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Design of a single moderator-type neutron spectrometer with enhanced energy resolution in the energy range from a few to 100 keV
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 547 (2005) 592–600 www.elsevier.com/locate/nima
Design of a single moderator-type neutron spectrometer with enhanced energy resolution in the energy range from a few to 100 keV Y. Tanimura, J. Saegusa, M. Yoshizawa, M. Yoshida Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 8 July 2004; received in revised form 4 February 2005; accepted 4 March 2005 Available online 23 May 2005
Abstract The moderator structure for a neutron spectrometer was optimized with the Monte Carlo code MCNP-4B. The spectrometer consists of a cylindrical moderator and a position-sensitive thermal neutron detector and obtains energy spectra from thermal neutron distribution along its cylindrical axis. The structure of the moderator was improved by using a low hydrogen density material on one end and a high hydrogen density on the other, and inserting a neutron absorber that eliminates thermal neutron diffusion. This design improves the energy resolution of the spectrometer, especially for low-energy neutrons from a few to 100 keV. The designed spectrometer can be applied to the measurement of energy spectra over a neutron energy range from a few keV to 20 MeV. r 2005 Elsevier B.V. All rights reserved. PACS: 29.30.Hs; 29.40.Yam Keywords: Neutron spectrometer; Moderator; Position-sensitive thermal neutron detector; Neutron spectrum; Reference field; MCNP-4B
1. Introduction In the measurement of neutron dose equivalents, it is ideal for the fluence response of a neutron dosemeter to comply fully with the Corresponding author. Tel.: +81 29 284 3567; fax: +81 29 282 5609. E-mail address: [email protected] (Y. Tanimura).
fluence-to-dose equivalent conversion coefficients, hF , at any energy. Virtually no neutron dosemeter possesses this ideal fluence response, and it is thus difficult to estimate accurate neutron dose equivalents in various neutron fields such as in nuclear power plants, fuel reprocessing facilities and highenergy particle accelerators. The implication is that dosemeters should be calibrated at neutron fields with energy spectra quite similar to those found at practical workplaces, that are called
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.03.162
ARTICLE IN PRESS Y. Tanimura et al. / Nuclear Instruments and Methods in Physics Research A 547 (2005) 592–600
simulated workplace neutron calibration fields [1–6]. These fields are produced using radionuclide sources, accelerators and reactors. Such calibration fields need to be traceable to the national standard. However, there are some issues in establishing traceability. A critical one is that there are few spectrometers that can be applied to a wide energy range of neutrons. For example, proton-recoil proportional counters are limited to the neutrons with the energy range from a few tens of keV to a few MeV [7]. Proton-recoil telescopes or liquid scintillation counters can be only applied to neutrons of more than a few MeV [2,8]. In contrast, spherical multimoderator spectrometer systems (generally known as Bonner multispheres) are applicable to a wide energy range of neutrons. These systems consist of several spherical moderators with different diameters and a thermal neutron detector at the center of the moderators. However, they require sequential measurements with combinations of the different moderators and the detector, and these measurements take a long time to perform [9,10]. This makes it difficult to confirm that the measurements are performed under the same condition, in particular for fields produced with accelerators or reactors whose intensity is likely to vary from moment to moment. In conclusion, there is a great demand for a spectrometer that can measure neutron spectra in a wide energy range without changing detectors or moderators. The Long Counter, which is a combination of a thermal neutron counter tube and a cylindrical moderator, has a flat energy response to neutron fluence [11,12]. This detector is extensively used over the wide energy range, but is not suited to establish traceability in the calibration fields for radiation protection with continuous spectra, because no energy information can be obtained from the detector. As the coefficients hF vary with neutron energy, not only the neutron fluence but also the energy spectrum data are needed to derive a reference dose equivalent rate of the field. Some researchers have developed spectrometers using position-sensitive-type detectors for the thermal neutron counter tube [13,14], which can estimate the energy of the incident neutron by determining the position along the cylindrical axis where the
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thermal neutrons are detected. However, the energy resolution of incident neutrons using their spectrometer is insufficient for our purpose. In this work, the spectrometer’s moderator was improved in order to measure neutrons in the simulated workplace neutron fields from a few keV to 20 MeV by optimizing the size, structure and material of the moderator using a Monte Carlo radiation transport code. In the low-energy region from a few to 100 keV, the coefficient hF rises drastically and the measurement of the neutron spectrum is important for the evaluation of dosimetric quantities [8,15]. The improvement in the present work was intended to enhance the energy resolution in this energy region.
2. Principle of the spectrometer The spectrometer was designed to be used in standardizing simulated workplace neutron fields for calibrating neutron dosemeters. Because such neutron fields have spectra spread over a wide energy range [1,16,17], neutron spectrum the spectrometer can measure should be as wide as possible. We designed a spectrometer that can measure neutrons ranging from a few keV to 20 MeV. The spectrometer consists of a cylindrical moderator and a position-sensitive thermal neutron detector. A schematic drawing of the designed spectrometer is shown in Fig. 1. This spectrometer can obtain energy information about the unidirectional neutrons entering through the front face parallel to the cylindrical axis. Therefore, it can be applied to fields with point-like sources, e.g., D2Omoderated fields and some accelerator-based neutron fields [4,6,18]. The material and structure of the moderator were improved by using two kinds of material with different hydrogen densities and by inserting a thermal neutron absorber. The shape of the absorber was optimized to suppress the diffusion of thermal neutrons that otherwise worsens the energy resolution. When neutrons enter from the left face of this spectrometer parallel to its cylindrical axis, they lose their energy in the moderator and become thermal neutrons. The thermalized neutrons diffuse in the
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Fig. 1. Schematic drawing of the neutron spectrometer with optimized moderator structure. In the figure, some trajectories calculated with the MCNP-4B code were represented. 1 and 2 indicate the trajectories of fast and slow neutrons, respectively.
moderator and are detected with the thermal neutron detector in the center of the moderator. The moderation depth of each incident neutron until becoming a thermal neutron depends on its energy; i.e., fast neutrons penetrate more deeply into the moderator than slow neutrons before they are thermalized. This means that the position profile of thermal neutrons detected along the moderator axis reflects the incident neutron energy distribution [13,14]. Therefore, we can measure the energy spectrum of the incident neutrons from the profile. The neutron spectrum may then be given by unfolding the measured profile with the response functions, which are defined as the position profile measured by the position-sensitive thermal neutron detector for various mono-energetic neutrons.
3. Design procedure The Monte Carlo simulation technique has become a very powerful tool for calculating the response functions of the spectrometer. This technique allows for trial-and-error design of its moderator. We employed the three-dimensional Monte Carlo code MCNP version 4B [19] and
neutron cross-sections from the JENDL-3.2 nuclear data library [20]. The Sða; bÞ data library was also used in order to accurately simulate the behavior of thermalized neutrons in the moderator. The response functions for various cylindrical moderators were calculated. As the neutron spectrum is obtained from unfolding methods based on differences in the shape of the response functions for different energies, these differences determine the energy resolution and are the most important property. The moderator structure was designed to make this difference as large as possible. As the first step, diameter and length of the cylindrical moderator were optimized for a homogeneous moderator made of polyethylene. In the optimization, the weighted mean position xw ðEÞ of the response function was introduced as an index of the energy resolution. Fig. 2 shows a typically shaped response function, i.e., the position profile of thermal neutrons along the axis. The weighted mean position, xw ðEÞ, was given by following equation: R RðE; xÞ x dx xw ðEÞ ¼ R (1) RðE; xÞ dx where RðE; xÞ is the response function at x cm position for monoenergetic neutrons with the
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incident energy E. In the response function the counts of the thermal neutrons rise as depth increases, reaching a maximum (hereinafter an maximum position); the counts fall. In the case of a simple polyethylene moderator, the following two things worsen the energy resolution of the spectrometer. Firstly, differences in the position xw ðEÞ are not large for neutrons in the low-energy region below 100 keV, owing to the high hydrogen density. A low hydrogen density material was used as a part of the moderator in order to lower moderation efficiency and thereby extend the differences in the position xw ðEÞ for low-energy neutrons. Secondly, the diffusion of thermal neutrons in the moderator has to be considered. Since thermal neutrons are assumed to diffuse isotropically in the moderator, the long
Maximum position
Counts
Weighted mean position
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diffusion length probably causes a large difference of position between where the neutron has been thermalized and where it is detected. This difference worsens the position profile in neutron detection and decreases the energy resolution, in particular when the neutron has been thermalized at an outer part of the moderator. A thermal neutron absorber, therefore, was inserted in the moderator in order to suppress the diffusion and improve the energy resolution. The main functions of the absorber are illustrated in Fig. 3. The most suitable combination of geometry and materials was selected on the basis of the results simulated with the MCNP-4B code. In the simulation a position-sensitive 3He proportional counter 2.54 cm in diameter and a mixed gas of 130 kPa 3He and 70 kPa CF4 were adopted for the thermal neutron detector. This counter can measure the detection position of neutrons with less than 1 cm spatial resolution for an active length of 100 cm [21]. The active region of the counter was divided into cells with 1 cm length along the axis. The number of 3He(n,p)3H reactions in each cell was tallied to obtain the position profile of thermal neutron detection.
4. Results and discussion 4.1. Dimension of moderator 0
10
20 Position (cm)
30
Fig. 2. Typical response function of the spectrometer.
40
The response functions of the spectrometer for mono-energetic neutrons were calculated with the MCNP-4B code. The results are shown in the semi-logarithmic and linear plots of Fig. 4. In this
Fig. 3. Schematic drawings to explain the principle of suppressing the difference between the position of neutron thermalized and detected with a thermal neutron absorber. The right figure shows how the absorber eliminates the diffusion of thermal neutrons in the moderator and subsequent detection at another, distant axial position.
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Fig. 4. Response functions for a simple cylindrical polyethylene moderator (30 cm in diameter, 100 cm in length) for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 1 keV neutrons; the normalization factors are labeled in the figure.
calculation the moderator was simply made of polyethylene, 30 cm in diameter and 100 cm in length. For neutrons up to 1 MeV, the counts of detected neutrons steeply decreased by more than three orders of magnitude at 40 cm. For higher energy neutrons over 10 MeV, they still decreased, even at 100 cm with a certain slope as seen from the logarithmic plot. An appropriate slope measurement is necessary to obtain a neutron spectrum with good energy resolution for the highenergy neutrons; this determination requires the accumulation of counts over many orders of
magnitude along the axis, but it is difficult to obtain such data in practical measurements. For the 20 MeV neutrons, the counts fell by about three orders of magnitude at 100 cm, as seen in Fig. 4. Hence, we decided the length of the moderator to be 100 cm for obtaining energy information up to 20 MeV. The weight mean position xw ðEÞ, defined in Eq. (1), was derived in order to decide the diameter of the moderator. Fig. 5 shows the relation between the diameter and the xw ðEÞ for monoenergetic neutrons from 1 keV to 20 MeV. A clear separation of the xw ðEÞ indicates good energy resolution by the spectrometer. When the diameter was small, the separation was not clear, especially for the high-energy region. Moreover, the detection efficiency was low because the number of neutrons entering the detector was small. Although a large diameter improves the separation, the uncertainty becomes larger because the spectrum is averaged over a wide area and the weight of the moderator increases in proportion with the square of the diameter. In addition, as the diffusion of thermal neutrons within the moderator is restricted due to the capture reaction in hydrogen, too large a diameter is unprofitable. The diameter should not much exceed the size of the dosemeters to be calibrated in the fields. From these considerations, the suitable diameter for the moderator was determined to be 30 cm.
Fig. 5. Relation between the moderator diameter and the weighted mean position xw ðEÞ of the response functions, defined in Eq. (1), for several mono-energetic neutrons.
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4.2. Structure and materials of moderator When the moderator was made solely of polyethylene, the difference in response functions was not large enough for the low-energy neutrons below 100 keV, as seen in Fig. 4. In order to improve the energy resolution for low-energy neutrons, the structure of the moderator was modified in the following ways. One was the use of a low hydrogen density material in the front part of the moderator. Polycarbonate was selected because it has good processibility and its hydrogen density is about half that of polyethylene. The length of the polycarbonate part was determined as 40 cm because most of the neutrons below 100 keV were thermalized within 40 cm (see Fig. 4). The remaining 60 cm part was made of polyethylene as a high hydrogen density material in order not to reduce the detection efficiency for the high-energy neutrons. Fig. 6(a) and (b) show the response functions for the spectrometer with this moderator using the MCNP-4B code calculated in semilogarithmic and linear plots, respectively. The polycarbonate in the front part of the moderator clearly made the decrease in counts more gradual than in Fig. 4. The differences of the positions xw ðEÞ for 10 eV and 100 keV neutrons were 0.94 and 1.8 cm in Figs. 4 and 6, respectively. This means that the polycarbonate moderator expanded the difference and improved the energy resolution in the low-energy region. For the highenergy neutrons, the differences between 10 and 20 MeV were 3.8 and 1.1 cm in Figs. 4 and 6, respectively, which means that the energy resolution worsened in the high-energy region. However, the neutrons in the keV region are more important than the high-energy region from the viewpoint of the dosimetric quantities, because the coefficient hF rises dramatically in the keV region but does not change much from 10 to 20 MeV. The second consideration was how to suppress the diffusion of the thermal neutrons, which lessens the difference in the response function and worsens the energy resolution. A thermal neutron absorber was inserted into the moderator to suppress the diffusion. The absorber was made of 0.5 mm thick cadmium, and the shape was
Fig. 6. Response functions for the spectrometer with 40 cm polycarbonate and 60 cm polyethylene moderator for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
optimized based on the calculations of the thermal neutron distribution in the moderator. First, using the MCNP-4B code, we calculated the axial and radial distributions of thermal neutrons in the moderator for each energy when a narrow beam of mono-energetic neutrons was incident on the center of the cylindrical moderator parallel to the cylindrical axis. Then we evaluated deviations of the radial distribution and the maximum position, defined in Fig. 2, for each energy. The radial deviations were obtained by fitting the radial distribution with the Gaussian distribution. Since, the absorber prevents the neutron thermalized in
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the outer side from getting into the counter in the center of the spectrometer, it reduces the detection efficiency of the spectrometer. The reduction was influenced by the shape of the absorber. We selected the position of absorber where the deviation was one and a half times the standard deviation of the Gaussian (1:5s) and included 90% of thermal neutrons within the Gaussian, in order to make the reduction in efficiency as small as possible. Fig. 7 shows the radial deviation of 1:5s as a function of the axial position for the polycarbonate and polyethylene moderator, calculated for mono-energetic neutrons in the range of 1 eV–15 MeV. The shape of the absorber was decided as shown by the broken bold line in Fig. 7. The response functions of the spectrometer with the thermal neutron absorber in the polyethylene moderator were calculated, and the results are given in Fig. 8. The difference in the xw ðEÞ between 10 eV and 100 keV neutrons was about 0.99 cm; a little larger than that in Fig. 4 (0.94 cm) but smaller than that in Fig. 6 (1.8 cm). This means that in the case of the polyethylene moderator, the employment of low hydrogen density material in the moderator is more effective than the insertion
Fig. 8. Response functions for the spectrometer with the optimized neutron absorber in a pure polyethylene moderator for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
Fig. 7. Relation between the radial deviation and the maximum position in the distribution of thermal neutrons in the polycarbonate and polyethylene moderator. The distribution was calculated by MCNP-4B. The radial deviation was decided as 1:5s in order to include 90% of the thermal neutron. Solid squares and diamonds indicate the data for mono-energetic neutrons. The bold broken lines show the optimized shapes of cadmium absorbers.
of the thermal neutron absorber to improve the energy resolution in the low-energy region. Then a thermal neutron absorber was inserted into the polycarbonate moderator combined with the polyethylene moderator as shown in Fig. 1. The response functions of the spectrometer with this improved moderator are shown in Fig. 9. The difference in the xw ðEÞ between 10 eV and 100 keV neutrons was about 2.2 cm. The insertion of the absorber was found to be effective in improving the energy resolution in the low-energy region since the difference became larger than that in Fig. 6 (1.8 cm). Between 10 and 20 MeV, the
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two neutron spectra were simulated with the MCNP-4B code. The spectra from a bare and D2O-moderated 252Cf source were selected to demonstrate effectiveness in the MeV and keV regions, respectively. Both spectra used in the simulation were taken from ISO 8529-1 [18]. As first guess spectra, both a flat and the Watt spectrum were used for the 252Cf source and a flat spectrum and the spectrum taken from the ISO 8529-1 were used for the D2O-moderated 252Cf source. Fig. 10(a) and (b) show the unfolded spectra of the bare and D2O-moderated 252Cf sources, respectively. The unfolded results using
Fig. 9. Response functions for the spectrometer with the optimized neutron absorber in the moderator for different mono-energetic neutrons. The moderator consists of a 40 cm polycarbonate and a 60 cm polyethylene, as shown in Fig. 1: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
difference was about 1.0 cm and there was no significant change compared with that in Fig. 6 (1.1 cm). Therefore, we selected this structure for the spectrometer. 4.3. Spectrum unfolding It was demonstrated that the neutron spectra can be obtained from the spectrometer by using the unfolding code SAND-II [22]. The demonstrations were performed by a computer simulation. The responses of the spectrometer for
Fig. 10. Neutron energy spectra unfolded with the SAND-II code: (a) the bare 252Cf spectra and (b) the D2O-moderated 252 Cf spectra. The response of the spectrometer was simulated with the MCNP-4B code using the neutron spectra from the bare and D2O-moderated 252Cf source.
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the Watt spectrum or that taken from ISO 8529-1 as the first guess agreed with the spectrum of the neutron source. Here, these spectra were similar or identical to the ones used as the source spectra in the simulation. Even when the flat spectrum was used as the first guess spectrum, the unfolded spectra were consistent with that of the neutron source in the simulation. This suggests that the spectrometer could measure the neutron spectrum without any information about the neutron source because the flat spectrum contains no spectral information.
5. Summary A moderator for a neutron spectrometer with a cylindrical moderator and a position-sensitive thermal neutron detector was designed with the Monte Carlo code MCNP-4B. Based on our analysis, the diameter and length of the moderator were optimized at 30 and 100 cm, respectively. Because a simple moderator made of polyethylene did not provide good energy resolution in the neutron energy range up to 100 keV, the material and structure of the moderator were modified. A low hydrogen density polycarbonate was used for the first 40 cm of the moderator, and a high hydrogen density polyethylene for the second 60 cm. Additionally, a neutron absorber made of a cadmium sheet was inserted to eliminate the diffusion of thermal neutrons in the moderator. The shape of the absorber was optimized on the basis of the calculated results of the thermal neutron distribution in the moderator. These adjustments improved the energy resolution below 100 keV; this energy is important from the viewpoint of dosimetric quantities because the coefficient hF rises drastically in this energy region. From the demonstration of the spectrum unfolding, the spectrometer could measure the neutron spectra of a bare and D2O-moderated 252Cf source.
Acknowledgements We would like to thank Prof. Emeritus C. Mori of Nagoya University for his helpful discussions on designing the moderator of the spectrometer.
References [1] ISO, Reference Neutron Radiations—Characteristics and Methods of Production of Simulated Workplace Neutron Fields, ISO 12789, 2000. [2] ICRU, Determination of operational dose equivalent quantities for neutrons, ICRU Report 66, 2001. [3] J.L. Chartier, B. Jansky, H. Kluge, H. Schraube, B. Wiegel, Radiat. Prot. Dosim. 70 (1997) 305. [4] B. Wiegel, B.R.L. Siebert, S. Guldbakke, J. Wittstock, Nucl. Instr. and Meth. A 422 (1999) 474. [5] J.C. McDonald, B.R.L. Siebert, W.G. Alberts, Nucl. Instr. and Meth. A 476 (1999) 347. [6] J. Saegusa, Y. Tanimura, M. Yoshida, M. Yoshizawa, Radiat. Prot. Dosim. 110 (2004) 91. [7] H. Ing, T. Clifford, T. McLean, W. Webb, T. Cousins, J. Dhermain, Radiat. Prot. Dosim. 70 (1997) 273. [8] F.D. Brooks, H. Klein, Nucl. Instr. and Meth. A 476 (2002) 1. [9] R.L. Bramblett, R.I. Ewing, T.W. Bonner, Nucl. Instr. and Meth. 9 (1960) 1. [10] A.V. Aleva, D.J. Thomas, Radiat. Protect. Dosim. 107 (2003) 37. [11] A.O. Hanson, J.L. McKibben, Phys. Rev. 72 (1947) 673. [12] G.F. Knoll, Radiation Detection and Measurement, third ed., Wiley, New York, 2000. [13] H. Toyokawa, A. Uritani, C. Mori, N. Takeda, K. Kudo, Proceedings of the Eighth ASTM-Euratom Symposium Reactor Dosimetry, 1993, pp. 263–270. [14] G.B. Spector, T. McCollum, A.R. Spowart, Nucl. Instr. and Meth. A 346 (1994) 273. [15] A. Aroua, M. Grecescu, S. Pretre, J.F. Valley, Radiat. Prot. Dosim. 70 (1997) 285. [16] R.V. Griffith, J. Palfalvi, U. Madhvanath, IAEA Tech. Rep. 318 (1990). [17] F. Posny, J.L. Chartier, M. Buxerolle, Radiat. Prot. Dosim. 44 (1993) 239. [18] ISO, Reference Neutron Radiations—Part 1: Characteristics and Methods of Production, ISO 8529-1, 2001. [19] J.F. Briesmeister (Ed.), A General Monte Carlo N-Particle Transport Code, Version 4B—Manual LA-12625-M, Los Alamos National Laboratory, 1997. [20] T. Nakagawa, K. Shibata, S. Chiba, et al., J. Nucl. Sci. Technol. 32 (1995) 1259. [21] Y. Tanimura, J. Saegusa, M. Yoshizawa, M. Yoshida, J. Nucl. Sci. Technol. (Suppl. 4) (2004) 411. [22] W.N. McElroy, S. Berg, T. Crokett. R.G. Hawkins, A Computer-Automated Iterative Method for Neutron Flux Spectra Determination by Foil Activation, AFWLTR-67-41, vol. 1, Air Force Weapons Laboratory, 1967.
Nuclear Instruments and Methods in Physics Research A 547 (2005) 592–600 www.elsevier.com/locate/nima
Design of a single moderator-type neutron spectrometer with enhanced energy resolution in the energy range from a few to 100 keV Y. Tanimura, J. Saegusa, M. Yoshizawa, M. Yoshida Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki 319-1195, Japan Received 8 July 2004; received in revised form 4 February 2005; accepted 4 March 2005 Available online 23 May 2005
Abstract The moderator structure for a neutron spectrometer was optimized with the Monte Carlo code MCNP-4B. The spectrometer consists of a cylindrical moderator and a position-sensitive thermal neutron detector and obtains energy spectra from thermal neutron distribution along its cylindrical axis. The structure of the moderator was improved by using a low hydrogen density material on one end and a high hydrogen density on the other, and inserting a neutron absorber that eliminates thermal neutron diffusion. This design improves the energy resolution of the spectrometer, especially for low-energy neutrons from a few to 100 keV. The designed spectrometer can be applied to the measurement of energy spectra over a neutron energy range from a few keV to 20 MeV. r 2005 Elsevier B.V. All rights reserved. PACS: 29.30.Hs; 29.40.Yam Keywords: Neutron spectrometer; Moderator; Position-sensitive thermal neutron detector; Neutron spectrum; Reference field; MCNP-4B
1. Introduction In the measurement of neutron dose equivalents, it is ideal for the fluence response of a neutron dosemeter to comply fully with the Corresponding author. Tel.: +81 29 284 3567; fax: +81 29 282 5609. E-mail address: [email protected] (Y. Tanimura).
fluence-to-dose equivalent conversion coefficients, hF , at any energy. Virtually no neutron dosemeter possesses this ideal fluence response, and it is thus difficult to estimate accurate neutron dose equivalents in various neutron fields such as in nuclear power plants, fuel reprocessing facilities and highenergy particle accelerators. The implication is that dosemeters should be calibrated at neutron fields with energy spectra quite similar to those found at practical workplaces, that are called
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.03.162
ARTICLE IN PRESS Y. Tanimura et al. / Nuclear Instruments and Methods in Physics Research A 547 (2005) 592–600
simulated workplace neutron calibration fields [1–6]. These fields are produced using radionuclide sources, accelerators and reactors. Such calibration fields need to be traceable to the national standard. However, there are some issues in establishing traceability. A critical one is that there are few spectrometers that can be applied to a wide energy range of neutrons. For example, proton-recoil proportional counters are limited to the neutrons with the energy range from a few tens of keV to a few MeV [7]. Proton-recoil telescopes or liquid scintillation counters can be only applied to neutrons of more than a few MeV [2,8]. In contrast, spherical multimoderator spectrometer systems (generally known as Bonner multispheres) are applicable to a wide energy range of neutrons. These systems consist of several spherical moderators with different diameters and a thermal neutron detector at the center of the moderators. However, they require sequential measurements with combinations of the different moderators and the detector, and these measurements take a long time to perform [9,10]. This makes it difficult to confirm that the measurements are performed under the same condition, in particular for fields produced with accelerators or reactors whose intensity is likely to vary from moment to moment. In conclusion, there is a great demand for a spectrometer that can measure neutron spectra in a wide energy range without changing detectors or moderators. The Long Counter, which is a combination of a thermal neutron counter tube and a cylindrical moderator, has a flat energy response to neutron fluence [11,12]. This detector is extensively used over the wide energy range, but is not suited to establish traceability in the calibration fields for radiation protection with continuous spectra, because no energy information can be obtained from the detector. As the coefficients hF vary with neutron energy, not only the neutron fluence but also the energy spectrum data are needed to derive a reference dose equivalent rate of the field. Some researchers have developed spectrometers using position-sensitive-type detectors for the thermal neutron counter tube [13,14], which can estimate the energy of the incident neutron by determining the position along the cylindrical axis where the
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thermal neutrons are detected. However, the energy resolution of incident neutrons using their spectrometer is insufficient for our purpose. In this work, the spectrometer’s moderator was improved in order to measure neutrons in the simulated workplace neutron fields from a few keV to 20 MeV by optimizing the size, structure and material of the moderator using a Monte Carlo radiation transport code. In the low-energy region from a few to 100 keV, the coefficient hF rises drastically and the measurement of the neutron spectrum is important for the evaluation of dosimetric quantities [8,15]. The improvement in the present work was intended to enhance the energy resolution in this energy region.
2. Principle of the spectrometer The spectrometer was designed to be used in standardizing simulated workplace neutron fields for calibrating neutron dosemeters. Because such neutron fields have spectra spread over a wide energy range [1,16,17], neutron spectrum the spectrometer can measure should be as wide as possible. We designed a spectrometer that can measure neutrons ranging from a few keV to 20 MeV. The spectrometer consists of a cylindrical moderator and a position-sensitive thermal neutron detector. A schematic drawing of the designed spectrometer is shown in Fig. 1. This spectrometer can obtain energy information about the unidirectional neutrons entering through the front face parallel to the cylindrical axis. Therefore, it can be applied to fields with point-like sources, e.g., D2Omoderated fields and some accelerator-based neutron fields [4,6,18]. The material and structure of the moderator were improved by using two kinds of material with different hydrogen densities and by inserting a thermal neutron absorber. The shape of the absorber was optimized to suppress the diffusion of thermal neutrons that otherwise worsens the energy resolution. When neutrons enter from the left face of this spectrometer parallel to its cylindrical axis, they lose their energy in the moderator and become thermal neutrons. The thermalized neutrons diffuse in the
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Fig. 1. Schematic drawing of the neutron spectrometer with optimized moderator structure. In the figure, some trajectories calculated with the MCNP-4B code were represented. 1 and 2 indicate the trajectories of fast and slow neutrons, respectively.
moderator and are detected with the thermal neutron detector in the center of the moderator. The moderation depth of each incident neutron until becoming a thermal neutron depends on its energy; i.e., fast neutrons penetrate more deeply into the moderator than slow neutrons before they are thermalized. This means that the position profile of thermal neutrons detected along the moderator axis reflects the incident neutron energy distribution [13,14]. Therefore, we can measure the energy spectrum of the incident neutrons from the profile. The neutron spectrum may then be given by unfolding the measured profile with the response functions, which are defined as the position profile measured by the position-sensitive thermal neutron detector for various mono-energetic neutrons.
3. Design procedure The Monte Carlo simulation technique has become a very powerful tool for calculating the response functions of the spectrometer. This technique allows for trial-and-error design of its moderator. We employed the three-dimensional Monte Carlo code MCNP version 4B [19] and
neutron cross-sections from the JENDL-3.2 nuclear data library [20]. The Sða; bÞ data library was also used in order to accurately simulate the behavior of thermalized neutrons in the moderator. The response functions for various cylindrical moderators were calculated. As the neutron spectrum is obtained from unfolding methods based on differences in the shape of the response functions for different energies, these differences determine the energy resolution and are the most important property. The moderator structure was designed to make this difference as large as possible. As the first step, diameter and length of the cylindrical moderator were optimized for a homogeneous moderator made of polyethylene. In the optimization, the weighted mean position xw ðEÞ of the response function was introduced as an index of the energy resolution. Fig. 2 shows a typically shaped response function, i.e., the position profile of thermal neutrons along the axis. The weighted mean position, xw ðEÞ, was given by following equation: R RðE; xÞ x dx xw ðEÞ ¼ R (1) RðE; xÞ dx where RðE; xÞ is the response function at x cm position for monoenergetic neutrons with the
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incident energy E. In the response function the counts of the thermal neutrons rise as depth increases, reaching a maximum (hereinafter an maximum position); the counts fall. In the case of a simple polyethylene moderator, the following two things worsen the energy resolution of the spectrometer. Firstly, differences in the position xw ðEÞ are not large for neutrons in the low-energy region below 100 keV, owing to the high hydrogen density. A low hydrogen density material was used as a part of the moderator in order to lower moderation efficiency and thereby extend the differences in the position xw ðEÞ for low-energy neutrons. Secondly, the diffusion of thermal neutrons in the moderator has to be considered. Since thermal neutrons are assumed to diffuse isotropically in the moderator, the long
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diffusion length probably causes a large difference of position between where the neutron has been thermalized and where it is detected. This difference worsens the position profile in neutron detection and decreases the energy resolution, in particular when the neutron has been thermalized at an outer part of the moderator. A thermal neutron absorber, therefore, was inserted in the moderator in order to suppress the diffusion and improve the energy resolution. The main functions of the absorber are illustrated in Fig. 3. The most suitable combination of geometry and materials was selected on the basis of the results simulated with the MCNP-4B code. In the simulation a position-sensitive 3He proportional counter 2.54 cm in diameter and a mixed gas of 130 kPa 3He and 70 kPa CF4 were adopted for the thermal neutron detector. This counter can measure the detection position of neutrons with less than 1 cm spatial resolution for an active length of 100 cm [21]. The active region of the counter was divided into cells with 1 cm length along the axis. The number of 3He(n,p)3H reactions in each cell was tallied to obtain the position profile of thermal neutron detection.
4. Results and discussion 4.1. Dimension of moderator 0
10
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30
Fig. 2. Typical response function of the spectrometer.
40
The response functions of the spectrometer for mono-energetic neutrons were calculated with the MCNP-4B code. The results are shown in the semi-logarithmic and linear plots of Fig. 4. In this
Fig. 3. Schematic drawings to explain the principle of suppressing the difference between the position of neutron thermalized and detected with a thermal neutron absorber. The right figure shows how the absorber eliminates the diffusion of thermal neutrons in the moderator and subsequent detection at another, distant axial position.
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Fig. 4. Response functions for a simple cylindrical polyethylene moderator (30 cm in diameter, 100 cm in length) for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 1 keV neutrons; the normalization factors are labeled in the figure.
calculation the moderator was simply made of polyethylene, 30 cm in diameter and 100 cm in length. For neutrons up to 1 MeV, the counts of detected neutrons steeply decreased by more than three orders of magnitude at 40 cm. For higher energy neutrons over 10 MeV, they still decreased, even at 100 cm with a certain slope as seen from the logarithmic plot. An appropriate slope measurement is necessary to obtain a neutron spectrum with good energy resolution for the highenergy neutrons; this determination requires the accumulation of counts over many orders of
magnitude along the axis, but it is difficult to obtain such data in practical measurements. For the 20 MeV neutrons, the counts fell by about three orders of magnitude at 100 cm, as seen in Fig. 4. Hence, we decided the length of the moderator to be 100 cm for obtaining energy information up to 20 MeV. The weight mean position xw ðEÞ, defined in Eq. (1), was derived in order to decide the diameter of the moderator. Fig. 5 shows the relation between the diameter and the xw ðEÞ for monoenergetic neutrons from 1 keV to 20 MeV. A clear separation of the xw ðEÞ indicates good energy resolution by the spectrometer. When the diameter was small, the separation was not clear, especially for the high-energy region. Moreover, the detection efficiency was low because the number of neutrons entering the detector was small. Although a large diameter improves the separation, the uncertainty becomes larger because the spectrum is averaged over a wide area and the weight of the moderator increases in proportion with the square of the diameter. In addition, as the diffusion of thermal neutrons within the moderator is restricted due to the capture reaction in hydrogen, too large a diameter is unprofitable. The diameter should not much exceed the size of the dosemeters to be calibrated in the fields. From these considerations, the suitable diameter for the moderator was determined to be 30 cm.
Fig. 5. Relation between the moderator diameter and the weighted mean position xw ðEÞ of the response functions, defined in Eq. (1), for several mono-energetic neutrons.
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4.2. Structure and materials of moderator When the moderator was made solely of polyethylene, the difference in response functions was not large enough for the low-energy neutrons below 100 keV, as seen in Fig. 4. In order to improve the energy resolution for low-energy neutrons, the structure of the moderator was modified in the following ways. One was the use of a low hydrogen density material in the front part of the moderator. Polycarbonate was selected because it has good processibility and its hydrogen density is about half that of polyethylene. The length of the polycarbonate part was determined as 40 cm because most of the neutrons below 100 keV were thermalized within 40 cm (see Fig. 4). The remaining 60 cm part was made of polyethylene as a high hydrogen density material in order not to reduce the detection efficiency for the high-energy neutrons. Fig. 6(a) and (b) show the response functions for the spectrometer with this moderator using the MCNP-4B code calculated in semilogarithmic and linear plots, respectively. The polycarbonate in the front part of the moderator clearly made the decrease in counts more gradual than in Fig. 4. The differences of the positions xw ðEÞ for 10 eV and 100 keV neutrons were 0.94 and 1.8 cm in Figs. 4 and 6, respectively. This means that the polycarbonate moderator expanded the difference and improved the energy resolution in the low-energy region. For the highenergy neutrons, the differences between 10 and 20 MeV were 3.8 and 1.1 cm in Figs. 4 and 6, respectively, which means that the energy resolution worsened in the high-energy region. However, the neutrons in the keV region are more important than the high-energy region from the viewpoint of the dosimetric quantities, because the coefficient hF rises dramatically in the keV region but does not change much from 10 to 20 MeV. The second consideration was how to suppress the diffusion of the thermal neutrons, which lessens the difference in the response function and worsens the energy resolution. A thermal neutron absorber was inserted into the moderator to suppress the diffusion. The absorber was made of 0.5 mm thick cadmium, and the shape was
Fig. 6. Response functions for the spectrometer with 40 cm polycarbonate and 60 cm polyethylene moderator for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
optimized based on the calculations of the thermal neutron distribution in the moderator. First, using the MCNP-4B code, we calculated the axial and radial distributions of thermal neutrons in the moderator for each energy when a narrow beam of mono-energetic neutrons was incident on the center of the cylindrical moderator parallel to the cylindrical axis. Then we evaluated deviations of the radial distribution and the maximum position, defined in Fig. 2, for each energy. The radial deviations were obtained by fitting the radial distribution with the Gaussian distribution. Since, the absorber prevents the neutron thermalized in
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the outer side from getting into the counter in the center of the spectrometer, it reduces the detection efficiency of the spectrometer. The reduction was influenced by the shape of the absorber. We selected the position of absorber where the deviation was one and a half times the standard deviation of the Gaussian (1:5s) and included 90% of thermal neutrons within the Gaussian, in order to make the reduction in efficiency as small as possible. Fig. 7 shows the radial deviation of 1:5s as a function of the axial position for the polycarbonate and polyethylene moderator, calculated for mono-energetic neutrons in the range of 1 eV–15 MeV. The shape of the absorber was decided as shown by the broken bold line in Fig. 7. The response functions of the spectrometer with the thermal neutron absorber in the polyethylene moderator were calculated, and the results are given in Fig. 8. The difference in the xw ðEÞ between 10 eV and 100 keV neutrons was about 0.99 cm; a little larger than that in Fig. 4 (0.94 cm) but smaller than that in Fig. 6 (1.8 cm). This means that in the case of the polyethylene moderator, the employment of low hydrogen density material in the moderator is more effective than the insertion
Fig. 8. Response functions for the spectrometer with the optimized neutron absorber in a pure polyethylene moderator for different mono-energetic neutrons: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
Fig. 7. Relation between the radial deviation and the maximum position in the distribution of thermal neutrons in the polycarbonate and polyethylene moderator. The distribution was calculated by MCNP-4B. The radial deviation was decided as 1:5s in order to include 90% of the thermal neutron. Solid squares and diamonds indicate the data for mono-energetic neutrons. The bold broken lines show the optimized shapes of cadmium absorbers.
of the thermal neutron absorber to improve the energy resolution in the low-energy region. Then a thermal neutron absorber was inserted into the polycarbonate moderator combined with the polyethylene moderator as shown in Fig. 1. The response functions of the spectrometer with this improved moderator are shown in Fig. 9. The difference in the xw ðEÞ between 10 eV and 100 keV neutrons was about 2.2 cm. The insertion of the absorber was found to be effective in improving the energy resolution in the low-energy region since the difference became larger than that in Fig. 6 (1.8 cm). Between 10 and 20 MeV, the
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two neutron spectra were simulated with the MCNP-4B code. The spectra from a bare and D2O-moderated 252Cf source were selected to demonstrate effectiveness in the MeV and keV regions, respectively. Both spectra used in the simulation were taken from ISO 8529-1 [18]. As first guess spectra, both a flat and the Watt spectrum were used for the 252Cf source and a flat spectrum and the spectrum taken from the ISO 8529-1 were used for the D2O-moderated 252Cf source. Fig. 10(a) and (b) show the unfolded spectra of the bare and D2O-moderated 252Cf sources, respectively. The unfolded results using
Fig. 9. Response functions for the spectrometer with the optimized neutron absorber in the moderator for different mono-energetic neutrons. The moderator consists of a 40 cm polycarbonate and a 60 cm polyethylene, as shown in Fig. 1: (a) a semi-logarithmic plot and (b) a linear plot. In the linear plot the peak heights are normalized to that for 10 eV neutrons; the normalization factors are labeled in the figure.
difference was about 1.0 cm and there was no significant change compared with that in Fig. 6 (1.1 cm). Therefore, we selected this structure for the spectrometer. 4.3. Spectrum unfolding It was demonstrated that the neutron spectra can be obtained from the spectrometer by using the unfolding code SAND-II [22]. The demonstrations were performed by a computer simulation. The responses of the spectrometer for
Fig. 10. Neutron energy spectra unfolded with the SAND-II code: (a) the bare 252Cf spectra and (b) the D2O-moderated 252 Cf spectra. The response of the spectrometer was simulated with the MCNP-4B code using the neutron spectra from the bare and D2O-moderated 252Cf source.
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the Watt spectrum or that taken from ISO 8529-1 as the first guess agreed with the spectrum of the neutron source. Here, these spectra were similar or identical to the ones used as the source spectra in the simulation. Even when the flat spectrum was used as the first guess spectrum, the unfolded spectra were consistent with that of the neutron source in the simulation. This suggests that the spectrometer could measure the neutron spectrum without any information about the neutron source because the flat spectrum contains no spectral information.
5. Summary A moderator for a neutron spectrometer with a cylindrical moderator and a position-sensitive thermal neutron detector was designed with the Monte Carlo code MCNP-4B. Based on our analysis, the diameter and length of the moderator were optimized at 30 and 100 cm, respectively. Because a simple moderator made of polyethylene did not provide good energy resolution in the neutron energy range up to 100 keV, the material and structure of the moderator were modified. A low hydrogen density polycarbonate was used for the first 40 cm of the moderator, and a high hydrogen density polyethylene for the second 60 cm. Additionally, a neutron absorber made of a cadmium sheet was inserted to eliminate the diffusion of thermal neutrons in the moderator. The shape of the absorber was optimized on the basis of the calculated results of the thermal neutron distribution in the moderator. These adjustments improved the energy resolution below 100 keV; this energy is important from the viewpoint of dosimetric quantities because the coefficient hF rises drastically in this energy region. From the demonstration of the spectrum unfolding, the spectrometer could measure the neutron spectra of a bare and D2O-moderated 252Cf source.
Acknowledgements We would like to thank Prof. Emeritus C. Mori of Nagoya University for his helpful discussions on designing the moderator of the spectrometer.
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