- Email: [email protected]
Neutron beam phase space mapping
ARTICLE IN PRESS
Physica B 385–386 (2006) 1253–1255 www.elsevier.com/locate/physb
Neutron beam phase space mapping Ja´nos Fu¨zia,b, a
Research Institute for Solid State Physics and Optics, Neutron Spectroscopy Department, P.O. Box 49, H-1525 Budapest, Hungary b Transilvania University R-2200 Brasov, Romania
Abstract The phase space of neutron beams is mapped by means of energy-resolved neutron imaging using a 2D position-sensitive detector in time-of-flight regime. The beam is viewed through a pinhole with adjustable position with respect to the beam axis, mapping the beam cross-section. The neutron beam flux and divergence are measured with respect to position and wavelength. The results can be used in subsequent downstream instrument design and optimization, as input and/or test data for simulation codes as well as for characterization of upstream elements (neutron sources, monochromators, guides etc). Results of measurements performed at the exit of a tapered supermirror guide on a beam at the Budapest Neutron Centre are presented. r 2006 Elsevier B.V. All rights reserved. PACS: 03.75.Be; 29.27.Fh; 29.27.Eg Keywords: Neutron optics; Neutron beam phase space
1. Introduction The five-dimensional neutron beam phase space in real space is characterized by two positional (x and y with respect to the beam axis or a laboratory reference axis), two angular (dx and dy with respect to the same axis) dimensions and wavelength (velocity, energy). One more parameter is added in case of polarized beams, namely the neutron spin state. The aim of this paper is to define measurement techniques, which allow evaluation of the neutron flux distribution with respect to these parameters. The results that can be obtained by this method can serve as experimental verification of numerical simulations; quality assessment of neutron optical components (brightness value and uniformity of moderators and cold-neutron sources; alignment accuracy, throughput of in-pile plugs, shutters; average reflectivity, alignment accuracy of beam guides; selectivity, transmission of monochromators, velocity selectors; transfer function of focusing devices) input
Research Institute for Solid State Physics and Optics, Neutron Spectroscopy Department, P.O. Box 49, H-1525 Budapest, Hungary. Tel.: +36 1 392 2222 1738; fax: +36 1 392 2501. E-mail address: [email protected].
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.06.023
information for corrective actions as well as data for downstream instrument design and optimization. 2. Measurement principle The neutron speed components with respect to the reference axis z are connected to the divergence angles by vx ¼ vz tan dx ; vy ¼ vz tan dy ;
v vz ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 1 þ tan2 dx þ tan2 dy
(1)
The neutrons originating from a pinhole situated at the position (x0, y0) with respect to the reference axis will reach the detector situated at distance l from the pinhole at x ¼ x0 þ l tan dx y ¼ y0 þ l tan dy :
(2)
The neutron wavelength is determined by measurement of the flight time t required for the neutron to cover the flight distance between the source and the detector. In case of continuous sources (e.g., fission reactors) a chopper is required to perform this measurement and the origin of the flight distance is at the chopper. The best choice is to have the pinhole and the chopper at the same position, leading
ARTICLE IN PRESS J. Fu¨zi / Physica B 385–386 (2006) 1253–1255
1254
to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ tl 1 þ tan2 dx þ tan2 dy ; l ¼ mhn v 3956 v ;
(3)
where h is the Planck constant and mn the neutron mass. The wavelength results in A˚ if the velocity is expressed in m/s. In case of pulsed (e.g. spallation) sources the time of flight can be measured with respect to the source pulse and the flight distance is that between the moderator and the detector. The use of a chopper in this case would allow the analysis of the wavelength (energy) distribution of the beam reaching the position of the chopper at the moment of the chopper opening with respect to the moment of the source pulse. Here again Eq. (3) can be used with l the chopper/pinhole–detector distance and t the chopper–detector time of flight. Varying the source pulse–chopper opening time interval, the entire pulse structure can be investigated. 3. Uncertainty evaluation The accuracy of these measurements is limited by a series of factors. The pinhole is not point like but has a finite area. When high-flux beams are measured (direct view of cores, cold sources or moderators, neutron guides) the pinhole can be rather small in order to reduce the level of detector saturation. The detector resolution is limited and the detector active depth has a non-zero, finite value. For the measurements presented in the sequel a 3He multiwire proportional counter has been used with pixel size s ¼ 0:75 mm, active depth d ¼ 35 mm and absorbing gas partial pressure p ¼ 2:5 bar, leading to estimated gas absorption efficiency xp x (4) Z ¼ 1 exp ¼ 1 exp l , m k ˚ The saturation of the detector with k ¼ 12:98 cm bar A. electronics can also affect the accuracy of the flux distribution evaluation. The 275 ps delay line length associated with 1.22 ns readout dead time [1] would lead to a limit count rate of 8 105 n=s for the 256 256 pixel detector area. In reality (without multiple-event handling) the saturation occurs around 105 n/s. The proportions of image are maintained, therefore dead-time corrections are possible even in case of high saturation level. The time of flight is measured with resolution t ¼ 1 ms. Data collection consists in saving the position of neutron detection events in finite time bins of length td leading to an nx ny nt array of limit size 256 256 4000. The finite chopper open time to also contributes to the uncertainty of the wavelength determination: Dl ¼
l 2
2
l d4
½ld þ 3956ðto þ td Þ.
(5)
The chopper open time for chopper opening equal to the pinhole size is r T, (6) to ¼ pR where r is the pinhole radius, R the distance between the pinhole and chopper axes and T the chopper period. The flux reaching the detector is reduced by the ratio to/T with respect to the continuous incoming flux, further improving the detector saturation conditions. The angular-accuracy limit is defined by the pinhole radius, parallax error, the detector pixel size and quality-filtering limit e defined as the accepted error of the sum of the delay times in the two senses with respect to the delay line length: Dd ¼
r þ d2 tan d þ s þ . l
(7)
The flight length and chopper period has to be set in such a manner that the desired wavelength accuracy (5) is reached and frame overlap is avoided (slow neutrons are not caught up by fast ones coming from a subsequent pulse), naturally within the geometrical constraints set by the actual measurement site. In case of pulsed sources the chopper has to be synchronized with the source. For a continuous source with wavelengths ranging up to ˚ pinhole radius r ¼ 0:5 mm, chopper radius lmax ¼ 40 A, R ¼ 170 mm and frequency f ¼ 50 Hz results in a required flight length of 2 m and with a time bin length of 10 ms (nt ¼ 2000) the wavelength measurement accuracy is Dl ¼ ˚ For a 0:075 A˚ at l ¼ 1 A˚ and Dl ¼ 0:23 A˚ at l ¼ 10 A. divergence of dmax ¼ 21 (when the cross-section of a supermirror neutron guide is investigated, this value is a function of the wavelength), FWHM position encoding error ¼ 0:5 s ¼ 0:4 mm, the angular accuracy would be Dd ¼ 1:2 mrad ¼ 0:071. In case of a 20 Hz repetition rate spallation source, a pinhole/chopper–detector distance of 5 m leads to lmax ¼ 40 A˚ (frame overlap is avoided if the moderator–chopper distance is also 5 m), Dl ¼ 0:052 A˚ at l ¼ 1 A˚ and Dl ¼ ˚ Since the resolution is better than the 0:11 A˚ at l ¼ 10 A. moderator pulse-width, the method is adequate to map the distribution of the latter, by using a chopper synchronized to certain time delays with respect to the proton pulse. 4. Measurement results The beam phase space at the exit of the tapered supermirror guide on a beam at the Budapest Neutron Centre has been investigated. The wavelength–vertical divergence cut: Z dx2 f 2 ðdy ; lÞ ¼ f ðx0 ; y0 ; x; dy ; lÞ dx, (8) dx1
and beam images for five wavelength range selections: Z l2 f 1 ðx0 ; y0 ; dx ; dy Þ ¼ f ðx0 ; y0 ; dx ; dy ; lÞdl, (9) l1
ARTICLE IN PRESS J. Fu¨zi / Physica B 385–386 (2006) 1253–1255
1255
Fig. 1. Wavelength–vertical divergence cut and beam images at selected wavelength ranges.
upstream graphite monochromator. The large dark stripes on the 4 – 4.5 A˚ picture and the darker rectangles in the wavelength–vertical divergence cut are due to the monochromator which is opaque at 4.3 A˚ (the wavelength diverted towards a reflectometer). The attenuation of several samples of scattering material have been measured as a function of neutron wavelength by comparing the transmitted flux through the sample to the reference flux measured without scatterer. Reduced summation area has been used around the beam axis defined by the pinhole position in order to avoid counting the neutrons scattered on the sample. The resulting transmission curves are plotted in Fig. 2.
5. Conclusions
Fig. 2. Transmission curves of polyethylene (PE) and Plexiglas (PMMA).
are represented in Fig. 1. These are restrictions of the phase space to the position of the pinhole with respect to the beam axis (x0, y0), while summations are performed for a narrow horizontal divergence range, respectively for the selected wavelength limits. It can be observed how the supermirrors come into effect as the critical angle increases with increasing wavelength. The narrow dark stripes are direct and reflected images of the 0.8 m long guide interruption at the location of an
The pinhole camera images taken by a position-sensitive detector in time-of-flight regime allows the mapping of the neutron beam phase space with acceptable resolution and accuracy. Each image allows the determination of the flux distribution with respect to divergence angles and wavelength, while moving the pinhole inside the investigated cross-section maps the phase space with respect to the two linear co-ordinates.
Reference [1] OTDC-TOF—four channel time-to-digital converter for 2D time of flight measurements, /www.openopto.kfkipark.huS
Physica B 385–386 (2006) 1253–1255 www.elsevier.com/locate/physb
Neutron beam phase space mapping Ja´nos Fu¨zia,b, a
Research Institute for Solid State Physics and Optics, Neutron Spectroscopy Department, P.O. Box 49, H-1525 Budapest, Hungary b Transilvania University R-2200 Brasov, Romania
Abstract The phase space of neutron beams is mapped by means of energy-resolved neutron imaging using a 2D position-sensitive detector in time-of-flight regime. The beam is viewed through a pinhole with adjustable position with respect to the beam axis, mapping the beam cross-section. The neutron beam flux and divergence are measured with respect to position and wavelength. The results can be used in subsequent downstream instrument design and optimization, as input and/or test data for simulation codes as well as for characterization of upstream elements (neutron sources, monochromators, guides etc). Results of measurements performed at the exit of a tapered supermirror guide on a beam at the Budapest Neutron Centre are presented. r 2006 Elsevier B.V. All rights reserved. PACS: 03.75.Be; 29.27.Fh; 29.27.Eg Keywords: Neutron optics; Neutron beam phase space
1. Introduction The five-dimensional neutron beam phase space in real space is characterized by two positional (x and y with respect to the beam axis or a laboratory reference axis), two angular (dx and dy with respect to the same axis) dimensions and wavelength (velocity, energy). One more parameter is added in case of polarized beams, namely the neutron spin state. The aim of this paper is to define measurement techniques, which allow evaluation of the neutron flux distribution with respect to these parameters. The results that can be obtained by this method can serve as experimental verification of numerical simulations; quality assessment of neutron optical components (brightness value and uniformity of moderators and cold-neutron sources; alignment accuracy, throughput of in-pile plugs, shutters; average reflectivity, alignment accuracy of beam guides; selectivity, transmission of monochromators, velocity selectors; transfer function of focusing devices) input
Research Institute for Solid State Physics and Optics, Neutron Spectroscopy Department, P.O. Box 49, H-1525 Budapest, Hungary. Tel.: +36 1 392 2222 1738; fax: +36 1 392 2501. E-mail address: [email protected].
0921-4526/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2006.06.023
information for corrective actions as well as data for downstream instrument design and optimization. 2. Measurement principle The neutron speed components with respect to the reference axis z are connected to the divergence angles by vx ¼ vz tan dx ; vy ¼ vz tan dy ;
v vz ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi . 1 þ tan2 dx þ tan2 dy
(1)
The neutrons originating from a pinhole situated at the position (x0, y0) with respect to the reference axis will reach the detector situated at distance l from the pinhole at x ¼ x0 þ l tan dx y ¼ y0 þ l tan dy :
(2)
The neutron wavelength is determined by measurement of the flight time t required for the neutron to cover the flight distance between the source and the detector. In case of continuous sources (e.g., fission reactors) a chopper is required to perform this measurement and the origin of the flight distance is at the chopper. The best choice is to have the pinhole and the chopper at the same position, leading
ARTICLE IN PRESS J. Fu¨zi / Physica B 385–386 (2006) 1253–1255
1254
to qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v ¼ tl 1 þ tan2 dx þ tan2 dy ; l ¼ mhn v 3956 v ;
(3)
where h is the Planck constant and mn the neutron mass. The wavelength results in A˚ if the velocity is expressed in m/s. In case of pulsed (e.g. spallation) sources the time of flight can be measured with respect to the source pulse and the flight distance is that between the moderator and the detector. The use of a chopper in this case would allow the analysis of the wavelength (energy) distribution of the beam reaching the position of the chopper at the moment of the chopper opening with respect to the moment of the source pulse. Here again Eq. (3) can be used with l the chopper/pinhole–detector distance and t the chopper–detector time of flight. Varying the source pulse–chopper opening time interval, the entire pulse structure can be investigated. 3. Uncertainty evaluation The accuracy of these measurements is limited by a series of factors. The pinhole is not point like but has a finite area. When high-flux beams are measured (direct view of cores, cold sources or moderators, neutron guides) the pinhole can be rather small in order to reduce the level of detector saturation. The detector resolution is limited and the detector active depth has a non-zero, finite value. For the measurements presented in the sequel a 3He multiwire proportional counter has been used with pixel size s ¼ 0:75 mm, active depth d ¼ 35 mm and absorbing gas partial pressure p ¼ 2:5 bar, leading to estimated gas absorption efficiency xp x (4) Z ¼ 1 exp ¼ 1 exp l , m k ˚ The saturation of the detector with k ¼ 12:98 cm bar A. electronics can also affect the accuracy of the flux distribution evaluation. The 275 ps delay line length associated with 1.22 ns readout dead time [1] would lead to a limit count rate of 8 105 n=s for the 256 256 pixel detector area. In reality (without multiple-event handling) the saturation occurs around 105 n/s. The proportions of image are maintained, therefore dead-time corrections are possible even in case of high saturation level. The time of flight is measured with resolution t ¼ 1 ms. Data collection consists in saving the position of neutron detection events in finite time bins of length td leading to an nx ny nt array of limit size 256 256 4000. The finite chopper open time to also contributes to the uncertainty of the wavelength determination: Dl ¼
l 2
2
l d4
½ld þ 3956ðto þ td Þ.
(5)
The chopper open time for chopper opening equal to the pinhole size is r T, (6) to ¼ pR where r is the pinhole radius, R the distance between the pinhole and chopper axes and T the chopper period. The flux reaching the detector is reduced by the ratio to/T with respect to the continuous incoming flux, further improving the detector saturation conditions. The angular-accuracy limit is defined by the pinhole radius, parallax error, the detector pixel size and quality-filtering limit e defined as the accepted error of the sum of the delay times in the two senses with respect to the delay line length: Dd ¼
r þ d2 tan d þ s þ . l
(7)
The flight length and chopper period has to be set in such a manner that the desired wavelength accuracy (5) is reached and frame overlap is avoided (slow neutrons are not caught up by fast ones coming from a subsequent pulse), naturally within the geometrical constraints set by the actual measurement site. In case of pulsed sources the chopper has to be synchronized with the source. For a continuous source with wavelengths ranging up to ˚ pinhole radius r ¼ 0:5 mm, chopper radius lmax ¼ 40 A, R ¼ 170 mm and frequency f ¼ 50 Hz results in a required flight length of 2 m and with a time bin length of 10 ms (nt ¼ 2000) the wavelength measurement accuracy is Dl ¼ ˚ For a 0:075 A˚ at l ¼ 1 A˚ and Dl ¼ 0:23 A˚ at l ¼ 10 A. divergence of dmax ¼ 21 (when the cross-section of a supermirror neutron guide is investigated, this value is a function of the wavelength), FWHM position encoding error ¼ 0:5 s ¼ 0:4 mm, the angular accuracy would be Dd ¼ 1:2 mrad ¼ 0:071. In case of a 20 Hz repetition rate spallation source, a pinhole/chopper–detector distance of 5 m leads to lmax ¼ 40 A˚ (frame overlap is avoided if the moderator–chopper distance is also 5 m), Dl ¼ 0:052 A˚ at l ¼ 1 A˚ and Dl ¼ ˚ Since the resolution is better than the 0:11 A˚ at l ¼ 10 A. moderator pulse-width, the method is adequate to map the distribution of the latter, by using a chopper synchronized to certain time delays with respect to the proton pulse. 4. Measurement results The beam phase space at the exit of the tapered supermirror guide on a beam at the Budapest Neutron Centre has been investigated. The wavelength–vertical divergence cut: Z dx2 f 2 ðdy ; lÞ ¼ f ðx0 ; y0 ; x; dy ; lÞ dx, (8) dx1
and beam images for five wavelength range selections: Z l2 f 1 ðx0 ; y0 ; dx ; dy Þ ¼ f ðx0 ; y0 ; dx ; dy ; lÞdl, (9) l1
ARTICLE IN PRESS J. Fu¨zi / Physica B 385–386 (2006) 1253–1255
1255
Fig. 1. Wavelength–vertical divergence cut and beam images at selected wavelength ranges.
upstream graphite monochromator. The large dark stripes on the 4 – 4.5 A˚ picture and the darker rectangles in the wavelength–vertical divergence cut are due to the monochromator which is opaque at 4.3 A˚ (the wavelength diverted towards a reflectometer). The attenuation of several samples of scattering material have been measured as a function of neutron wavelength by comparing the transmitted flux through the sample to the reference flux measured without scatterer. Reduced summation area has been used around the beam axis defined by the pinhole position in order to avoid counting the neutrons scattered on the sample. The resulting transmission curves are plotted in Fig. 2.
5. Conclusions
Fig. 2. Transmission curves of polyethylene (PE) and Plexiglas (PMMA).
are represented in Fig. 1. These are restrictions of the phase space to the position of the pinhole with respect to the beam axis (x0, y0), while summations are performed for a narrow horizontal divergence range, respectively for the selected wavelength limits. It can be observed how the supermirrors come into effect as the critical angle increases with increasing wavelength. The narrow dark stripes are direct and reflected images of the 0.8 m long guide interruption at the location of an
The pinhole camera images taken by a position-sensitive detector in time-of-flight regime allows the mapping of the neutron beam phase space with acceptable resolution and accuracy. Each image allows the determination of the flux distribution with respect to divergence angles and wavelength, while moving the pinhole inside the investigated cross-section maps the phase space with respect to the two linear co-ordinates.
Reference [1] OTDC-TOF—four channel time-to-digital converter for 2D time of flight measurements, /www.openopto.kfkipark.huS