geometrically. Fig. 5 is the phase distribution after storing between two RSFs with reflection of the mirror. The most of the phase was distributed in the range of about a half of p. The neutron intensity was 800 times larger than the setup only with the two pinholes. This can be understood as the effect of the expansion of the beam divergence. Fig. 6 shows the simulation result of spin echo signals with the above setup using elliptic
mirrors. Same setup was arranged after elastic scattering for 2nd precession region. The path length difference between before and after scattering was calculated geometrically. Clear echo signals was observed in the simulation. Although the pinholes were expanded to 18 mm for the echo signal with the same visibility, the intensity was 1/60 of the setup with elliptic mirrors.
elliptic mirror
Fig. 3. NRSE with Elliptic mirrors.
2D elliptic mirror
Fig. 4. Simulation setup.
100000 with mirror without mirror same visibility
10000
1000
100
10
1
Small correction
neutron spin states
-10
-5
0
5
10
15
20
25
relative phase [rad]
Fresnel coil Fig. 1. Concept of Fresnel coils. Black arrow shows spin quantization axis. Spin precession is in the plane perpendicular to the axis (gray arrows). Neutrons with larger incident angle are added larger correction.
RSF
neutron spin states
pinhole on focus
pinhole on focus
Large correction
B
RSF
RSF
neutron counts [arb. unit]
zero-field for ideal case, is required in NRSE, it is difficult to utilize the Fresnel coils due to the stray field.
2471
Fig. 5. Phase distribution storing between two RSFs. Solid line shows the distribution with the correction using 2D elliptic mirror. Dashed line shows the distribution only with pinholes. Dotted line shows that with expanded pinholes.
zero (weak guide) field
RSF
sample
adiabatic transition field
Fig. 2. Fresnel coils in NRSE. Gray gradation area expresses the distribution of the field strength. Transition of spin state before and after very weak guide field makes deviation of the relative phase.
2472
M. Kitaguchi et al. / Physica B 406 (2011) 2470–2472
frequency has been developed for the NRSE with pulsed neutrons [13]. We are planning experiments to confirm the phase correction with the focusing mirrors.
5000
neutron intensity [arb. unit]
with mirror 4000
Acknowledgments 3000
This work was supported by the inter-university program for common use JAEA and KUR, and financially by the program of Development of System and Technology for Advanced Measurement and Analysis (SENTAN), JST and by a Grant-in-Aid for Scientific Research No. 21760050 and No. 21656237 of JSPS.
2000
1000
References 0 -60
-40
-20
0
20
40
60
phase [rad] Fig. 6. Spin echo signals with the elliptic mirrors. The width of neutron wavelength was 20% of the wavelength.
4. Conclusions We demonstrated the feasibility of correction for the beam divergence effect in high resolution NRSE spectrometer by the numerical calculation and Monte-Carlo simulation. By using 2D focusing elliptic mirrors, the beam divergence effect can be corrected to observe clear spin echo signals with fourier time of 400 ns. Now we are planning to construct resonance spin echo spectrometers in pulsed neutrons like J-PARC [12]. The RSF with high
¨ [1] R. Gahler, R. Golub, Z. Phys. B 65 (1987) 43. [2] F. Mezei, Z. Phys. 255 (1972) 146. [3] C.M.E. Zeyen, P.C. Rem, R.A. Hartmann, L.J.M. van de Klundert, IEEE Trans. Magn. 24 (1988) 1540. [4] M. Monkenbusch, Nucl. Instr. and Meth. A 287 (1990) 465. ¨ [5] M. Monkenbusch, R. Schatzler, D. Richter, Nucl. Instr. and Meth. A 399 (1997) 301. [6] P. Schleger, et al., Physica B 266 (1999) 49. [7] M. Monkenbusch, Nucl. Instr. and Meth. A 437 (1999) 455. [8] M. Bleuel, et al., Neutron Spin Echo Spectroscopy, Basics, Trends and Applications, Lecture Notes in Physics, vol. 601, Springer, Berlin, 2003, p. 176. ¨ [9] W. Haussler, U. Schmidt, G. Ehlers, F. Mezei, Chem. Phys. 292 (2003) 501. [10] M. Kitaguchi, M. Hino, Y. Kawabata, H. Hayashida, S. Tasaki, R. Maruyama, T. Ebisawa, Meas. Sci. Technol. 19 (2008) 034014. [11] R. Maruyama, M. Hino, H. Hayashida, M. Kitaguchi, N. Achiwa, D. Yamazaki, T. Ebisawa, K. Soyama, Physica B 404 (2009) 2594. [12] Y. Kawabata, M. Hino, M. Kitaguchi, H. Hayashida, S. Tasaki, T. Ebisawa, D. Yamazaki, R. Maruyama, H. Seto, M. Nagaoe, T. Kanaya, Nucl. Instr. and Meth. A 574 (2006) 1122. [13] H. Hayashida, M. Kitaguchi, M. Hino, Y. Kawabata, R. Maruyama, T. Ebisawa, Nucl. Instr. and Meth. A 530 (2007) 292.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
High resolution NRSE spectrometer with 2D-focusing supermirrors Masaaki Kitaguchi a,, Masahiro Hino a, Yuji Kawabata a, Seiji Tasaki b, Ryuji Maruyama c, Toru Ebisawa c a b c
Research Reactor Institute, Kyoto University, Kumatori, Sennan, Osaka 590-0494, Japan Department of Nuclear Engineering, Kyoto University, Sakyo, Kyoto 606-8501, Japan J-PARC Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan
a r t i c l e i n f o
a b s t r a c t
Available online 25 November 2010
In the neutron resonance spin echo (NRSE) spectrometer [1] the divergent beam provides the deviation of the flight length, which makes the phase difference between neutron spin states and also decreases the contrast of the spin echo signals. The flight length can be adjusted by using parabolic focusing mirrors [11], which can be fabricated with replica technique. Correction for beam divergence effect in the NRSE spectrometer using 2D-focusing supermirrors will be discussed. & 2010 Elsevier B.V. All rights reserved.
Keywords: Neutron resonance spin echo Beam divergence effect Focusing mirror
1. Introduction Neutron spin echo (NSE) is one of the techniques with the highest energy resolution for quasi-elastic scattering [2]. The difference between incident and scattered neutron velocity is measured as the difference between the spin precession provided by static magnetic fields before and after the sample. The energy resolution is limited by the deviation of the precession due to the inhomogeneity of the magnetic fields and the divergent beam because the precession is proportional to the field integral. Correction of the precession for the ‘‘beam divergence effect’’ is needed in order to keep the neutron intensity by taking the divergent beam. The use of ‘‘Fresnel coils’’ enables the measurements. The beam divergence effect can be successfully corrected with the arrangement of three Fresnel coils in the static magnetic field of NSE. The arrangement of Fresnel coils enable us to perform the measurement with the Fourier time up to 400 ns [3–6]. Neutron resonance spin echo (NRSE) spectrometer, which is a variety of neutron spin echo, contains resonance spin flippers (RSFs) and zero-fields instead of the homogeneous static magnetic fields for spin precession in the conventional NSE [1]. It has the advantage to be constructed in small area and to perform measurements with less sensitivity of magnetic environment. In the case of NRSE, the energy resolution is limited mainly by the effect of the divergent beam. The beam divergence makes the deviation of the relative phase between up- and down-spin components, which is equivalent to spin precession, because the relative phase is proportional to the neutron flight length. Some methods to correct the beam divergence effect for NRSE have been proposed and demonstrated [7–10], however, they could not be applied for high
Corresponding author.
E-mail address: [email protected] (M. Kitaguchi). 0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2010.11.062
resolution NRSE spectrometer. Now we discuss on the correction for much higher resolution NRSE by using 2D-focusing mirrors.
2. Correction in NRSE The relative phase between the two spin components is proportional to the neutron flight length and the difference of wavenumber between the components. For the beam with the incident angle of y, the length is changed from L to L=cosy, where L is the distance between the two RSFs. The relative phase becomes
f ¼ DkL=cosy,
ð1Þ
where Dk is the difference of wavenumber between the two spin components, which is made by a RSF. Fresnel coils adjust Dk by magnetic field distribution in order to keep the total phase constant. In NSE, the spin quantization axis is parallel to the direction of the neutron beam. The direction of the correction fields which make the additional field integral is also along to the beam. The magnetic field with the strength depending on the radius and with the direction along the beam can be provided by the Fresnel coil (Fig. 1). However, it is very difficult to arrange the Fresnel coils to be applied for NRSE, because the spin quantization axis is generally transverse to the beam. The vertical magnetic fields in RSFs is required for the welldefined zero-field for high resolution NRSE. The spin quantization axis need to be changed adiabatically from the vertical direction of RSFs into the longitudinal direction of Fresnel coils in zero-field between the RSFs. The magnetic field for the transition of the spin quantization axis makes the vertical asymmetric distribution of the field integral. When neutrons pass through the two transition fields at the entrance and the exit of the weak field between the RSFs, the relative phase is distributed depending on the difference of the field integral (Fig. 2). Although the weak guide field between the RSFs, or
M. Kitaguchi et al. / Physica B 406 (2011) 2470–2472
3. Elliptic focusing mirror in NRSE Now we consider the devices which focus the beam from a RSF to the next RSF. The length of the ray from the focus of the elliptic mirror to the other focus is constant. When the RSFs are set on the two focuses and the neutrons are reflected by the elliptic mirror, the length between the two RSFs is constant (Fig. 3). The relative phase DkL is also constant. This idea using elliptic mirror has already proposed, however, has not been investigated minutely. By using 1-dimensional focusing mirror we reported that the relative phase was corrected according to the paths of reflected neutrons [11]. The large and 2-dimensional elliptic mirror is required to accept larger and 2-dimensional divergent angle of neutrons. It was very difficult to make the base of such neutron mirror, which has both smooth surface and precise shape. Nowadays we can fabricate the ‘‘supermirror sheet’’ (established by M. Hino, patent pending). Neutron multilayer supermirror is fabricated by ion beam sputtering method on a silicon wafer and covered by a flexible sheet. The multilayer glued on the sheet tightly is peeled from the silicon wafer. The multilayer on the sheet can be bent and re-shape freely. The correction method using large elliptic mirrors can be discussed as a feasible idea now. We performed Monte-Carlo simulation of the setup of the NRSE with elliptic mirrors. The width and length of the elliptic mirror was 100 and 1000 mm. The major and minor dimension of the ellipse was 1250 and 65.4 mm, respectively. This means the precession region of 2.5 m. The incident angle at the center of the mirror was 31. The supermirror was assumed to reflect all neutrons. The effective frequency of the RFSs was 0.8 MHz and the neutron wavelength was 2 nm. Therefore we got NRSE with the fourier time of 400 ns. The pinholes with the diameter of 5 mm was put on the focuses (Fig. 4). The path length through the two pinholes and reflected by the mirror was calculated geometrically. Fig. 5 is the phase distribution after storing between two RSFs with reflection of the mirror. The most of the phase was distributed in the range of about a half of p. The neutron intensity was 800 times larger than the setup only with the two pinholes. This can be understood as the effect of the expansion of the beam divergence. Fig. 6 shows the simulation result of spin echo signals with the above setup using elliptic
mirrors. Same setup was arranged after elastic scattering for 2nd precession region. The path length difference between before and after scattering was calculated geometrically. Clear echo signals was observed in the simulation. Although the pinholes were expanded to 18 mm for the echo signal with the same visibility, the intensity was 1/60 of the setup with elliptic mirrors.
elliptic mirror
Fig. 3. NRSE with Elliptic mirrors.
2D elliptic mirror
Fig. 4. Simulation setup.
100000 with mirror without mirror same visibility
10000
1000
100
10
1
Small correction
neutron spin states
-10
-5
0
5
10
15
20
25
relative phase [rad]
Fresnel coil Fig. 1. Concept of Fresnel coils. Black arrow shows spin quantization axis. Spin precession is in the plane perpendicular to the axis (gray arrows). Neutrons with larger incident angle are added larger correction.
RSF
neutron spin states
pinhole on focus
pinhole on focus
Large correction
B
RSF
RSF
neutron counts [arb. unit]
zero-field for ideal case, is required in NRSE, it is difficult to utilize the Fresnel coils due to the stray field.
2471
Fig. 5. Phase distribution storing between two RSFs. Solid line shows the distribution with the correction using 2D elliptic mirror. Dashed line shows the distribution only with pinholes. Dotted line shows that with expanded pinholes.
zero (weak guide) field
RSF
sample
adiabatic transition field
Fig. 2. Fresnel coils in NRSE. Gray gradation area expresses the distribution of the field strength. Transition of spin state before and after very weak guide field makes deviation of the relative phase.
2472
M. Kitaguchi et al. / Physica B 406 (2011) 2470–2472
frequency has been developed for the NRSE with pulsed neutrons [13]. We are planning experiments to confirm the phase correction with the focusing mirrors.
5000
neutron intensity [arb. unit]
with mirror 4000
Acknowledgments 3000
This work was supported by the inter-university program for common use JAEA and KUR, and financially by the program of Development of System and Technology for Advanced Measurement and Analysis (SENTAN), JST and by a Grant-in-Aid for Scientific Research No. 21760050 and No. 21656237 of JSPS.
2000
1000
References 0 -60
-40
-20
0
20
40
60
phase [rad] Fig. 6. Spin echo signals with the elliptic mirrors. The width of neutron wavelength was 20% of the wavelength.
4. Conclusions We demonstrated the feasibility of correction for the beam divergence effect in high resolution NRSE spectrometer by the numerical calculation and Monte-Carlo simulation. By using 2D focusing elliptic mirrors, the beam divergence effect can be corrected to observe clear spin echo signals with fourier time of 400 ns. Now we are planning to construct resonance spin echo spectrometers in pulsed neutrons like J-PARC [12]. The RSF with high
¨ [1] R. Gahler, R. Golub, Z. Phys. B 65 (1987) 43. [2] F. Mezei, Z. Phys. 255 (1972) 146. [3] C.M.E. Zeyen, P.C. Rem, R.A. Hartmann, L.J.M. van de Klundert, IEEE Trans. Magn. 24 (1988) 1540. [4] M. Monkenbusch, Nucl. Instr. and Meth. A 287 (1990) 465. ¨ [5] M. Monkenbusch, R. Schatzler, D. Richter, Nucl. Instr. and Meth. A 399 (1997) 301. [6] P. Schleger, et al., Physica B 266 (1999) 49. [7] M. Monkenbusch, Nucl. Instr. and Meth. A 437 (1999) 455. [8] M. Bleuel, et al., Neutron Spin Echo Spectroscopy, Basics, Trends and Applications, Lecture Notes in Physics, vol. 601, Springer, Berlin, 2003, p. 176. ¨ [9] W. Haussler, U. Schmidt, G. Ehlers, F. Mezei, Chem. Phys. 292 (2003) 501. [10] M. Kitaguchi, M. Hino, Y. Kawabata, H. Hayashida, S. Tasaki, R. Maruyama, T. Ebisawa, Meas. Sci. Technol. 19 (2008) 034014. [11] R. Maruyama, M. Hino, H. Hayashida, M. Kitaguchi, N. Achiwa, D. Yamazaki, T. Ebisawa, K. Soyama, Physica B 404 (2009) 2594. [12] Y. Kawabata, M. Hino, M. Kitaguchi, H. Hayashida, S. Tasaki, T. Ebisawa, D. Yamazaki, R. Maruyama, H. Seto, M. Nagaoe, T. Kanaya, Nucl. Instr. and Meth. A 574 (2006) 1122. [13] H. Hayashida, M. Kitaguchi, M. Hino, Y. Kawabata, R. Maruyama, T. Ebisawa, Nucl. Instr. and Meth. A 530 (2007) 292.