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Numerical Simulation of a Beam Divergence Correction for NRSE Spectrometer using Polygonal 2D-focusing Supermirrors
Available online at www.sciencedirect.com
Physics Procedia 42 (2013) 121 – 124
PNCMI 2012 - Polarized Neutrons for Condensed Matter Investigations 2012
Numerical simulation of a beam divergence correction for NRSE spectrometer using polygonal 2D-focusing supermirrors Tatsuro Odaa,∗, Masahiro Hinob , Masaaki Kitaguchib , Yuji Kawabatab a Department
of Nuclear Engineering, Kyoto University, Nishikyo-ku, Kyoto 6158530, Japan Reactor Institute, Kyoto University, Kumatori, Osaka 5900494, Japan
b Research
Abstract By inserting two-dimensional (2D) elliptical focusing mirrors between each pair of RSFs in neutron resonance spin echo spectrometer, the flight path lengths between the pair of RSFs can be made equal even for any divergent beam. We investigate numerically the feasibility of using polygonal 2D elliptical focusing mirrors as beam correction devices, and we show the relation of the energy resolution and the neutron intensity including effect of gravity. © 2013 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the Organizing Committee ofof thethe 9thorganizing International Workshopfor on Polarised c 2012 Elsevier BV. Selection and/or peer-review under responsibility committee PNCMI 2012. Neutrons in Condensed Matter Investigations
Keywords: Neutron resonance spin echo, Elliptical focusing mirror
1. Introduction The Neutron spin echo (NSE) method is a powerful inelastic neutron scattering spectroscopy with high energy resolution [1]. The neutron velocity change by a sample is observed as the contrast modulation of the NSE signal. In the neutron resonance spin echo (NRSE), Larmor precession field in Mezei-type NSE instruments is replaced by zero or weak magnetic field between a pair of resonance spin flippers (RSF) [2, 3]. In NSE, the energy resolution is limited by the deviation of the precession due to the inhomogeneity of magnetic fields and the divergence of the beam. It is important to keep the neutron intensity by taking the divergent beam and Fresnel coil is used a beam correction device to keep the number of Larmor precession for the divergent beam in the conventional NSE spectrometers [4]. The resolution of NRSE is also limited by the effect of beam divergence. It is impossible to apply the Fresnel coil in NRSE since the spin quantization axis is not parallel to the neutron flight path. When the two dimensional (2D) elliptical focusing mirror is installed between a pair of RSFs and they are placed at the focal points of the ellipse, we can keep the same path length between the RSFs for high resolution NRSE measurement [5, 6]. It is very difficult to realize an ideal 2D elliptical mirror with large scale and we consider that polygonal focusing mirror can be used as a substitute for the ideal elliptical mirror. The polygonal mirror consists of small pieces of planar mirror instead of ideally elliptical ones. In this study, we discuss the feasibility of the polygonal focusing mirror as a beam divergence correction device for NRSE of VIN ROSE (Village of neutron resonance spin echo spectrometers). The VIN ROSE will be installed to the BL06 beam line in J-PARC/MLF under the ∗ Email:
t [email protected]
1875-3892 © 2013 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the Organizing Committee of the 9th International Workshop on Polarised Neutrons in Condensed Matter Investigations doi:10.1016/j.phpro.2013.03.184
122
Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
cooperation of Kyoto University and KEK [7]. We also estimate achievable Fourier time τ as a function of wavelength with typical pinhole apertures in the focal points. 2. Numerical simulation Figure 1(a) shows the schematic top layout of NRSE spectrometer at the VIN ROSE. The path lengths between the pair of RSFs (RSF1-RSF2, RSF3-RSF4) were calculated by using Monte Carlo technique. The simulation settings were as follows. The width and length of the elliptical mirror were set as 100 and 1000 mm, respectively. The semi-major and semi-minor axis of the ellipse were 1250 and 65.4 mm, respectively. The length between the pair of RSFs was 2.5 m and pinhole apertures with diameter of 5 mm (or 3 mm) were put on the focal points. The incident angle at the center of the mirror was 3◦ and the reflectivity of mirror was set at 1 since we had an interest in longer wavelength and the supermirror development has been improved dramatically last decade. If we assume the beam direction to be along the z-axis, the cross section of the ellipsoid in the minor axis forms a circle in the xy plane as shown in Fig 1(b). We approximated the shape of a circle with a polygon tangent to it and the length of one side in xy plane is represented by u. The cross section of the ellipsoid in the major axis forms an ellipse in the xz plane (Fig 1(c)). We divided this ellipse such that the maximum displacement of the mirror section was less than the value dv.
Fig. 1. Schematic view for (a) NRSE spectrometer with a pair of 2D elliptical focusing mirror in xz plane. The difference between the polygonal and ideal 2D elliptical mirror in (b) xy and (c) xz plane.
3. Results and Discussion Figure 2(a) and 2(b) show the histograms of the neutron path length difference of various u vales without and with gravity, respectively. The diameter of pinhole aperture was set at 5 mm and incident neutron wavelength was 2 nm. The displacement value (dv) of the mirror segments was equal to 1 μm and the mirror shape was nearly ideal ellipse in the xz plane. There is no difference in comparison with Fig. 2(a) and 2(b), and the effect of gravity is negligible small in this condition. In the case of u = 1 mm, the mirror was nearly ideal 2D elliptical focusing mirror and the number of partitions was 100 in the minor axis. Figure 2(c) shows the histogram of neutron path length difference of various displacement dv from 1 to 50 μm with u = 5 mm. In this pinhole size (φ = 5 mm), the neutron intensity is sensitive to the difference from the ideal ellipsoidal shape, however, the deviation of the path length difference is not sensitive. It is considered that trajectory of neutrons is selected by the pinholes and the path length deviation is suppressed. It means that the imperfectness of the 2D elliptical mirror, such as flexure, misalignment, is not severe for the beam divergence correction but important for the intensity. It is not so difficult to realize 1D elliptical mirror [8] and this simulation result supports that the polygonal 2D elliptical focusing mirrors function as beam correction devices well. Figure 3(a) and 3(b) show the expected Fourier time τ as a function of the neutron wavelength by using polygonal mirrors when the pinhole size was set as φ = 5 and φ = 3 mm,
Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
respectively. The displacement value dv = 1 μm. The Fourier time was obtained under the condition that the relative phase difference of the neutron spin was less than π/5 radians. Even in conservative conditions; use of 2D polygonal focusing mirror (u = 5 mm, dv = 10 μm), pinhole size φ = 5 mm, neutron wavelength of 2 nm, effective frequency of RSF 0.8 MHz, The contrast of NRSE signal was estimated to be 0.76 with τ = 100 ns and the intensity gain was over 200. This gain was obtained by the ratio of neutron intensity with and without a pair of focusing mirrors between a pair of RSFs.
Fig. 2. Histograms of the deviation of neutron flight path length (a) polygonal approximation in the xy plane (dv = 1 μm) (b) with gravity (c) polygonal approximation in the xz plane (u = 5 mm)
Fig. 3. Expected Fourier time τ using 2D polygonal focusing mirrors for pinhole size of (a) φ = 5 mm (b) φ = 3 mm
4. Concluding remarks We showed the feasibility of using 2D polygonal focusing mirror as a beam divergence correction device for the NRSE spectrometer via Monte Carlo simulations. When the pinhole diameter is less than 5 mm and the length between a pair of RSFs is 2.5 m, the path length deviation is not sensitive to the polygonal approximation of the ideal mirror shape and gravity effect. On the other hand, the neutron intensity decreases rapidly with an increasing number of partitions of the polygonal mirror. It indicates
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Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
that the neutron trajectories are selected by the pinholes and the imperfectness of 2D mirror is not severe as the beam divergence correction device. In this geometry for the VIN ROSE, improvement of correction device is necessary to realize higher Fourier time (τ > 200 ns). This simulation clearly shows that the effect of gravity is negilisible small for divergent beam and that the similar extension can increase the Fourier time without loss of intensity and extra developments. It means that the NRSE with 2D elliptical focusing mirrors is suitable for intense long pulse source like ESS. Acknowledgements This study was supported by Grant-in-Aid for Scientific Research Grant No. 23360428 of JSPS. The construction of the BL06 beam line for VIN ROSE was supported by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal No. 2009S07). References [1] [2] [3] [4] [5] [6] [7] [8]
F. Mezei, Z. Phys. 255 (1972) 146. R. Golub and R. G¨ahler, Phys. Lett. A123 (1987) 43. R. G¨ahler, R. Golub, Z. Phys. B65 (1987) 269. P. Schleger, G. Ehlers, A. Kollmar, B. Alefeld, J.F. Barthelemy, H. Casalta, B. Farago, P. Giraud, C. Hayes, C. Lartigue, F. Mezei, D. Richter, Physica B 266 (1999) 49. M. Bleuel, et al., Neutron Spin Echo Spectroscopy, Lecture Notesin Physics, vol.601, Springer, Berlin, 2003, p.176. M. Kitaguchi, M. Hino, Y. Kawabata, S. Tasaki, R. Maruyama, T. Ebisawa, Physica B 406 (2011) 2470. M. Hino, T. Oda, M. Kitaguchi, N.L. Yamada, H. Sagehashi, Y. Kawabata, T. Ebisawa, H. Seto, in this conference paper. R. Maruyama, M. Hino, H. Hayashida, M. Kitaguchi, N. Achiwa, D. Yamazaki, T. Ebisawa, K. Soyama, Physica B 404 (2009) 2594.
Physics Procedia 42 (2013) 121 – 124
PNCMI 2012 - Polarized Neutrons for Condensed Matter Investigations 2012
Numerical simulation of a beam divergence correction for NRSE spectrometer using polygonal 2D-focusing supermirrors Tatsuro Odaa,∗, Masahiro Hinob , Masaaki Kitaguchib , Yuji Kawabatab a Department
of Nuclear Engineering, Kyoto University, Nishikyo-ku, Kyoto 6158530, Japan Reactor Institute, Kyoto University, Kumatori, Osaka 5900494, Japan
b Research
Abstract By inserting two-dimensional (2D) elliptical focusing mirrors between each pair of RSFs in neutron resonance spin echo spectrometer, the flight path lengths between the pair of RSFs can be made equal even for any divergent beam. We investigate numerically the feasibility of using polygonal 2D elliptical focusing mirrors as beam correction devices, and we show the relation of the energy resolution and the neutron intensity including effect of gravity. © 2013 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the Organizing Committee ofof thethe 9thorganizing International Workshopfor on Polarised c 2012 Elsevier BV. Selection and/or peer-review under responsibility committee PNCMI 2012. Neutrons in Condensed Matter Investigations
Keywords: Neutron resonance spin echo, Elliptical focusing mirror
1. Introduction The Neutron spin echo (NSE) method is a powerful inelastic neutron scattering spectroscopy with high energy resolution [1]. The neutron velocity change by a sample is observed as the contrast modulation of the NSE signal. In the neutron resonance spin echo (NRSE), Larmor precession field in Mezei-type NSE instruments is replaced by zero or weak magnetic field between a pair of resonance spin flippers (RSF) [2, 3]. In NSE, the energy resolution is limited by the deviation of the precession due to the inhomogeneity of magnetic fields and the divergence of the beam. It is important to keep the neutron intensity by taking the divergent beam and Fresnel coil is used a beam correction device to keep the number of Larmor precession for the divergent beam in the conventional NSE spectrometers [4]. The resolution of NRSE is also limited by the effect of beam divergence. It is impossible to apply the Fresnel coil in NRSE since the spin quantization axis is not parallel to the neutron flight path. When the two dimensional (2D) elliptical focusing mirror is installed between a pair of RSFs and they are placed at the focal points of the ellipse, we can keep the same path length between the RSFs for high resolution NRSE measurement [5, 6]. It is very difficult to realize an ideal 2D elliptical mirror with large scale and we consider that polygonal focusing mirror can be used as a substitute for the ideal elliptical mirror. The polygonal mirror consists of small pieces of planar mirror instead of ideally elliptical ones. In this study, we discuss the feasibility of the polygonal focusing mirror as a beam divergence correction device for NRSE of VIN ROSE (Village of neutron resonance spin echo spectrometers). The VIN ROSE will be installed to the BL06 beam line in J-PARC/MLF under the ∗ Email:
t [email protected]
1875-3892 © 2013 The Authors. Published by Elsevier B.V. Selection and peer-review under responsibility of the Organizing Committee of the 9th International Workshop on Polarised Neutrons in Condensed Matter Investigations doi:10.1016/j.phpro.2013.03.184
122
Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
cooperation of Kyoto University and KEK [7]. We also estimate achievable Fourier time τ as a function of wavelength with typical pinhole apertures in the focal points. 2. Numerical simulation Figure 1(a) shows the schematic top layout of NRSE spectrometer at the VIN ROSE. The path lengths between the pair of RSFs (RSF1-RSF2, RSF3-RSF4) were calculated by using Monte Carlo technique. The simulation settings were as follows. The width and length of the elliptical mirror were set as 100 and 1000 mm, respectively. The semi-major and semi-minor axis of the ellipse were 1250 and 65.4 mm, respectively. The length between the pair of RSFs was 2.5 m and pinhole apertures with diameter of 5 mm (or 3 mm) were put on the focal points. The incident angle at the center of the mirror was 3◦ and the reflectivity of mirror was set at 1 since we had an interest in longer wavelength and the supermirror development has been improved dramatically last decade. If we assume the beam direction to be along the z-axis, the cross section of the ellipsoid in the minor axis forms a circle in the xy plane as shown in Fig 1(b). We approximated the shape of a circle with a polygon tangent to it and the length of one side in xy plane is represented by u. The cross section of the ellipsoid in the major axis forms an ellipse in the xz plane (Fig 1(c)). We divided this ellipse such that the maximum displacement of the mirror section was less than the value dv.
Fig. 1. Schematic view for (a) NRSE spectrometer with a pair of 2D elliptical focusing mirror in xz plane. The difference between the polygonal and ideal 2D elliptical mirror in (b) xy and (c) xz plane.
3. Results and Discussion Figure 2(a) and 2(b) show the histograms of the neutron path length difference of various u vales without and with gravity, respectively. The diameter of pinhole aperture was set at 5 mm and incident neutron wavelength was 2 nm. The displacement value (dv) of the mirror segments was equal to 1 μm and the mirror shape was nearly ideal ellipse in the xz plane. There is no difference in comparison with Fig. 2(a) and 2(b), and the effect of gravity is negligible small in this condition. In the case of u = 1 mm, the mirror was nearly ideal 2D elliptical focusing mirror and the number of partitions was 100 in the minor axis. Figure 2(c) shows the histogram of neutron path length difference of various displacement dv from 1 to 50 μm with u = 5 mm. In this pinhole size (φ = 5 mm), the neutron intensity is sensitive to the difference from the ideal ellipsoidal shape, however, the deviation of the path length difference is not sensitive. It is considered that trajectory of neutrons is selected by the pinholes and the path length deviation is suppressed. It means that the imperfectness of the 2D elliptical mirror, such as flexure, misalignment, is not severe for the beam divergence correction but important for the intensity. It is not so difficult to realize 1D elliptical mirror [8] and this simulation result supports that the polygonal 2D elliptical focusing mirrors function as beam correction devices well. Figure 3(a) and 3(b) show the expected Fourier time τ as a function of the neutron wavelength by using polygonal mirrors when the pinhole size was set as φ = 5 and φ = 3 mm,
Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
respectively. The displacement value dv = 1 μm. The Fourier time was obtained under the condition that the relative phase difference of the neutron spin was less than π/5 radians. Even in conservative conditions; use of 2D polygonal focusing mirror (u = 5 mm, dv = 10 μm), pinhole size φ = 5 mm, neutron wavelength of 2 nm, effective frequency of RSF 0.8 MHz, The contrast of NRSE signal was estimated to be 0.76 with τ = 100 ns and the intensity gain was over 200. This gain was obtained by the ratio of neutron intensity with and without a pair of focusing mirrors between a pair of RSFs.
Fig. 2. Histograms of the deviation of neutron flight path length (a) polygonal approximation in the xy plane (dv = 1 μm) (b) with gravity (c) polygonal approximation in the xz plane (u = 5 mm)
Fig. 3. Expected Fourier time τ using 2D polygonal focusing mirrors for pinhole size of (a) φ = 5 mm (b) φ = 3 mm
4. Concluding remarks We showed the feasibility of using 2D polygonal focusing mirror as a beam divergence correction device for the NRSE spectrometer via Monte Carlo simulations. When the pinhole diameter is less than 5 mm and the length between a pair of RSFs is 2.5 m, the path length deviation is not sensitive to the polygonal approximation of the ideal mirror shape and gravity effect. On the other hand, the neutron intensity decreases rapidly with an increasing number of partitions of the polygonal mirror. It indicates
123
124
Tatsuro Oda et al. / Physics Procedia 42 (2013) 121 – 124
that the neutron trajectories are selected by the pinholes and the imperfectness of 2D mirror is not severe as the beam divergence correction device. In this geometry for the VIN ROSE, improvement of correction device is necessary to realize higher Fourier time (τ > 200 ns). This simulation clearly shows that the effect of gravity is negilisible small for divergent beam and that the similar extension can increase the Fourier time without loss of intensity and extra developments. It means that the NRSE with 2D elliptical focusing mirrors is suitable for intense long pulse source like ESS. Acknowledgements This study was supported by Grant-in-Aid for Scientific Research Grant No. 23360428 of JSPS. The construction of the BL06 beam line for VIN ROSE was supported by the Neutron Scattering Program Advisory Committee of IMSS, KEK (Proposal No. 2009S07). References [1] [2] [3] [4] [5] [6] [7] [8]
F. Mezei, Z. Phys. 255 (1972) 146. R. Golub and R. G¨ahler, Phys. Lett. A123 (1987) 43. R. G¨ahler, R. Golub, Z. Phys. B65 (1987) 269. P. Schleger, G. Ehlers, A. Kollmar, B. Alefeld, J.F. Barthelemy, H. Casalta, B. Farago, P. Giraud, C. Hayes, C. Lartigue, F. Mezei, D. Richter, Physica B 266 (1999) 49. M. Bleuel, et al., Neutron Spin Echo Spectroscopy, Lecture Notesin Physics, vol.601, Springer, Berlin, 2003, p.176. M. Kitaguchi, M. Hino, Y. Kawabata, S. Tasaki, R. Maruyama, T. Ebisawa, Physica B 406 (2011) 2470. M. Hino, T. Oda, M. Kitaguchi, N.L. Yamada, H. Sagehashi, Y. Kawabata, T. Ebisawa, H. Seto, in this conference paper. R. Maruyama, M. Hino, H. Hayashida, M. Kitaguchi, N. Achiwa, D. Yamazaki, T. Ebisawa, K. Soyama, Physica B 404 (2009) 2594.