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Determination of uranium fission rate in an arbitrary neutron field using fission track detectors
Radiation Measurements 43 (2008) S204 – S209 www.elsevier.com/locate/radmeas
Determination of uranium fission rate in an arbitrary neutron field using fission track detectors S.R. Hashemi-Nezhad a,∗ , I.V. Zhuk b , A.S. Potapenko b , M.I. Krivopustov c , W. Westmeier d , R. Brandt d a School of Physics, A28, University of Sydney, NSW 2006, Australia b Joint Institute of Power and Nuclear Research-Sosny NASB, 220109 Minsk, Belarus c Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation d Fachbereich Chemie, Philipps University, Marburg, Germany
Abstract In accelerator driven systems, particularly near the spallation target, the neutron spectrum covers a very wide range of energies and has a complex angular distribution. It is possible to determine the fission rate of fissionable nuclei in such neutron fields using fission track technique. We use the mean density of fission tracks in the two track detectors in contact with two faces of a fission foil (radiator). A calibration factor, w, relating the number of fission events to the track density is needed and was determined in a very well-known neutron field. It was used to estimate the fission rate in a uranium–lead assembly when the lead target was irradiated with protons of energy 1 GeV. Experimental results are compared with Monte Carlo predictions using MCNPX code. © 2008 Elsevier Ltd. All rights reserved. Keywords: Accelerator driven systems; ADS; Fission rate; Fission tracks; Mica detector; MCNPX code
1. Introduction
2. Determination of the calibration factor
The accelerator driven system (ADS) refers to a sub-critical nuclear assembly in which a chain reaction is sustained by spallation neutrons, produced by interaction of high-energy particles with a heavy nuclei target material. In an ADS, neutrons have a very wide range of energies extending from thermal to several hundred MeV. As the experimental values of the fission cross section for fissionable nuclei relevant to ADS are not known for all required neutron energies, determining the fission rate in these systems without requiring such knowledge is extremely important. Solid state nuclear track detectors (Fleischer et al., 1975) provide one of the best tools for such studies. Track detectors become a useful tool for fission-rate determination only if the fission track density in the detectors could be converted to fission rate via a calibration factor.
We give a brief description of the procedure for determining the calibration factor. For more details see Hashemi-Nezhad et al. (2006). The track density in a track detector in close contact with a foil in which fission events take place is given by the following equation (Malykhin et al., 1970): ∞ f (E)(E) dE (1) = n · · · d · Nv · t
∗ Corresponding author. Tel.: +61 2 93515964; fax: +61 2 93517726.
E-mail address: [email protected] (S.R. Hashemi-Nezhad). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.03.073
0
where is the detectable fission track density at the detector surface (tracks/cm2 ), n is the number of the fragments emitted per fission, d is the thickness of the foil, is an efficiency factor which includes the critical angle effect as well as the limitations imposed by the minimum detectable track size and track observation conditions, Nv is the number of fissionable nuclei per unit volume of the foil, f (E) and (E) are the energy dependent fission cross section and projectile flux, respectively.
S.R. Hashemi-Nezhad et al. / Radiation Measurements 43 (2008) S204 – S209
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Table 1 The experimentally determined calibration factors w in units of (1019 track cm−2 neutron−1 ) for thick fission-foils and different types of track detectors Type of SSNTD
Lavsan (ethylene terephthalate) Natural mica Artificial mica (fluorophlogopite) Soda glass (microscope cover glass)
Etching conditions
Calibration factor w
Etchant
Concentration
Temperature (◦ C)
Etching time (min)
NaOH HF HF HF
10.4 N 20% 7% 2%
60 60 60 20
120 80 25 20
1.18 ± 0.04 1.07 ± 0.04 0.99 ± 0.03 0.59 ± 0.02
Also given are the overall efficiencies of the detectors.
accounts for different foil thicknesses d and the mean range of fission fragments in the foil material R, and is given by the following relations: ⎧1 d ⎪ for d < R 1− ⎪ ⎪ 2R 2 ⎪ ⎪ ⎨ = 1 (2) for d = R ⎪ 4 ⎪ ⎪ ⎪ ⎪1R ⎩ for d > R 4d ∞ In Eq. (1) the quantity t 0 f (E)(E) dE gives the fission per atom of fissionable nuclei in the foil during the irradiation time t. We define a calibration factor w as w = n · · · d · Nv
(3)
This definition of w implies that the ratio of /w represents the number of fissions per atom of fissionable nuclei in the foil during irradiation. Metallic foils of natural uranium and uranium foils with enriched 235 U were used as fissionable materials. These foils had diameter of 7 mm and thickness ∼ 0.1 mm (d > R). The U-foils were placed in close contact between two track detector sheets. The sample irradiations were performed at two standard neutron fields with energies of thermal and 14.7 MeV. After appropriate etching of the detectors (see Table 1) the track density in the detectors were determined and w for each detector was calculated using Eq. (1) and neutron flux in the standard neutron field and known fission cross section values for 238 U and 235 U (Hashemi-Nezhad et al., 2006). The experimental w-values for thick metallic uranium foils and for the four types of track detectors are given in Table 1. All w-values are the mean of those obtained for the track detectors in contact with either of the two faces of the relevant fission foil (Hashemi-Nezhad et al., 2006). It must be noted that the calibration factors reported in Table 1 are valid for the etching and observation conditions used in this work. 3. Determination of natural uranium fission rate 3.1. Experimental setup We used the above technique to measure the fission rate in the “Energy plus Transmutation (EPT)” experimental setup
of the Joint Institute for Nuclear Research (JINR), Dubna, Russia. Figs. 1a and b are schematic drawings of the EPT installation. Detailed description of this setup is given elsewhere (Krivopustov et al., 2004). The EPT system contains four cylindrical lead targets each with diameter 8.4 cm and length 11.4 cm surrounded by a natural uranium blanket. Each uranium blanket is composed of 30 uranium rods of diameter 3.6 cm and length 10.4 cm hermetically sealed in aluminum cladding. The weight of natural uranium in each blanket section is 51.6 kg and whole setup contains a total of 206.4 kg of natural uranium. The four target-blanket sections are aligned along the Z-axis (the target axis) with 0.8 cm gap between the sections. In these gaps are placed activation foils, track detectors and other sensors used in the study of the neutron field within the system. The whole target-blanket system was placed within a wooden container which was then filled with granulated polyethylene of average density 0.7 g cm−3 ; dimensions and the arrangements are shown in Fig. 1. The inner walls of the container were covered with a Cd foil of thickness 1 mm, as shown in Figs. 1a and b. Fig. 2a shows the schematic drawing of a mica–uranium sandwich used for fission-rate determination. Artificial mica track detectors were placed in close contact with a natural uranium foil (fission-foil) of thickness ∼ 0.1 mm similar to the foils used in the calibration experiment. Five of these foil–mica sets were mounted on a sample plate along the positive Y-axis at radial distances R = 0, 3, 6, 8.5, 11 and 13.5 cm as shown in Fig. 2b. Samples at R < 4.2 cm were within target area, the sample with R = 13.5 was outside of the blanket and the rest were within the uranium blanket. Five such plates were prepared and placed in front, back and in the three gaps between the target-blanket sections as shown in Fig. 1a. The five sample plates in Fig. 1a from left to right will be referred to as plates 1–5. The EPT setup was irradiated with protons of energy 1 GeV from the nuclotron accelerator of the JINR. The fluence of the protons was determined by activation of aluminum via the 27 Al(p, 3pn) 24 Na reaction as (2.92 ± 0.11) × 1013 protons. The proton beam intensity distributions along the X- and Y-axis were found using the nat Pb(p, f) reaction in conjunction with mica track detectors (Zhuk et al., 2006). It was found that beam distributions along both the X- and Y-axes could be explained with Gaussian distribution with beam center
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Fig. 1. Schematic drawings of the “Energy plus Transmutation” experimental setup: (a) YZ cross section and (b) XY cross section.
3.2. Monte Carlo calculations
Fig. 2. (a) Natural uranium and artificial mica sandwich used for fission-rate determination and (b) a sample plate containing five U-mica samples along the Y -axis at radial distances R = 0, 3, 6, 8.5, 11 and 13.5 cm. Samples at R < 4.2 cm are within the target area and sample with R = 13.5 is outside of the uranium blanket and rest are within the blanket. The schematic drawings are not to the scale.
coordinates of Xc = 0.06 cm and Yc = 0.33 cm. The full width at half maximum for Gaussian distributions along the X- and Y-axes was 2.3 and 3.3 cm, respectively. After exposure, the track detectors were etched in 7% HF at 60 ◦ C for a period of 25 min. To obtain an accurate measure of the track density many photographic images of each sample r were made using an optical microscope and tracks in each image were counted manually. For each foil, the mean of track densities was determined in the two mica detectors of the unit, one on each side.
We used MCNPX 2.5e (beta version) Monte Carlo (MC) code (Hendricks et al., 2004) to simulate the behavior of neutrons and other secondary particles in the experimental setup. In the MCNPX calculations, neutrons, protons, pions and photons were transported. The high energy data tables for neutrons and protons were used whenever available (Chadwick et al., 1999); otherwise data tables of the ENDF/B-VI libraries were used. In all calculations the statistical uncertainties were less than ±3% except for the case of the proton- and pioninduced fission events at large radial distances where fluxes of these particles were very low and the calculation statistics were about ±6%. Fig. 3 shows some of the MCNPX results on the neutronics of the EPT setup at incident proton energy of 1 GeV. In Fig. 3a the angular distribution of the neutrons crossing the sample plate 2 at Z = 11.8 cm is shown. The horizontal axis in Fig. 3a refers to the angle of the neutron directions with target axis. The angular intervals 0–90◦ and 90–180◦ refer to the neutrons that travel in upstream and downstream directions. From Fig. 3a it is evident that directions of the neutrons are not isotropic and majority of the neutrons cross the surface at angles of ∼ 50◦ and 140◦ . Fig. 3b illustrates the energy spectrum of the neutrons in the entire uranium blanket. The neutron spectrum in the blanket region of the EPT is dominated by epithermal, fast and “superfast” neutrons. Fig. 3c shows natural uranium fission rate in the entire blanket as a function of neutron energy. The calculations showed that in the entire blanket 2.07% of fission events are induced
S.R. Hashemi-Nezhad et al. / Radiation Measurements 43 (2008) S204 – S209
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Fig. 3. (a) Angular distribution of the neutrons that cross the plate located within the gap between the 1st and 2nd blankets. (b) Energy distribution of the neutrons in the uranium blanket. (c) Average fission rate in the blanket.
by neutrons of energy En 1 eV, 1.78% induced by neutrons of 1 eV < En 100 keV and 96.15% induced by neutrons of En > 100 keV. This implies that the spatial distribution of the natural uranium fission rate in the EPT setup is determined, predominantly, by the distribution of the neutrons with E > 100 keV in the system. 3.3. Fission-rate determination results As shown in Fig. 3 the neutrons that induce fission in uranium have energies that extend from thermal to ∼ 1 GeV and their
angle of incidence to the surfaces of the fission-foils are not isotropic. The calibration factors given in Table 1 have been obtained using thermal and 14.7 MeV neutrons in the standard neutron fields. In the case of the thermal neutrons their angle of incidence to the fission foil was random while in the case of the 14.7 MeV neutrons their directions were normal to the fissionfoil surface. It is shown that a w obtained via low energy particle induced fission can be used for determining the fission rate in a neutron field of unknown characteristics (energy and angular distribution) if in the determination of w and in its subsequent use the mean density of the tracks in the track detectors on
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Fig. 4. Variations of the calculated and experimentally obtained natural uranium fission rate with radial distance R for five sample plates used in the experiment. The data are shown for the case when the EPT setup was irradiated with protons of energy 1 GeV. Fig. 4b is same as Fig. 4a with the difference that in 4b the vertical axis is expanded and only data points for R 4 cm are shown. The MC-fission rates are the same as those of the experiment include the proton, neutron and pion-induced fission events.
either side of the fission foil is used (Hashemi-Nezhad et al., 2006). Using the value w = (9.9 ± 0.03) × 1018 track/(cm2 neutron) for thick uranium foil and artificial mica system, the mean track density of each fission foil was converted to fission rates for total proton fluence of (2.92 ± 0.11) × 1013 . Fig. 4 shows the variations of the experimental and calculated fission rates as a function of radial distance from the target axis for all five sample plates used in the experiment. As protons and pions also induce fission in uranium, the MC calculations take into account the contribution of these particles to fission in natural (Hashemi-Nezhad et al., 2008). Contribution of the pion-induced fission to total fission rate was negligible. Due to the very high fluence of the incident protons (2.92 ± 0.11) × 1013 , and the secondary particles produced, the track densities in the mica detectors in samples at R < 4.2 cm (target area) were very high (as high as 4 × 107 tracks/cm2 ). For this type of sample track density measurements were less accurate and in some cases were meaningless because of large number of overlapping tracks. The experimental uncertainties result from the errors in (i) proton fluence 3.8%, (ii) calibration factor 3%, (iii) radial distance R—MC calculations showed that an error of 2 mm in R results in 1.5% to 7% uncertainty in the fission-rate values—and
(iv) track density measurements which is in the range of 5–50% depending on the track population in the mica detector. In Fig. 4 the experimental uncertainties are shown at 1 level. In the blanket region (R > 4.2 cm) and for plates 2, 3 and 4 the experimental results and calculations are in agreement within the experimental uncertainties. However this is not the case for samples in plates 1 and 5; especially for plate 1 in which the experimental and calculated results deviate by up to 75% as shown in Fig. 4b (same as the Fig. 4a but with expanded vertical axis). In plate 5, the difference between the MC and the experimental fission rate is in the range of 4–34% for the all R-values. Reasons for such large discrepancies in plates 1 and 5 are under investigation. For plates 1 and 5 the experimental and calculated results are in agreement at 2 level. 3.4. Fission rate in the EPT assembly Due to the large experimental errors in the track density measurements in samples from plate 1, these samples are not included in the following calculations. The mean value of the fission rate in all MC samples in the blanket area and in plates 2–5 is (5.76±0.84)×10−27 fission/atom/proton. Taking into account the mass of the natural uranium in the blanket (206.4 kg) one obtains (3.00 ± 0.44) fission/proton in the whole blanket.
S.R. Hashemi-Nezhad et al. / Radiation Measurements 43 (2008) S204 – S209
If we use only MC samples in locations identical to those of experimental setup we obtain (2.93 ± 0.69) fission/proton. A direct MC calculation of the fission rate in the whole blanket, predicts (2.67 ± 0.08) neutron-induced fissions and (0.16 ± 0.01) proton-induced fissions, which results in total number of (2.83 ± 0.08) fission/proton. This value is in agreement with that obtained from the mean fission rate of the MC samples in the blanket area. From the mean value of the fission rates in the experimental samples in the blanket region and in plates 2–5, we obtain the overall fission rate of (3.41±0.73) fission/proton which, within experimental uncertainties, is in agreement with MC prediction of (2.83 ± 0.08) fission/proton. 4. Conclusions Fission rate of natural uranium in spallation-fission neutron field of the “Energy plus Transmutation (EPT)” setup of the JINR was measured when the target was irradiated with protons of energy 1 GeV. The natural uranium foils in conjunction with artificial mica were used for recoding fission tracks from fission events induced by primary and secondary particles. A calibration factor for nat U-mica system determined in a standard neutron field was used to convert fission-track densities to fission-rate values. The behavior of the primary and secondary particles in the system was simulated using MCNPX 2.5e Monte Carlo Code. It was found that within the experimental uncertainties, the experimental and calculated fission rates for samples placed in plates 2–4 are in agreement, while this is not the case for plates 1 and 5 and especially plate 1. The overall fission rate in the natural uranium blanket of the EPT assembly was calculated from the mean of the experimental fission rates in the samples within the blanket area in plates 2–5 as (2.63 ± 0.51) which is in agreement with Monte Carlo prediction of (2.83 ± 0.08) fission/proton. Acknowledgments We would like to thank Veksler and Baldin Laboratory of High Energies (VBLHE), Joint Institute for Nuclear Research
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(JINR), Dubna, Russia, and staff of the Nuclotron accelerator for providing us the research facilities used in these experiments. SRH-N would like to thank the Department of Education, Science and Training of the Government of Australia for the AMRFP grant and the School of Physics, University of Sydney for Denison research grant in support of this work. References Chadwick, M.B., Young, P.G., Chiba, S., Frankle, S.C., Hale, G.M., Hughes, H.G., Koning, A.J., Little, R.C., MacFarlane, R.E., Prael, R.E., Waters, L.S., 1999. Cross section evaluations to 150 MeV for accelerator-driven systems and implementation in MCNPX. Nucl. Sci. Eng. 131, 293. Fleischer, R.L., Price, P.B., Walker, R.M., 1975. Nuclear Tracks in Solids. University of California Press, Hashemi-Nezhad, S.R., Zhuk, I., Potapenko, A.S., Krivopustov, M.I., 2006. Calibration of track detectors for fission rate determination: an experimental and theoretical study. JINR report E1-2006-54. Nucl. Instrum. Methods Phys. Res. A 568, 816–825. Hashemi-Nezhad, S.R., Zhuk, I., Kievets, M., Krivopustov, M.I., Sosnin, A.N., Westmeier, W., Brandt, R., 2008. Determination of natural uranium 47 fission rate in fast spallation neutron field: an experimental and Monte Carlo studies. Nucl. Instrum. Methods A, in press, doi:10.1016/j.nima. 2008.02.101. Hendricks, J.S., McKinney, G.W., Waters, L.S., Roberts, T.L., Egdorf, H.W., Finch, J.P., Trellue, H.R., Pitcher, E.J., Mayo, D.R., Swinhoe, M.T., Tobin, S.J., Gallmeier, F.X., David, J.-C., Hamilton, W.B., Lebenhaft, J., 2004. MCNPX, VERSION 2.5.e, Report No. LA-UR-04-0569, Los Alamos National Laboratory. Krivopustov, M.I., Adam, J., Balabekyan, A.R., Batusov, Y.A., Bielewicz, M., Brandt, R., Chaloun, P., Chultem, D., Elishev, A.F., Fragopoulou, M.V., Henzl, V., Henzlová, D., Kalinnikov, G., Kievets, M.K., Krása, A., Krizek, F., Kugler, A., Manolopoulou, M., Mariin, I.I., Odoj, R., Pavlyuk, A.V., Pronskikh, V.S., Robotham, H., Siemon, K., Szuta, M., Stegailov, V.I., Solnyshkin, A.A., Sosnin, A.N., Stoulos, S., Tsoupko-Sitnikov, V.M., Tumendelger, T., Wojecehowski, A., Wagner, V., Westmeier, W., ZamaniValasiadou, M., Zaveryukha, O.S., Zhuk, I.V., 2004. Investigation of neutron spectra and transmutation studies of 129I, 237Np and other nuclides with 1.5 GeV protons from the nuclotron. JINR preprint E1-200479. Malykhin, A.P., Yaroshevich, O.I., Levadni, V.A., Roginetc, L.P., 1970. Measurement of fission density distributions on critical facilities by solid track detector method. Vestsi AS BSSR Ser. Phys.-Energ. Navuk 2, 16– 23 (in Russian). Zhuk, I.V., Hashemi-Nezhad, S.R., Potapenko, A.S., Krivopustov, M.I., 2006. Determination of high-energy proton beam profile using track detectors. This Conference.
Determination of uranium fission rate in an arbitrary neutron field using fission track detectors S.R. Hashemi-Nezhad a,∗ , I.V. Zhuk b , A.S. Potapenko b , M.I. Krivopustov c , W. Westmeier d , R. Brandt d a School of Physics, A28, University of Sydney, NSW 2006, Australia b Joint Institute of Power and Nuclear Research-Sosny NASB, 220109 Minsk, Belarus c Joint Institute for Nuclear Research, 141980 Dubna, Russian Federation d Fachbereich Chemie, Philipps University, Marburg, Germany
Abstract In accelerator driven systems, particularly near the spallation target, the neutron spectrum covers a very wide range of energies and has a complex angular distribution. It is possible to determine the fission rate of fissionable nuclei in such neutron fields using fission track technique. We use the mean density of fission tracks in the two track detectors in contact with two faces of a fission foil (radiator). A calibration factor, w, relating the number of fission events to the track density is needed and was determined in a very well-known neutron field. It was used to estimate the fission rate in a uranium–lead assembly when the lead target was irradiated with protons of energy 1 GeV. Experimental results are compared with Monte Carlo predictions using MCNPX code. © 2008 Elsevier Ltd. All rights reserved. Keywords: Accelerator driven systems; ADS; Fission rate; Fission tracks; Mica detector; MCNPX code
1. Introduction
2. Determination of the calibration factor
The accelerator driven system (ADS) refers to a sub-critical nuclear assembly in which a chain reaction is sustained by spallation neutrons, produced by interaction of high-energy particles with a heavy nuclei target material. In an ADS, neutrons have a very wide range of energies extending from thermal to several hundred MeV. As the experimental values of the fission cross section for fissionable nuclei relevant to ADS are not known for all required neutron energies, determining the fission rate in these systems without requiring such knowledge is extremely important. Solid state nuclear track detectors (Fleischer et al., 1975) provide one of the best tools for such studies. Track detectors become a useful tool for fission-rate determination only if the fission track density in the detectors could be converted to fission rate via a calibration factor.
We give a brief description of the procedure for determining the calibration factor. For more details see Hashemi-Nezhad et al. (2006). The track density in a track detector in close contact with a foil in which fission events take place is given by the following equation (Malykhin et al., 1970): ∞ f (E)(E) dE (1) = n · · · d · Nv · t
∗ Corresponding author. Tel.: +61 2 93515964; fax: +61 2 93517726.
E-mail address: [email protected] (S.R. Hashemi-Nezhad). 1350-4487/$ - see front matter © 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2008.03.073
0
where is the detectable fission track density at the detector surface (tracks/cm2 ), n is the number of the fragments emitted per fission, d is the thickness of the foil, is an efficiency factor which includes the critical angle effect as well as the limitations imposed by the minimum detectable track size and track observation conditions, Nv is the number of fissionable nuclei per unit volume of the foil, f (E) and (E) are the energy dependent fission cross section and projectile flux, respectively.
S.R. Hashemi-Nezhad et al. / Radiation Measurements 43 (2008) S204 – S209
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Table 1 The experimentally determined calibration factors w in units of (1019 track cm−2 neutron−1 ) for thick fission-foils and different types of track detectors Type of SSNTD
Lavsan (ethylene terephthalate) Natural mica Artificial mica (fluorophlogopite) Soda glass (microscope cover glass)
Etching conditions
Calibration factor w
Etchant
Concentration
Temperature (◦ C)
Etching time (min)
NaOH HF HF HF
10.4 N 20% 7% 2%
60 60 60 20
120 80 25 20
1.18 ± 0.04 1.07 ± 0.04 0.99 ± 0.03 0.59 ± 0.02
Also given are the overall efficiencies of the detectors.
accounts for different foil thicknesses d and the mean range of fission fragments in the foil material R, and is given by the following relations: ⎧1 d ⎪ for d < R 1− ⎪ ⎪ 2R 2 ⎪ ⎪ ⎨ = 1 (2) for d = R ⎪ 4 ⎪ ⎪ ⎪ ⎪1R ⎩ for d > R 4d ∞ In Eq. (1) the quantity t 0 f (E)(E) dE gives the fission per atom of fissionable nuclei in the foil during the irradiation time t. We define a calibration factor w as w = n · · · d · Nv
(3)
This definition of w implies that the ratio of /w represents the number of fissions per atom of fissionable nuclei in the foil during irradiation. Metallic foils of natural uranium and uranium foils with enriched 235 U were used as fissionable materials. These foils had diameter of 7 mm and thickness ∼ 0.1 mm (d > R). The U-foils were placed in close contact between two track detector sheets. The sample irradiations were performed at two standard neutron fields with energies of thermal and 14.7 MeV. After appropriate etching of the detectors (see Table 1) the track density in the detectors were determined and w for each detector was calculated using Eq. (1) and neutron flux in the standard neutron field and known fission cross section values for 238 U and 235 U (Hashemi-Nezhad et al., 2006). The experimental w-values for thick metallic uranium foils and for the four types of track detectors are given in Table 1. All w-values are the mean of those obtained for the track detectors in contact with either of the two faces of the relevant fission foil (Hashemi-Nezhad et al., 2006). It must be noted that the calibration factors reported in Table 1 are valid for the etching and observation conditions used in this work. 3. Determination of natural uranium fission rate 3.1. Experimental setup We used the above technique to measure the fission rate in the “Energy plus Transmutation (EPT)” experimental setup
of the Joint Institute for Nuclear Research (JINR), Dubna, Russia. Figs. 1a and b are schematic drawings of the EPT installation. Detailed description of this setup is given elsewhere (Krivopustov et al., 2004). The EPT system contains four cylindrical lead targets each with diameter 8.4 cm and length 11.4 cm surrounded by a natural uranium blanket. Each uranium blanket is composed of 30 uranium rods of diameter 3.6 cm and length 10.4 cm hermetically sealed in aluminum cladding. The weight of natural uranium in each blanket section is 51.6 kg and whole setup contains a total of 206.4 kg of natural uranium. The four target-blanket sections are aligned along the Z-axis (the target axis) with 0.8 cm gap between the sections. In these gaps are placed activation foils, track detectors and other sensors used in the study of the neutron field within the system. The whole target-blanket system was placed within a wooden container which was then filled with granulated polyethylene of average density 0.7 g cm−3 ; dimensions and the arrangements are shown in Fig. 1. The inner walls of the container were covered with a Cd foil of thickness 1 mm, as shown in Figs. 1a and b. Fig. 2a shows the schematic drawing of a mica–uranium sandwich used for fission-rate determination. Artificial mica track detectors were placed in close contact with a natural uranium foil (fission-foil) of thickness ∼ 0.1 mm similar to the foils used in the calibration experiment. Five of these foil–mica sets were mounted on a sample plate along the positive Y-axis at radial distances R = 0, 3, 6, 8.5, 11 and 13.5 cm as shown in Fig. 2b. Samples at R < 4.2 cm were within target area, the sample with R = 13.5 was outside of the blanket and the rest were within the uranium blanket. Five such plates were prepared and placed in front, back and in the three gaps between the target-blanket sections as shown in Fig. 1a. The five sample plates in Fig. 1a from left to right will be referred to as plates 1–5. The EPT setup was irradiated with protons of energy 1 GeV from the nuclotron accelerator of the JINR. The fluence of the protons was determined by activation of aluminum via the 27 Al(p, 3pn) 24 Na reaction as (2.92 ± 0.11) × 1013 protons. The proton beam intensity distributions along the X- and Y-axis were found using the nat Pb(p, f) reaction in conjunction with mica track detectors (Zhuk et al., 2006). It was found that beam distributions along both the X- and Y-axes could be explained with Gaussian distribution with beam center
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S.R. Hashemi-Nezhad et al. / Radiation Measurements 43 (2008) S204 – S209
Fig. 1. Schematic drawings of the “Energy plus Transmutation” experimental setup: (a) YZ cross section and (b) XY cross section.
3.2. Monte Carlo calculations
Fig. 2. (a) Natural uranium and artificial mica sandwich used for fission-rate determination and (b) a sample plate containing five U-mica samples along the Y -axis at radial distances R = 0, 3, 6, 8.5, 11 and 13.5 cm. Samples at R < 4.2 cm are within the target area and sample with R = 13.5 is outside of the uranium blanket and rest are within the blanket. The schematic drawings are not to the scale.
coordinates of Xc = 0.06 cm and Yc = 0.33 cm. The full width at half maximum for Gaussian distributions along the X- and Y-axes was 2.3 and 3.3 cm, respectively. After exposure, the track detectors were etched in 7% HF at 60 ◦ C for a period of 25 min. To obtain an accurate measure of the track density many photographic images of each sample r were made using an optical microscope and tracks in each image were counted manually. For each foil, the mean of track densities was determined in the two mica detectors of the unit, one on each side.
We used MCNPX 2.5e (beta version) Monte Carlo (MC) code (Hendricks et al., 2004) to simulate the behavior of neutrons and other secondary particles in the experimental setup. In the MCNPX calculations, neutrons, protons, pions and photons were transported. The high energy data tables for neutrons and protons were used whenever available (Chadwick et al., 1999); otherwise data tables of the ENDF/B-VI libraries were used. In all calculations the statistical uncertainties were less than ±3% except for the case of the proton- and pioninduced fission events at large radial distances where fluxes of these particles were very low and the calculation statistics were about ±6%. Fig. 3 shows some of the MCNPX results on the neutronics of the EPT setup at incident proton energy of 1 GeV. In Fig. 3a the angular distribution of the neutrons crossing the sample plate 2 at Z = 11.8 cm is shown. The horizontal axis in Fig. 3a refers to the angle of the neutron directions with target axis. The angular intervals 0–90◦ and 90–180◦ refer to the neutrons that travel in upstream and downstream directions. From Fig. 3a it is evident that directions of the neutrons are not isotropic and majority of the neutrons cross the surface at angles of ∼ 50◦ and 140◦ . Fig. 3b illustrates the energy spectrum of the neutrons in the entire uranium blanket. The neutron spectrum in the blanket region of the EPT is dominated by epithermal, fast and “superfast” neutrons. Fig. 3c shows natural uranium fission rate in the entire blanket as a function of neutron energy. The calculations showed that in the entire blanket 2.07% of fission events are induced
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Fig. 3. (a) Angular distribution of the neutrons that cross the plate located within the gap between the 1st and 2nd blankets. (b) Energy distribution of the neutrons in the uranium blanket. (c) Average fission rate in the blanket.
by neutrons of energy En 1 eV, 1.78% induced by neutrons of 1 eV < En 100 keV and 96.15% induced by neutrons of En > 100 keV. This implies that the spatial distribution of the natural uranium fission rate in the EPT setup is determined, predominantly, by the distribution of the neutrons with E > 100 keV in the system. 3.3. Fission-rate determination results As shown in Fig. 3 the neutrons that induce fission in uranium have energies that extend from thermal to ∼ 1 GeV and their
angle of incidence to the surfaces of the fission-foils are not isotropic. The calibration factors given in Table 1 have been obtained using thermal and 14.7 MeV neutrons in the standard neutron fields. In the case of the thermal neutrons their angle of incidence to the fission foil was random while in the case of the 14.7 MeV neutrons their directions were normal to the fissionfoil surface. It is shown that a w obtained via low energy particle induced fission can be used for determining the fission rate in a neutron field of unknown characteristics (energy and angular distribution) if in the determination of w and in its subsequent use the mean density of the tracks in the track detectors on
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Fig. 4. Variations of the calculated and experimentally obtained natural uranium fission rate with radial distance R for five sample plates used in the experiment. The data are shown for the case when the EPT setup was irradiated with protons of energy 1 GeV. Fig. 4b is same as Fig. 4a with the difference that in 4b the vertical axis is expanded and only data points for R 4 cm are shown. The MC-fission rates are the same as those of the experiment include the proton, neutron and pion-induced fission events.
either side of the fission foil is used (Hashemi-Nezhad et al., 2006). Using the value w = (9.9 ± 0.03) × 1018 track/(cm2 neutron) for thick uranium foil and artificial mica system, the mean track density of each fission foil was converted to fission rates for total proton fluence of (2.92 ± 0.11) × 1013 . Fig. 4 shows the variations of the experimental and calculated fission rates as a function of radial distance from the target axis for all five sample plates used in the experiment. As protons and pions also induce fission in uranium, the MC calculations take into account the contribution of these particles to fission in natural (Hashemi-Nezhad et al., 2008). Contribution of the pion-induced fission to total fission rate was negligible. Due to the very high fluence of the incident protons (2.92 ± 0.11) × 1013 , and the secondary particles produced, the track densities in the mica detectors in samples at R < 4.2 cm (target area) were very high (as high as 4 × 107 tracks/cm2 ). For this type of sample track density measurements were less accurate and in some cases were meaningless because of large number of overlapping tracks. The experimental uncertainties result from the errors in (i) proton fluence 3.8%, (ii) calibration factor 3%, (iii) radial distance R—MC calculations showed that an error of 2 mm in R results in 1.5% to 7% uncertainty in the fission-rate values—and
(iv) track density measurements which is in the range of 5–50% depending on the track population in the mica detector. In Fig. 4 the experimental uncertainties are shown at 1 level. In the blanket region (R > 4.2 cm) and for plates 2, 3 and 4 the experimental results and calculations are in agreement within the experimental uncertainties. However this is not the case for samples in plates 1 and 5; especially for plate 1 in which the experimental and calculated results deviate by up to 75% as shown in Fig. 4b (same as the Fig. 4a but with expanded vertical axis). In plate 5, the difference between the MC and the experimental fission rate is in the range of 4–34% for the all R-values. Reasons for such large discrepancies in plates 1 and 5 are under investigation. For plates 1 and 5 the experimental and calculated results are in agreement at 2 level. 3.4. Fission rate in the EPT assembly Due to the large experimental errors in the track density measurements in samples from plate 1, these samples are not included in the following calculations. The mean value of the fission rate in all MC samples in the blanket area and in plates 2–5 is (5.76±0.84)×10−27 fission/atom/proton. Taking into account the mass of the natural uranium in the blanket (206.4 kg) one obtains (3.00 ± 0.44) fission/proton in the whole blanket.
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If we use only MC samples in locations identical to those of experimental setup we obtain (2.93 ± 0.69) fission/proton. A direct MC calculation of the fission rate in the whole blanket, predicts (2.67 ± 0.08) neutron-induced fissions and (0.16 ± 0.01) proton-induced fissions, which results in total number of (2.83 ± 0.08) fission/proton. This value is in agreement with that obtained from the mean fission rate of the MC samples in the blanket area. From the mean value of the fission rates in the experimental samples in the blanket region and in plates 2–5, we obtain the overall fission rate of (3.41±0.73) fission/proton which, within experimental uncertainties, is in agreement with MC prediction of (2.83 ± 0.08) fission/proton. 4. Conclusions Fission rate of natural uranium in spallation-fission neutron field of the “Energy plus Transmutation (EPT)” setup of the JINR was measured when the target was irradiated with protons of energy 1 GeV. The natural uranium foils in conjunction with artificial mica were used for recoding fission tracks from fission events induced by primary and secondary particles. A calibration factor for nat U-mica system determined in a standard neutron field was used to convert fission-track densities to fission-rate values. The behavior of the primary and secondary particles in the system was simulated using MCNPX 2.5e Monte Carlo Code. It was found that within the experimental uncertainties, the experimental and calculated fission rates for samples placed in plates 2–4 are in agreement, while this is not the case for plates 1 and 5 and especially plate 1. The overall fission rate in the natural uranium blanket of the EPT assembly was calculated from the mean of the experimental fission rates in the samples within the blanket area in plates 2–5 as (2.63 ± 0.51) which is in agreement with Monte Carlo prediction of (2.83 ± 0.08) fission/proton. Acknowledgments We would like to thank Veksler and Baldin Laboratory of High Energies (VBLHE), Joint Institute for Nuclear Research
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(JINR), Dubna, Russia, and staff of the Nuclotron accelerator for providing us the research facilities used in these experiments. SRH-N would like to thank the Department of Education, Science and Training of the Government of Australia for the AMRFP grant and the School of Physics, University of Sydney for Denison research grant in support of this work. References Chadwick, M.B., Young, P.G., Chiba, S., Frankle, S.C., Hale, G.M., Hughes, H.G., Koning, A.J., Little, R.C., MacFarlane, R.E., Prael, R.E., Waters, L.S., 1999. Cross section evaluations to 150 MeV for accelerator-driven systems and implementation in MCNPX. Nucl. Sci. Eng. 131, 293. Fleischer, R.L., Price, P.B., Walker, R.M., 1975. Nuclear Tracks in Solids. University of California Press, Hashemi-Nezhad, S.R., Zhuk, I., Potapenko, A.S., Krivopustov, M.I., 2006. Calibration of track detectors for fission rate determination: an experimental and theoretical study. JINR report E1-2006-54. Nucl. Instrum. Methods Phys. Res. A 568, 816–825. Hashemi-Nezhad, S.R., Zhuk, I., Kievets, M., Krivopustov, M.I., Sosnin, A.N., Westmeier, W., Brandt, R., 2008. Determination of natural uranium 47 fission rate in fast spallation neutron field: an experimental and Monte Carlo studies. Nucl. Instrum. Methods A, in press, doi:10.1016/j.nima. 2008.02.101. Hendricks, J.S., McKinney, G.W., Waters, L.S., Roberts, T.L., Egdorf, H.W., Finch, J.P., Trellue, H.R., Pitcher, E.J., Mayo, D.R., Swinhoe, M.T., Tobin, S.J., Gallmeier, F.X., David, J.-C., Hamilton, W.B., Lebenhaft, J., 2004. MCNPX, VERSION 2.5.e, Report No. LA-UR-04-0569, Los Alamos National Laboratory. Krivopustov, M.I., Adam, J., Balabekyan, A.R., Batusov, Y.A., Bielewicz, M., Brandt, R., Chaloun, P., Chultem, D., Elishev, A.F., Fragopoulou, M.V., Henzl, V., Henzlová, D., Kalinnikov, G., Kievets, M.K., Krása, A., Krizek, F., Kugler, A., Manolopoulou, M., Mariin, I.I., Odoj, R., Pavlyuk, A.V., Pronskikh, V.S., Robotham, H., Siemon, K., Szuta, M., Stegailov, V.I., Solnyshkin, A.A., Sosnin, A.N., Stoulos, S., Tsoupko-Sitnikov, V.M., Tumendelger, T., Wojecehowski, A., Wagner, V., Westmeier, W., ZamaniValasiadou, M., Zaveryukha, O.S., Zhuk, I.V., 2004. Investigation of neutron spectra and transmutation studies of 129I, 237Np and other nuclides with 1.5 GeV protons from the nuclotron. JINR preprint E1-200479. Malykhin, A.P., Yaroshevich, O.I., Levadni, V.A., Roginetc, L.P., 1970. Measurement of fission density distributions on critical facilities by solid track detector method. Vestsi AS BSSR Ser. Phys.-Energ. Navuk 2, 16– 23 (in Russian). Zhuk, I.V., Hashemi-Nezhad, S.R., Potapenko, A.S., Krivopustov, M.I., 2006. Determination of high-energy proton beam profile using track detectors. This Conference.