Applied Radiation and Isotopes 90 (2014) 192–196
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
The design of a multisource americium–beryllium (Am–Be) neutron irradiation facility using MCNP for the neutronic performance calculation R.B.M. Sogbadji a,b,n, R.G. Abrefah a, B.J.B. Nyarko a,b, E.H.K. Akaho a, H.C. Odoi a, S. Attakorah-Birinkorang a a b
University of Ghana, School of Nuclear and Allied Science, P.O. Box AE1, Atomic Energy, Accra, Ghana Ghana Atomic Energy Commission, National Nuclear Research Institute, P.O. Box LG80, Legon, Ghana
H I G H L I G H T S
Thermal neutron flux for single Am–Be source varies at different position. The proposed channel has higher neutron flux than the existing channels being used. Multi source Am–Be was design has neutron flux more than three folds that of the single source. NAA and PGNAA were experiment discovered to be feasible for this new design. Research institutes that cannot purchase research reactor could adopt the Multi source Am–Be design.
art ic l e i nf o
a b s t r a c t
Article history: Received 17 December 2013 Received in revised form 7 March 2014 Accepted 10 March 2014 Available online 13 April 2014
The americium–beryllium neutron irradiation facility at the National Nuclear Research Institute (NNRI), Ghana, was re-designed with four 20 Ci sources using Monte Carlo N-Particle (MCNP) code to investigate the maximum amount of flux that is produced by the combined sources. The results were compared with a single source Am–Be irradiation facility. The main objective was to enable us to harness the maximum amount of flux for the optimization of neutron activation analysis and to enable smaller sample sized samples to be irradiated. Using MCNP for the design construction and neutronic performance calculation, it was realized that the single-source Am–Be design produced a thermal neutron flux of (1.87 0.0007) 106 n=cm2 s and the four-source Am–Be design produced a thermal neutron flux of (5.4 70.0007) 106 n=cm2 s which is a factor of 3.5 fold increase compared to the single-source Am–Be design. The criticality effective, keff, of the single-source and the four-source Am–Be designs were found to be 0.00115 7 0.0008 and 0.001437 0.0008, respectively. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Neutron flux Americium‐Beryllium source Thermal Neutrons Multi-source irradiation
1. Introduction It is possible to fabricate a small self-contained neutron source by mixing an alpha emitter isotope with a suitable target material because energetic alpha particles are available from the direct decay of a number of conveniently available radionuclides. Several different target materials can lead to the (α, n) reaction with the alpha particle energies that are readily available in radioactive decay. The
n
Corresponding author. E-mail address: [email protected] (R.B.M. Sogbadji).
http://dx.doi.org/10.1016/j.apradiso.2014.03.017 0969-8043/& 2014 Elsevier Ltd. All rights reserved.
maximum neutron yield is obtained when beryllium is chosen as the target and produces neutrons through the reaction (Knoll, 1989). 9 4 4 Beþ 2 p
1 -12 6 C þ 0n
ð1Þ
Most of the alpha particles simply are stopped in the target and only 1 in approximately 104 reacts with a beryllium nucleus. The same yield can be obtained from a mixture of the alpha particle emitter and beryllium provided the alpha emitter is homogeneously distributed throughout the beryllium in a small relative concentration. All of the alpha emitters of practical interest are actinide elements and investigations have shown that a stable alloy can be formed between the actinide and the beryllium. There are several choices for alpha emitters. However, the choice is
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
primarily based on availability, cost and half-life. Preferably, the half-life should be as short as possible and consistent with application so that the specific activity of the emitter is high. The Am–Be source is probably the most widely used of the (α, n) isotropic neutron sources. To increase the neutron yield without increasing the physical source, alpha emitters with higher specific activities are used. Therefore, sources incorporate 241Am (half-life of 433 yr) for high neutron yields (Knoll, 1989). The Am–Be neutron source is widely employed as a calibration source for neutron instrumentation, and as a portable source for a variety of applications. It is well known that the neutron source also gives off penetrating γ-rays of 4.438 MeV that are mainly associated with the neutron group leaving 12C in the first excited state in the 9Be(α, n)12C reaction. There is a compacted mixture of AmO2 and 9Be fine powder in the source construction. It is obvious that the cluster size, mixture ratio and compacted density of the active zone and the physical size of the source have strong influence on the neutron yield and the finer structure of the emerging neutron spectrum (Lui et al., 2007). The IAEA supplied and installed a 20 Ci 241Am–Be neutron irradiation facility at the National Nuclear Research Institute (NNRI) of the Ghana Atomic Energy Commission in 1977 for Neutron Activation Analyses (NAA) (Osae and Amoh, 1996; Osae and AkotoBamford, 1986; Tetteh, 1980). Figs. 1 and 2 show schematic diagrams of the Am–Be source at NNRI. The main advantage of the Am–Be neutron source irradiator is its very stable neutron flux, thus eliminating the need for a standard material in the measurement of induced activity in samples (Zevallos-Chávez and Zamboni, 2005). The main objective of this research was to redesign the Am–Be neutron source with multiple sources to increase the thermal flux of the Am–Be neutron source. This will enable us to reduce the physical size of samples being irradiated (the existing Am–Be neutron source produces a relatively small thermal flux; as such large samples must be irradiated to obtain good sensitivity). The Am–Be neutron source is an important neutron source for neutron activation analyses. It is relatively inexpensive, easy to shield and portable in addition to producing a stable neutron flux.
193
2. Methodology The simulation of the neutron particle histories was performed in the computer simulation laboratory at NNRI in March, 2011. The first Am–Be source design contained an AmO2 compound in a mixture of beryllium powder in a double layered stainless steel shell (Lui et al., 2007). The source was surrounded by water for moderation and for a shielding effect. The MCNP5 program was used to model 36 irradiation channels in a concentric ring pattern around the source in other to monitor the neutron fluxes in all directions. The whole system is housed in a plastic containment. Fig. 3 shows a well-labeled cross-sectional view of the single-source Am–Be irradiation facility design. The arrows in the diagram show the direction in which the radial neutron flux distributions were monitored. The second Am–Be source was designed with four americium– beryllium sources. The four sources were chosen to create a
Fig. 2. Horizontal cross-section of the Am–Be neutron source facility at NNRI.
Fig. 1. Schematic vertical cross-sectional view of the Am–Be neutron source facility at NNRI.
194
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
where P is the power of the Am–Be source. The normalization factor for the tallies is calculated by ϕi ¼
3:2709 1010 PðWÞ ν tally volume
ð4Þ
where i represents the energy group of the neutron being analyzed, i.e. thermal, epithermal or fast and ν is the number of neutrons/fission and it is given by X-5 Monte Carlo Team (2003a, 2003b) ν¼
1 loss to fission
ð5Þ
Fig. 3. Cross-sectional view of the single Am–Be neutron source irradiation facility.
symmetrical geometry in terms of the source distribution and also to prevent the necessity of modifying the containment due to gamma shielding because americium–beryllium sources have high gamma emissions. The source contained an AmO2 compound mixed with Be powder compressed into a cylindrical pellet and then encapsulated in a double-layered welded stainless steel. The MCNP5 program was used to model 33 channels in a concentric ring pattern around the source to monitor the flux in all directions so that it could be compared with the values recorded in the single source Am–Be design. Fig. 4 shows a well-labeled cross-sectional view of the four-source Am–Be irradiation facility design. The arrows in the diagram show the direction in which the radial neutron flux distributions were monitored.
Fig. 4. Cross-sectional view of the four Am–Be neutron source irradiation facility.
2.1. Monte Carlo calculations The neutron fluxes under study in this work are the thermal, epithermal and fast neutron fluxes. According to the MCNP input file we prepared, the thermal neutron flux energy ranges from (0 to 6.25 10 7) MeV, the epithermal neutron flux energy ranges from (6.25 10 7 to 8.21 10 1) MeV and that of the fast neutron flux ranges from (8.21 10 1 to 20.00) MeV. To reduce the margin of error, 125,000 particles were simulated for each of the 400 cycles, making 50 106 particle histories monitored in the MCNP simulation. Radial flux tallies (F4) were created in the 36 and 33 irradiation channels for the one-source and the multisource design, respectively. The position of the four sources in the four source design was carefully chosen after many trial runs. The positions finally chosen were selected because these positions produced the most stable fluxes as well as the most uniform fluxes. The results from the tallies retrieved from the output file were normalized and interpreted into graphs using excel worksheet as shown in Figs. 5 and 6. The results were then normalized to obtain the actual fluxes. To accomplish this, some parameters such as the fission q-value and the loss to fission that are included in the output are called from the MCNP output to calculate the normalization factor. The search menu was used to find these parameters. The conversion factor C was used to interpret the MCNP tally results in the output file (X-5 Monte Carlo Team, 2003a, 2003b).
C¼
1 J=s W
Fig. 5. Radial neutron flux distribution of the single 20 Ci Am–Be neutron source design.
1 MeV fission ¼ 3:2709 1010 fission=W s 190:83 MeV 1:60205e 13 J
ð2Þ The source strength of the reactor is calculated by the factor ð3:2709 1010 PÞW
ð3Þ
Fig. 6. Radial neutron flux distribution of the four 20 Ci Am–Be neutron source design.
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
3. Theory MCNP can be used to theoretically duplicate a statistical process (such as the interaction of nuclear particles with materials) and is particularly useful for complex problems that cannot be solved with deterministic methods. The individual probabilistic events that comprise a process are simulated sequentially. The probability distributions governing these events are statistically sampled to describe the total phenomenon. The MCNP code tracks each particle from its birth to the time of its death (absorption or capture). As more particle histories are followed, the neutron and photon distributions become better known (X-5 Monte Carlo Team, 2003a, 2003b). Within a given cell of fixed composition, the method of sampling a collision along the track is determined using the following theory. The probability of a first collision for a particle between l and l þdl along its line of flight is given by pðlÞdl ¼ e Σ t l Σ t dl
ð6Þ
where Σ t is the total macroscopic cross section of the medium and is interpreted as the probability per unit length of a collision. Setting ξ the random number on [0, 1], to be Z ξ¼
1 0
e Σ t s Σ t ds ¼ 1 e Σ t l
ð7Þ
it then follows that l¼
1 lnð1 ξÞ Σt
ð8Þ
However, because 1 ξ is distributed in the same manner as ξ and hence may be replaced by ξ, we obtain a well-known expression for the distance to collision as X-5 Monte Carlo Team (2003a, 2003b) l¼
1 lnðξÞ Σt
ð9Þ
4. Results and discussion 4.1. Neutronic performance After the 400 cycles and 50 million particle histories of the MCNP simulation for both designs, the keff of the single source design obtained is 0.00115 70.0008 and that of the four sources design is 0.0014370.0008. The maximum thermal neutron flux yield in the single source design was (1.870.0007) 106 n=cm2 s. Fig. 5 shows the graph of the radial neutron flux distribution of the thermal, epithermal and fast neutrons of the single Am–Be source design. Fig. 5 shows that the neutron fluxes were equally distributed on both sides of the single source obeying a Gaussian distribution. The thermal neutron flux ranges from (1.80 7 0.0008) 106 n=cm2 s to (2.28 70.0008) 105 n=cm2 s The epithermal neutron flux ranges from (8.20 70.0008) 105 n=cm2 s to (3.73 70.0008) 104 n=cm2 s and that of the fast neutron flux ranges from (4.2 70.0008) 105 to (1.72 70.0008) 104. The highest neutron flux was recorded in the first concentric ring which shows that as we move away from the source we record lower flux values. Asamoah et al. (2011), recorded a thermal flux of (1.9839 70.0014) 104 n=cm2 s at a distance of 13.1 cm. The neutron flux yielded by the four-source Am–Be design is more than that of the single source design because the maximum thermal neutron flux yield in the four-source Am–Be design is (5.47 0.0007) 106 n=cm2 s. Fig. 4 represents the growth of the
195
radial neutron flux distribution of the four 20 Ci Am–Be neutron source design. The maximum flux was recorded in positions where three sources surround a channel which is not necessarily the first concentric ring. This shows that the more the sources, the greater the number of sources, the greater the thermal flux but the epithermal flux and fast flux still remain Gaussian. The epithermal flux and the fast neutron flux were equally distributed from the center of the containment. However, the thermal neutron flux appears to be skewed to the right side of the graph showing an uneven distribution of the thermal neutron flux as shown in Fig. 6. The multisource design was intended to enable thermal neutrons to attain maximum values in positions where prospective irradiation channels will be installed so that samples could receive the maximum flux. However, the epithermal and fast neutron flux did not change from the normal Gaussian distribution. The thermal neutron flux ranges from (5.470.0007) 106 n=cm2 s to (1.007 0.0007) 106 n=cm2 s. The epithermal neutron flux ranges from (4.01 70.0007) 106 n=cm2 s to (1.727 0.0007) 105 n=cm2 s and that of the fast neutron flux ranges from 2.59 70.0007 106 n=cm2 s to 7.60 7 0.0007 104 n=cm2 s. The fast neutron fluence recorded in the multisource design could be harnessed to enable prompt gamma neutron activation analyses by installing a prompt gamma detection system in the Am–Be source. Prompt Gamma Neutron Activation Analyses (PGNAA) would enable us identify lighter elements such as hydrogen, boron and carbon. The PGNAA detector system as well as the conventional Instrumental neutron activation analysis (INAA) method will help increase research output. This will in turn solve many socioeconomic problems in Ghana. Commercial activities at the Am–Be source facilities will also increase much-needed revenue in the institute.
5. Conclusion The neutron yield of the multisource Am–Be design is more than that of the single Am–Be source design. This shows that increasing the number of Am–Be sources in the design facility and arranging them in specific geometry can increase the neutron yield. The neutron flux peaked in the first ring of the single source, while the channels at the intersection of the sources showed maximum flux as shown in Fig. 4. The multisource Am–Be design shows more than a three-fold increase in neutron flux compared to the single source. PGNAA could be introduced if a prompt gamma detection system was installed. This would expand the research scope and increase revenue. The model can be adopted by universities in Africa and thirdworld countries, to enable such countries to harness the benefits of nuclear science using neutron activation analyses. Acknowledgement Sincere thanks goes to Emmanuel Ampomah Amoako and Mathew Asamoah all of the Graduate School of Nuclear and Allied Science, University of Ghana, for their support. References Asamoah, M., et al., 2011. Neutron flux distribution in the irradiation channels of Am–Be neutron source irradiation facility. Ann. Nucl. Energy , http://dx.doi.org/ 10.1016/j.anucene.2011.02.014. Knoll G.F., 1989. Radiation detection and measurement, second edition, 21–25. Osae, E.K., Akoto-Bamford, S., 1986. Neutron Flux Determination by the Activation of MnO2 Pellets, GAEC Technical Report, Department of Physics, Ghana Atomic Energy Commission, Kwabenya. Accra, Ghana.
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Osae, E.K., Amoh, G.K., 1996. Determination of the thermal neutron flux of Am–Be neutron source. J. Univ. Sci. Technol. Kumasi 16, 3. Tetteh, G.K., 1980. GAEC Technical Report, Department of Physics, Ghana Atomic Energy Commission, Kwabenya. Accra, Ghana. X-5 Monte Carlo Team. 2003a. MCNP—A General Monte Carlo N-Particle Transport Code, Version 5 Volume I: Overview and Theory, pp 60–61.
X-5 Monte Carlo Team. 2003b. MCNP—A General Monte Carlo N-Particle Transport Code, Version 5 Volume II: User’s Guide, p 362. Zevallos-Chávez, J.Y., Zamboni, C.B., 2005. Braz. J. Phys. 3B, 35. Zhenzhou Lui, Jinxiang Chen, Pei Zhu Yongming Li, Gouhui Zhang, 2007. The 4.43 MeV to Neutron Ratio for the Am–Be Neutron Source. 1319.
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
The design of a multisource americium–beryllium (Am–Be) neutron irradiation facility using MCNP for the neutronic performance calculation R.B.M. Sogbadji a,b,n, R.G. Abrefah a, B.J.B. Nyarko a,b, E.H.K. Akaho a, H.C. Odoi a, S. Attakorah-Birinkorang a a b
University of Ghana, School of Nuclear and Allied Science, P.O. Box AE1, Atomic Energy, Accra, Ghana Ghana Atomic Energy Commission, National Nuclear Research Institute, P.O. Box LG80, Legon, Ghana
H I G H L I G H T S
Thermal neutron flux for single Am–Be source varies at different position. The proposed channel has higher neutron flux than the existing channels being used. Multi source Am–Be was design has neutron flux more than three folds that of the single source. NAA and PGNAA were experiment discovered to be feasible for this new design. Research institutes that cannot purchase research reactor could adopt the Multi source Am–Be design.
art ic l e i nf o
a b s t r a c t
Article history: Received 17 December 2013 Received in revised form 7 March 2014 Accepted 10 March 2014 Available online 13 April 2014
The americium–beryllium neutron irradiation facility at the National Nuclear Research Institute (NNRI), Ghana, was re-designed with four 20 Ci sources using Monte Carlo N-Particle (MCNP) code to investigate the maximum amount of flux that is produced by the combined sources. The results were compared with a single source Am–Be irradiation facility. The main objective was to enable us to harness the maximum amount of flux for the optimization of neutron activation analysis and to enable smaller sample sized samples to be irradiated. Using MCNP for the design construction and neutronic performance calculation, it was realized that the single-source Am–Be design produced a thermal neutron flux of (1.87 0.0007) 106 n=cm2 s and the four-source Am–Be design produced a thermal neutron flux of (5.4 70.0007) 106 n=cm2 s which is a factor of 3.5 fold increase compared to the single-source Am–Be design. The criticality effective, keff, of the single-source and the four-source Am–Be designs were found to be 0.00115 7 0.0008 and 0.001437 0.0008, respectively. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Neutron flux Americium‐Beryllium source Thermal Neutrons Multi-source irradiation
1. Introduction It is possible to fabricate a small self-contained neutron source by mixing an alpha emitter isotope with a suitable target material because energetic alpha particles are available from the direct decay of a number of conveniently available radionuclides. Several different target materials can lead to the (α, n) reaction with the alpha particle energies that are readily available in radioactive decay. The
n
Corresponding author. E-mail address: [email protected] (R.B.M. Sogbadji).
http://dx.doi.org/10.1016/j.apradiso.2014.03.017 0969-8043/& 2014 Elsevier Ltd. All rights reserved.
maximum neutron yield is obtained when beryllium is chosen as the target and produces neutrons through the reaction (Knoll, 1989). 9 4 4 Beþ 2 p
1 -12 6 C þ 0n
ð1Þ
Most of the alpha particles simply are stopped in the target and only 1 in approximately 104 reacts with a beryllium nucleus. The same yield can be obtained from a mixture of the alpha particle emitter and beryllium provided the alpha emitter is homogeneously distributed throughout the beryllium in a small relative concentration. All of the alpha emitters of practical interest are actinide elements and investigations have shown that a stable alloy can be formed between the actinide and the beryllium. There are several choices for alpha emitters. However, the choice is
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
primarily based on availability, cost and half-life. Preferably, the half-life should be as short as possible and consistent with application so that the specific activity of the emitter is high. The Am–Be source is probably the most widely used of the (α, n) isotropic neutron sources. To increase the neutron yield without increasing the physical source, alpha emitters with higher specific activities are used. Therefore, sources incorporate 241Am (half-life of 433 yr) for high neutron yields (Knoll, 1989). The Am–Be neutron source is widely employed as a calibration source for neutron instrumentation, and as a portable source for a variety of applications. It is well known that the neutron source also gives off penetrating γ-rays of 4.438 MeV that are mainly associated with the neutron group leaving 12C in the first excited state in the 9Be(α, n)12C reaction. There is a compacted mixture of AmO2 and 9Be fine powder in the source construction. It is obvious that the cluster size, mixture ratio and compacted density of the active zone and the physical size of the source have strong influence on the neutron yield and the finer structure of the emerging neutron spectrum (Lui et al., 2007). The IAEA supplied and installed a 20 Ci 241Am–Be neutron irradiation facility at the National Nuclear Research Institute (NNRI) of the Ghana Atomic Energy Commission in 1977 for Neutron Activation Analyses (NAA) (Osae and Amoh, 1996; Osae and AkotoBamford, 1986; Tetteh, 1980). Figs. 1 and 2 show schematic diagrams of the Am–Be source at NNRI. The main advantage of the Am–Be neutron source irradiator is its very stable neutron flux, thus eliminating the need for a standard material in the measurement of induced activity in samples (Zevallos-Chávez and Zamboni, 2005). The main objective of this research was to redesign the Am–Be neutron source with multiple sources to increase the thermal flux of the Am–Be neutron source. This will enable us to reduce the physical size of samples being irradiated (the existing Am–Be neutron source produces a relatively small thermal flux; as such large samples must be irradiated to obtain good sensitivity). The Am–Be neutron source is an important neutron source for neutron activation analyses. It is relatively inexpensive, easy to shield and portable in addition to producing a stable neutron flux.
193
2. Methodology The simulation of the neutron particle histories was performed in the computer simulation laboratory at NNRI in March, 2011. The first Am–Be source design contained an AmO2 compound in a mixture of beryllium powder in a double layered stainless steel shell (Lui et al., 2007). The source was surrounded by water for moderation and for a shielding effect. The MCNP5 program was used to model 36 irradiation channels in a concentric ring pattern around the source in other to monitor the neutron fluxes in all directions. The whole system is housed in a plastic containment. Fig. 3 shows a well-labeled cross-sectional view of the single-source Am–Be irradiation facility design. The arrows in the diagram show the direction in which the radial neutron flux distributions were monitored. The second Am–Be source was designed with four americium– beryllium sources. The four sources were chosen to create a
Fig. 2. Horizontal cross-section of the Am–Be neutron source facility at NNRI.
Fig. 1. Schematic vertical cross-sectional view of the Am–Be neutron source facility at NNRI.
194
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
where P is the power of the Am–Be source. The normalization factor for the tallies is calculated by ϕi ¼
3:2709 1010 PðWÞ ν tally volume
ð4Þ
where i represents the energy group of the neutron being analyzed, i.e. thermal, epithermal or fast and ν is the number of neutrons/fission and it is given by X-5 Monte Carlo Team (2003a, 2003b) ν¼
1 loss to fission
ð5Þ
Fig. 3. Cross-sectional view of the single Am–Be neutron source irradiation facility.
symmetrical geometry in terms of the source distribution and also to prevent the necessity of modifying the containment due to gamma shielding because americium–beryllium sources have high gamma emissions. The source contained an AmO2 compound mixed with Be powder compressed into a cylindrical pellet and then encapsulated in a double-layered welded stainless steel. The MCNP5 program was used to model 33 channels in a concentric ring pattern around the source to monitor the flux in all directions so that it could be compared with the values recorded in the single source Am–Be design. Fig. 4 shows a well-labeled cross-sectional view of the four-source Am–Be irradiation facility design. The arrows in the diagram show the direction in which the radial neutron flux distributions were monitored.
Fig. 4. Cross-sectional view of the four Am–Be neutron source irradiation facility.
2.1. Monte Carlo calculations The neutron fluxes under study in this work are the thermal, epithermal and fast neutron fluxes. According to the MCNP input file we prepared, the thermal neutron flux energy ranges from (0 to 6.25 10 7) MeV, the epithermal neutron flux energy ranges from (6.25 10 7 to 8.21 10 1) MeV and that of the fast neutron flux ranges from (8.21 10 1 to 20.00) MeV. To reduce the margin of error, 125,000 particles were simulated for each of the 400 cycles, making 50 106 particle histories monitored in the MCNP simulation. Radial flux tallies (F4) were created in the 36 and 33 irradiation channels for the one-source and the multisource design, respectively. The position of the four sources in the four source design was carefully chosen after many trial runs. The positions finally chosen were selected because these positions produced the most stable fluxes as well as the most uniform fluxes. The results from the tallies retrieved from the output file were normalized and interpreted into graphs using excel worksheet as shown in Figs. 5 and 6. The results were then normalized to obtain the actual fluxes. To accomplish this, some parameters such as the fission q-value and the loss to fission that are included in the output are called from the MCNP output to calculate the normalization factor. The search menu was used to find these parameters. The conversion factor C was used to interpret the MCNP tally results in the output file (X-5 Monte Carlo Team, 2003a, 2003b).
C¼
1 J=s W
Fig. 5. Radial neutron flux distribution of the single 20 Ci Am–Be neutron source design.
1 MeV fission ¼ 3:2709 1010 fission=W s 190:83 MeV 1:60205e 13 J
ð2Þ The source strength of the reactor is calculated by the factor ð3:2709 1010 PÞW
ð3Þ
Fig. 6. Radial neutron flux distribution of the four 20 Ci Am–Be neutron source design.
R.B.M. Sogbadji et al. / Applied Radiation and Isotopes 90 (2014) 192–196
3. Theory MCNP can be used to theoretically duplicate a statistical process (such as the interaction of nuclear particles with materials) and is particularly useful for complex problems that cannot be solved with deterministic methods. The individual probabilistic events that comprise a process are simulated sequentially. The probability distributions governing these events are statistically sampled to describe the total phenomenon. The MCNP code tracks each particle from its birth to the time of its death (absorption or capture). As more particle histories are followed, the neutron and photon distributions become better known (X-5 Monte Carlo Team, 2003a, 2003b). Within a given cell of fixed composition, the method of sampling a collision along the track is determined using the following theory. The probability of a first collision for a particle between l and l þdl along its line of flight is given by pðlÞdl ¼ e Σ t l Σ t dl
ð6Þ
where Σ t is the total macroscopic cross section of the medium and is interpreted as the probability per unit length of a collision. Setting ξ the random number on [0, 1], to be Z ξ¼
1 0
e Σ t s Σ t ds ¼ 1 e Σ t l
ð7Þ
it then follows that l¼
1 lnð1 ξÞ Σt
ð8Þ
However, because 1 ξ is distributed in the same manner as ξ and hence may be replaced by ξ, we obtain a well-known expression for the distance to collision as X-5 Monte Carlo Team (2003a, 2003b) l¼
1 lnðξÞ Σt
ð9Þ
4. Results and discussion 4.1. Neutronic performance After the 400 cycles and 50 million particle histories of the MCNP simulation for both designs, the keff of the single source design obtained is 0.00115 70.0008 and that of the four sources design is 0.0014370.0008. The maximum thermal neutron flux yield in the single source design was (1.870.0007) 106 n=cm2 s. Fig. 5 shows the graph of the radial neutron flux distribution of the thermal, epithermal and fast neutrons of the single Am–Be source design. Fig. 5 shows that the neutron fluxes were equally distributed on both sides of the single source obeying a Gaussian distribution. The thermal neutron flux ranges from (1.80 7 0.0008) 106 n=cm2 s to (2.28 70.0008) 105 n=cm2 s The epithermal neutron flux ranges from (8.20 70.0008) 105 n=cm2 s to (3.73 70.0008) 104 n=cm2 s and that of the fast neutron flux ranges from (4.2 70.0008) 105 to (1.72 70.0008) 104. The highest neutron flux was recorded in the first concentric ring which shows that as we move away from the source we record lower flux values. Asamoah et al. (2011), recorded a thermal flux of (1.9839 70.0014) 104 n=cm2 s at a distance of 13.1 cm. The neutron flux yielded by the four-source Am–Be design is more than that of the single source design because the maximum thermal neutron flux yield in the four-source Am–Be design is (5.47 0.0007) 106 n=cm2 s. Fig. 4 represents the growth of the
195
radial neutron flux distribution of the four 20 Ci Am–Be neutron source design. The maximum flux was recorded in positions where three sources surround a channel which is not necessarily the first concentric ring. This shows that the more the sources, the greater the number of sources, the greater the thermal flux but the epithermal flux and fast flux still remain Gaussian. The epithermal flux and the fast neutron flux were equally distributed from the center of the containment. However, the thermal neutron flux appears to be skewed to the right side of the graph showing an uneven distribution of the thermal neutron flux as shown in Fig. 6. The multisource design was intended to enable thermal neutrons to attain maximum values in positions where prospective irradiation channels will be installed so that samples could receive the maximum flux. However, the epithermal and fast neutron flux did not change from the normal Gaussian distribution. The thermal neutron flux ranges from (5.470.0007) 106 n=cm2 s to (1.007 0.0007) 106 n=cm2 s. The epithermal neutron flux ranges from (4.01 70.0007) 106 n=cm2 s to (1.727 0.0007) 105 n=cm2 s and that of the fast neutron flux ranges from 2.59 70.0007 106 n=cm2 s to 7.60 7 0.0007 104 n=cm2 s. The fast neutron fluence recorded in the multisource design could be harnessed to enable prompt gamma neutron activation analyses by installing a prompt gamma detection system in the Am–Be source. Prompt Gamma Neutron Activation Analyses (PGNAA) would enable us identify lighter elements such as hydrogen, boron and carbon. The PGNAA detector system as well as the conventional Instrumental neutron activation analysis (INAA) method will help increase research output. This will in turn solve many socioeconomic problems in Ghana. Commercial activities at the Am–Be source facilities will also increase much-needed revenue in the institute.
5. Conclusion The neutron yield of the multisource Am–Be design is more than that of the single Am–Be source design. This shows that increasing the number of Am–Be sources in the design facility and arranging them in specific geometry can increase the neutron yield. The neutron flux peaked in the first ring of the single source, while the channels at the intersection of the sources showed maximum flux as shown in Fig. 4. The multisource Am–Be design shows more than a three-fold increase in neutron flux compared to the single source. PGNAA could be introduced if a prompt gamma detection system was installed. This would expand the research scope and increase revenue. The model can be adopted by universities in Africa and thirdworld countries, to enable such countries to harness the benefits of nuclear science using neutron activation analyses. Acknowledgement Sincere thanks goes to Emmanuel Ampomah Amoako and Mathew Asamoah all of the Graduate School of Nuclear and Allied Science, University of Ghana, for their support. References Asamoah, M., et al., 2011. Neutron flux distribution in the irradiation channels of Am–Be neutron source irradiation facility. Ann. Nucl. Energy , http://dx.doi.org/ 10.1016/j.anucene.2011.02.014. Knoll G.F., 1989. Radiation detection and measurement, second edition, 21–25. Osae, E.K., Akoto-Bamford, S., 1986. Neutron Flux Determination by the Activation of MnO2 Pellets, GAEC Technical Report, Department of Physics, Ghana Atomic Energy Commission, Kwabenya. Accra, Ghana.
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