- Email: [email protected]
Geometry corrections for cylindrical neutron area survey meters
ARTICLE IN PRESS Applied Radiation and Isotopes 68 (2010) 546–549
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Geometry corrections for cylindrical neutron area survey meters G.C. Taylor National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK
a r t i c l e in f o
a b s t r a c t
Keywords: Calibration Geometry correction Neutron
MCNP calculations have been performed to investigate the effects of beam divergence on the response of selected cylindrical neutron area survey meters irradiated by selected neutron sources. By comparing the results to calculations performed using plane-parallel beam irradiations, geometry correction factors have been calculated that can be applied to instrument calibrations. The results indicate that the effective centres of cylindrical detectors may not lie on the axis of symmetry, as previously assumed. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Legal requirement for instrument calibrations Neutron area survey meters require annual testing to confirm that they are fit for purpose, just like all other radiation monitoring equipment (Health and Safety Commission, 2000). For end users performing ambient dose equivalent rate surveys in the workplace, the requirement is often met by a simple a pass/ fail test, where the device is passed as fit for purpose if the response is within 30% of the conventional true value. Certain applications, however, require much more stringent evaluations, such as the calibration of transfer instruments used by secondary standards laboratories.
1.2. Factors affecting instrument calibrations The instrument reading for any neutron irradiation varies with the experimental conditions. Factors include: the type and strength of the neutron source, the source encapsulation, the source–detector distance, and the size and layout of the irradiation area. Quantifying the impact of these factors is particularly important for facilities performing instrument calibrations to high precision and accuracy. In order to calibrate the detector response from an instrument reading, all of the above factors need to be taken into consideration, and the result should be a value for the detector response that is independent of the experimental conditions. The international standard ISO 8529 part 2 (2000) addresses all of the factors mentioned above through a number of parameters and corrections, and can be summarised in the following Fax: + 44 208 943 7082.
E-mail address: [email protected]
expression for the instrument reading MT0 ðlÞ: BtF1 ðyÞ F1 ðlÞ 0 MT0 ðlÞ ¼ RF þ F F ðlÞ1 L 2 FA ðlÞ 4pl2
ð1Þ
where l represents the distance from the source centre to the detector reference point, RF represents the fluence response of the instrument, B represents the neutron source strength (i.e. emission rate into 4p sr), t represents the duration of the measurement, F1(y) represents the source anisotropy (influenced by the encapsulation and source type), FL represents the detector linearity correction, F1(l) represents the geometry correction (influenced by the source–detector distance, the source size and the detector size), FA(l) represents air attenuation or the air outscatter correction (influenced by the source–detector distance and the source type) and F20 ðlÞ represents the neutron scatter correction (influenced by the source–detector distance, the source type, the instrument type, and the size and layout of the irradiation area).
1.3. Specification of geometry correction factors ISO 8529 part 2 discusses the implementation of the above parameters in considerable detail; some areas, however, are not covered as comprehensively as others. One particular area that is lacking in depth is the provision of guidance on geometry correction factors for calibrating cylindrical neutron area survey meters such as the Andersson–Braun design (Andersson and Braun, 1963, 1964), and the Studsvik design (Widell and Svansson, 1973), which are normally calibrated side-on, i.e. through the curved surface of the moderator. A geometry correction term is necessary for shorter irradiation distances to take account of the beam divergence and variation in fluence rate over the detector as a consequence of the inversesquare law. In other words, the measured detector response needs
0969-8043/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2010.01.026
ARTICLE IN PRESS G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
to be corrected so that it is representative of a plane-parallel beam irradiation. The expression included in ISO 8529 part 2 for calculating the geometry correction F1(l) for spherical detectors irradiated by point sources (originally published by Hunt, 1984) takes the form: 8 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 9 <2l2 rD2 5 = 41 1 F1 ðlÞ ¼ 1 þ d 1 ; : rD2 l2
ð2Þ
where l represents the distance between the source and the detector centre, rD the radius of the detector and d the neutron effectiveness parameter, which has a recommended value of 0.5 70.1. The lack of information regarding geometry corrections for cylindrical detector calibrations is acknowledged in the standard, and the only guidance offered is the recommendation that such calibrations are performed at distances greater than twice the instrument diameter, where any geometry correction should be close to unity. This rather limited guidance cannot be regarded as a flaw in the standard itself as very little work has been published in this area. This is due, in part, to the lack of symmetry in a system comprising a cylindrical detector being irradiated through its curved surface, which does not lend itself to the type of mathematical solution that has been derived for cylindrically symmetric systems such as a spherical detector undergoing irradiation (Axton, 1972; Hunt, 1984; Kluge et al., 1990; Pulpa´n and Kra´lik, 1991) or a cylindrical detector being irradiated end-on (Pulpa´n and Kra´lik, 1991).
547
3. Results 3.1. Geometry factors calculated with MCNP Fig. 1 shows the variation in the geometry effect with distance as calculated by MCNP for a Studsvik 2202D irradiated by a point 252 Cf source, together with the results for a 10.4 cm radius spherical detector for validation purposes, and the theoretical curve for that sphere as calculated using Eq. (2), including standard uncertainties due to the neutron effectiveness parameter. It can be seen that the effect remains significant at greater distances for the Studsvik than for the spherical detector. This came as something of a surprise, particularly as such an effect implies that the cylindrical instrument’s effective centre (i.e. the point at which the instrument acts as a point detector that follows the inverse square law) is displaced from the axis of cylindrical symmetry. This is illustrated by the solid line that approximately fits the data, which has the form Y = X/(X 1.9), i.e. the effective centre is displaced 1.9 cm towards the source. The possibility that the model itself might be at fault was checked by running a simplified model consisting of a simple NM2B-type moderator irradiated by a single neutron energy (1 MeV) and tallying the thermal neutron fluence (taken, for this purpose, to be all neutrons with an energy below 0.5 eV) within a central cavity for both divergent and plane-parallel beam irradiations. The same effect, albeit much more pronounced, was observed as shown in Fig. 2, which is reasonably well fitted by Y = X/(X 3.7), at least for distances of 20 cm or greater. Following this result further tests were performed to confirm that the plane-parallel and divergent neutron field distributions were being generated as expected.
2. Monte Carlo methods
3.2. Comparisons with measurement: Studsvik/252Cf
2.1. Past and present Monte Carlo studies
Records for calibrations performed at NPL on Studsvik 2202D detectors using 252Cf sources were examined to see if there was any sign of a pronounced geometry effect in the measured data. In order for the data to be considered, measurements must have been acquiring the pulse output of the detector, in order to keep the counting statistics at a reasonable level. Furthermore, these measurements have been performed on a specific detector at more than one distance with the same neutron source in order to
These days pragmatic solutions to an enormous range of problems can be achieved by modelling the systems of interest using radiation transport codes. One such study (Tanner et al., 2006) investigated the responses of a number of neutron area survey meters exposed to a range of neutron sources, and involved the development of sophisticated models for use in the Los Alamos radiation transport code MCNP version 4C2 (Briesmeister, 2000). The work presented here complements the above study, and uses modified versions of certain models to investigate geometry effects for source–detector combinations commonly measured at NPL, namely Studsvik 2202D and Thermo Fisher Scientific (originally NE) NM2B instruments calibrated with 252Cf and 241Am–Be radionuclide sources, but concentrating on the Studsvik/252Cf combination. MCNP was used to model detector responses under both plane-parallel and divergent beam conditions. The effect of the irradiation geometry was quantified simply by determining the ratio of the two cases. The approach was validated by performing equivalent tests on a model of a simple spherical detector, and comparing the results to the standard geometry correction equation found in ISO 8529 part 2. Multiple runs were performed for each model configuration, each using a different seed for the random number generator, supplied via the dbcn card. The resulting detector tallies were averaged and the standard deviation of the values compared to the uncertainties generated by MCNP itself. The only optimisation performed was to restrict the neutron field so that it only just illuminated the detector, and the calculated responses were scaled to unit fluence.
Fig. 1. Geometry factors calculated using MCNP for a Studsvik detector (solid circles) and a 10.4 cm spherical detector (open squares) irradiated by 252Cf neutrons. The line through the solid circles is of the form Y= X/(X 1.9). The lower line is the geometry factor for spherical detectors calculated using Eq. (2), with standard uncertainties.
ARTICLE IN PRESS 548
G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
It can be seen that the agreement between the scaled measurement data and the Monte Carlo calculations is quite good, bearing in mind that the measurement uncertainties are relatively large. Although not entirely conclusive, the results do indicate that the effective centre of the cylindrical detectors may not lie on the cylindrical axis of symmetry.
3.3. Comparisons with measurement: Studsvik/241Am–Be
Fig. 2. Geometry factors calculated using MCNP for an NM2B-style moderator irradiated by 1 MeV neutrons. The line through the solid circles is of the form Y =X/ (X 3.7).
Hardly any measurement data meeting the criteria outlined earlier could be found for 241Am–Be irradiations of Studsvik detectors, and the few sets analysed were all measured at distances beyond 1 m where the measurement uncertainties swamped any geometry effects. Monte Carlo calculations did show the effect, however, exhibiting geometry factors of 1.076370.0033 at 20 cm, 1.025370.0025 at 50 cm, 1.011770.0033 at 100 cm and 1.0072 70.0023 at 200 cm. These are slightly lower than the values observed for 252Cf.
3.4. Comparisons with measurement: NM2B/241Am–Be The comparison between measured and calculated data for Am–Be irradiations of an NM2B are shown in Fig. 4. There appears to be an inconsistency in the measured data, with the two measurement groups showing distinctly different geometry effects at shorter irradiation distances. This could stem from two possible sources. Firstly, they represent different source encapsulations: the data symbolised by open triangles originate from an X3 encapsulation (3 cm 1.5 cm), whereas the data symbolised by open squares originate from an X14 encapsulation (6 cm 3 cm). The second possibility is due to dead time effects: the NM2B irradiated by the X14 capsule was counting at over 1000 cps at the nearest distance; however, an unfeasibly large dead-time correction of 30 ms would be necessary to bring the data point onto the calculated curve. It should be borne in mind, however, that the uncertainties on the point in question are very large, and that this may simply be a measurement outlier. 241
Fig. 3. Geometry factors for a Studsvik detector irradiated by 252Cf neutrons calculated using MCNP (solid circles), compared to measurement data (open symbols). The measurement data have been arbitrarily scaled to see if it follows the general trend of the calculated data, which has been fitted by the expression Y= X/(X 1.74) +0.0034. Also shown are data for the spherical Mk7 NRM detector (solid diamonds) which has a 10.4 cm radius, together with the theoretical geometry factor (dash-dotted line) as calculated using Eq. (2).
eliminate uncertainties in the source emission rate. Each detector response then had removed any geometry correction that may have been applied at the time (based on the algorithm for spherical detectors: any correction being better than none). The results in each measurement group were then compared in order to see if there was any trend with measurement distance. The possibility of there being an inherent flaw in any of the corrections applied to calibration measurements at NPL, manifesting as a systematic variation with distance, was tested by analysing data for a spherical instrument (a Mk7 NRM) in the same way. The results for 252Cf irradiations of a Studsvik are shown in Fig. 3 (open symbols), together with some results for a Mk7 NRM (solid diamonds). Each measurement group has been arbitrarily scaled in order to facilitate comparison with either the MCNPcalculated values (solid circles) or the standard spherical geometry correction (dash-dotted line). A slightly modified function, which now includes a constant term, has been used to fit the data, of the form Y = X/(X 1.74)+0.0034 (solid line). No underlying mechanism can be attributed to this form, it just fits the data reasonably well.
Fig. 4. Geometry factors for a NM2B detector irradiated by 241Am–Be neutrons calculated using MCNP (solid circles), compared to measurement data (open symbols). The measurement data have been arbitrarily scaled to see if it follows the general trend of the calculated data, which has been fitted by the expression Y= X/(X 2.1480)+ 0.0040. The discrepancy between the two data sets is most probably due to differences in the source encapsulation.
ARTICLE IN PRESS G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
549
meters at source–detector distances beyond 1 m. Whether this is due to an off-axis effective centre or to some other mechanism is an interesting question, but it is secondary the apparent presence of the effect whatever the cause. Monte Carlo calculations, backed up to some extent by experimental data point to the fact that even calibrations performed at distances beyond 1 m may be wrong by 1% or more: not a critical amount for a simple pass/fail test to 30%, but significant enough for standards laboratories to consider. Further measurements need to be performed with much higher statistical precision in order to confirm the presence of this effect: although many checks have been performed on the Monte Carlo models, only by experiment can the true scale of this effect be quantified. Such measurements are planned for the near future at NPL.
Acknowledgements
Fig. 5. Schematic representation of cylindrical and spherical detectors undergoing irradiation by plane-parallel and divergent neutron fields.
The author wishes to thank Dr. Hamid Tagziria of the JRC, Ispra, Italy, for the development of the original models used in this study while working at NPL. This work was carried out as part of the National Metrology System research programme funded by the UK Department for Innovation, Universities, & Skills.
4. Discussion 4.1. The feasibility of off-axis effectives centre in cylindrical detectors
References
Although it may appear counter-intuitive for the effective centre of a cylindrical detector to be displaced from the axis of cylindrical symmetry, there are physical reasons why this may be possible. Fig. 5 shows schematics of cylindrical and spherical detectors being irradiated by divergent and plane-parallel neutron fields. Two points become apparent when comparing the different configurations. Firstly, for the plane-parallel beam cases, the path length through the cylindrical detector remains constant regardless of the vertical displacement of the neutron field, whereas for the spherical detector the path length shortens away from the axis of irradiation. Secondly, for the divergent beam cases, the path length through the cylindrical detector actually increases with angle, whereas for the spherical detector, the path length decreases. These differences may be sufficient to result in the cylindrical detector having an effective centre displaced from the cylindrical axis.
¨ ., Braun, J., 1963. A neutron rem counter with uniform sensitivity Andersson, I.O from 0.025 eV to 10 MeV. In: Proceedings of the Symposium on Neutron Dosimetry, vol. 2, Harwell, UK, 1962 (Vienna: IAEA), pp. 85–89. ¨ ., Braun, J., 1964. A neutron rem counter. Nucleonik 6, 237–241. Andersson, I.O Axton, E.J., 1972. The effective centre of a moderating sphere when used as an instrument for fast neutron flux measurement. J. Nucl. Energy 26, 581–583. Briesmeister, J.F. (Ed.) 2000. MCNP—a general Monte Carlo N-particle transport code, Version 4C. LANL Report LA-13709-M. Health and Safety Commission, 2000. Working with ionising radiation: ionising radiations regulations 1999 approved code of practice. ISBN 0-7176-1746-7. Hunt, J.B., 1984. The calibration of neutron sensitive spherical devices. Radiat. Prot. Dosim. 8, 239–251. International Organisation for Standardisation, 2000. Reference neutron radiations—Part 2: calibration fundamentals of radiation protection devices related to the basic quantities characterizing the radiation field. International Standard ISO 8529-2. Kluge, H., Weise, K., Hunt, J.B., 1990. Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes. Radiat. Prot. Dosim. 32, 233–244. Pulpa´n, J., Kra´lik, M., 1991. Geometrical correction factor. Radiat. Prot. Dosim. 35, 159–165. Tanner, R.J., Molinos, C., Roberts, N.J., Bartlett, D.T., Hager, L.G., Jones, L.N., Taylor, G.C., Thomas, D.J., 2006. Practical implications of neutron survey instrument performance. HPA Report HPA-RPD-016. Widell, C.-O., Svansson, L., 1973. A neutron monitor for radiation protection. In: Proceedings of the Symposium on Neutron Monitoring for Radiation Protection Purposes, Vienna, 1972 (Vienna: IAEA), pp. 225–230.
5. Conclusions There is strong evidence for a significant geometry effect being present in the irradiation of cylindrical neutron area survey
Contents lists available at ScienceDirect
Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso
Geometry corrections for cylindrical neutron area survey meters G.C. Taylor National Physical Laboratory, Hampton Road, Teddington, Middlesex TW11 0LW, UK
a r t i c l e in f o
a b s t r a c t
Keywords: Calibration Geometry correction Neutron
MCNP calculations have been performed to investigate the effects of beam divergence on the response of selected cylindrical neutron area survey meters irradiated by selected neutron sources. By comparing the results to calculations performed using plane-parallel beam irradiations, geometry correction factors have been calculated that can be applied to instrument calibrations. The results indicate that the effective centres of cylindrical detectors may not lie on the axis of symmetry, as previously assumed. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Legal requirement for instrument calibrations Neutron area survey meters require annual testing to confirm that they are fit for purpose, just like all other radiation monitoring equipment (Health and Safety Commission, 2000). For end users performing ambient dose equivalent rate surveys in the workplace, the requirement is often met by a simple a pass/ fail test, where the device is passed as fit for purpose if the response is within 30% of the conventional true value. Certain applications, however, require much more stringent evaluations, such as the calibration of transfer instruments used by secondary standards laboratories.
1.2. Factors affecting instrument calibrations The instrument reading for any neutron irradiation varies with the experimental conditions. Factors include: the type and strength of the neutron source, the source encapsulation, the source–detector distance, and the size and layout of the irradiation area. Quantifying the impact of these factors is particularly important for facilities performing instrument calibrations to high precision and accuracy. In order to calibrate the detector response from an instrument reading, all of the above factors need to be taken into consideration, and the result should be a value for the detector response that is independent of the experimental conditions. The international standard ISO 8529 part 2 (2000) addresses all of the factors mentioned above through a number of parameters and corrections, and can be summarised in the following Fax: + 44 208 943 7082.
E-mail address: [email protected]
expression for the instrument reading MT0 ðlÞ: BtF1 ðyÞ F1 ðlÞ 0 MT0 ðlÞ ¼ RF þ F F ðlÞ1 L 2 FA ðlÞ 4pl2
ð1Þ
where l represents the distance from the source centre to the detector reference point, RF represents the fluence response of the instrument, B represents the neutron source strength (i.e. emission rate into 4p sr), t represents the duration of the measurement, F1(y) represents the source anisotropy (influenced by the encapsulation and source type), FL represents the detector linearity correction, F1(l) represents the geometry correction (influenced by the source–detector distance, the source size and the detector size), FA(l) represents air attenuation or the air outscatter correction (influenced by the source–detector distance and the source type) and F20 ðlÞ represents the neutron scatter correction (influenced by the source–detector distance, the source type, the instrument type, and the size and layout of the irradiation area).
1.3. Specification of geometry correction factors ISO 8529 part 2 discusses the implementation of the above parameters in considerable detail; some areas, however, are not covered as comprehensively as others. One particular area that is lacking in depth is the provision of guidance on geometry correction factors for calibrating cylindrical neutron area survey meters such as the Andersson–Braun design (Andersson and Braun, 1963, 1964), and the Studsvik design (Widell and Svansson, 1973), which are normally calibrated side-on, i.e. through the curved surface of the moderator. A geometry correction term is necessary for shorter irradiation distances to take account of the beam divergence and variation in fluence rate over the detector as a consequence of the inversesquare law. In other words, the measured detector response needs
0969-8043/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.apradiso.2010.01.026
ARTICLE IN PRESS G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
to be corrected so that it is representative of a plane-parallel beam irradiation. The expression included in ISO 8529 part 2 for calculating the geometry correction F1(l) for spherical detectors irradiated by point sources (originally published by Hunt, 1984) takes the form: 8 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 9 <2l2 rD2 5 = 41 1 F1 ðlÞ ¼ 1 þ d 1 ; : rD2 l2
ð2Þ
where l represents the distance between the source and the detector centre, rD the radius of the detector and d the neutron effectiveness parameter, which has a recommended value of 0.5 70.1. The lack of information regarding geometry corrections for cylindrical detector calibrations is acknowledged in the standard, and the only guidance offered is the recommendation that such calibrations are performed at distances greater than twice the instrument diameter, where any geometry correction should be close to unity. This rather limited guidance cannot be regarded as a flaw in the standard itself as very little work has been published in this area. This is due, in part, to the lack of symmetry in a system comprising a cylindrical detector being irradiated through its curved surface, which does not lend itself to the type of mathematical solution that has been derived for cylindrically symmetric systems such as a spherical detector undergoing irradiation (Axton, 1972; Hunt, 1984; Kluge et al., 1990; Pulpa´n and Kra´lik, 1991) or a cylindrical detector being irradiated end-on (Pulpa´n and Kra´lik, 1991).
547
3. Results 3.1. Geometry factors calculated with MCNP Fig. 1 shows the variation in the geometry effect with distance as calculated by MCNP for a Studsvik 2202D irradiated by a point 252 Cf source, together with the results for a 10.4 cm radius spherical detector for validation purposes, and the theoretical curve for that sphere as calculated using Eq. (2), including standard uncertainties due to the neutron effectiveness parameter. It can be seen that the effect remains significant at greater distances for the Studsvik than for the spherical detector. This came as something of a surprise, particularly as such an effect implies that the cylindrical instrument’s effective centre (i.e. the point at which the instrument acts as a point detector that follows the inverse square law) is displaced from the axis of cylindrical symmetry. This is illustrated by the solid line that approximately fits the data, which has the form Y = X/(X 1.9), i.e. the effective centre is displaced 1.9 cm towards the source. The possibility that the model itself might be at fault was checked by running a simplified model consisting of a simple NM2B-type moderator irradiated by a single neutron energy (1 MeV) and tallying the thermal neutron fluence (taken, for this purpose, to be all neutrons with an energy below 0.5 eV) within a central cavity for both divergent and plane-parallel beam irradiations. The same effect, albeit much more pronounced, was observed as shown in Fig. 2, which is reasonably well fitted by Y = X/(X 3.7), at least for distances of 20 cm or greater. Following this result further tests were performed to confirm that the plane-parallel and divergent neutron field distributions were being generated as expected.
2. Monte Carlo methods
3.2. Comparisons with measurement: Studsvik/252Cf
2.1. Past and present Monte Carlo studies
Records for calibrations performed at NPL on Studsvik 2202D detectors using 252Cf sources were examined to see if there was any sign of a pronounced geometry effect in the measured data. In order for the data to be considered, measurements must have been acquiring the pulse output of the detector, in order to keep the counting statistics at a reasonable level. Furthermore, these measurements have been performed on a specific detector at more than one distance with the same neutron source in order to
These days pragmatic solutions to an enormous range of problems can be achieved by modelling the systems of interest using radiation transport codes. One such study (Tanner et al., 2006) investigated the responses of a number of neutron area survey meters exposed to a range of neutron sources, and involved the development of sophisticated models for use in the Los Alamos radiation transport code MCNP version 4C2 (Briesmeister, 2000). The work presented here complements the above study, and uses modified versions of certain models to investigate geometry effects for source–detector combinations commonly measured at NPL, namely Studsvik 2202D and Thermo Fisher Scientific (originally NE) NM2B instruments calibrated with 252Cf and 241Am–Be radionuclide sources, but concentrating on the Studsvik/252Cf combination. MCNP was used to model detector responses under both plane-parallel and divergent beam conditions. The effect of the irradiation geometry was quantified simply by determining the ratio of the two cases. The approach was validated by performing equivalent tests on a model of a simple spherical detector, and comparing the results to the standard geometry correction equation found in ISO 8529 part 2. Multiple runs were performed for each model configuration, each using a different seed for the random number generator, supplied via the dbcn card. The resulting detector tallies were averaged and the standard deviation of the values compared to the uncertainties generated by MCNP itself. The only optimisation performed was to restrict the neutron field so that it only just illuminated the detector, and the calculated responses were scaled to unit fluence.
Fig. 1. Geometry factors calculated using MCNP for a Studsvik detector (solid circles) and a 10.4 cm spherical detector (open squares) irradiated by 252Cf neutrons. The line through the solid circles is of the form Y= X/(X 1.9). The lower line is the geometry factor for spherical detectors calculated using Eq. (2), with standard uncertainties.
ARTICLE IN PRESS 548
G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
It can be seen that the agreement between the scaled measurement data and the Monte Carlo calculations is quite good, bearing in mind that the measurement uncertainties are relatively large. Although not entirely conclusive, the results do indicate that the effective centre of the cylindrical detectors may not lie on the cylindrical axis of symmetry.
3.3. Comparisons with measurement: Studsvik/241Am–Be
Fig. 2. Geometry factors calculated using MCNP for an NM2B-style moderator irradiated by 1 MeV neutrons. The line through the solid circles is of the form Y =X/ (X 3.7).
Hardly any measurement data meeting the criteria outlined earlier could be found for 241Am–Be irradiations of Studsvik detectors, and the few sets analysed were all measured at distances beyond 1 m where the measurement uncertainties swamped any geometry effects. Monte Carlo calculations did show the effect, however, exhibiting geometry factors of 1.076370.0033 at 20 cm, 1.025370.0025 at 50 cm, 1.011770.0033 at 100 cm and 1.0072 70.0023 at 200 cm. These are slightly lower than the values observed for 252Cf.
3.4. Comparisons with measurement: NM2B/241Am–Be The comparison between measured and calculated data for Am–Be irradiations of an NM2B are shown in Fig. 4. There appears to be an inconsistency in the measured data, with the two measurement groups showing distinctly different geometry effects at shorter irradiation distances. This could stem from two possible sources. Firstly, they represent different source encapsulations: the data symbolised by open triangles originate from an X3 encapsulation (3 cm 1.5 cm), whereas the data symbolised by open squares originate from an X14 encapsulation (6 cm 3 cm). The second possibility is due to dead time effects: the NM2B irradiated by the X14 capsule was counting at over 1000 cps at the nearest distance; however, an unfeasibly large dead-time correction of 30 ms would be necessary to bring the data point onto the calculated curve. It should be borne in mind, however, that the uncertainties on the point in question are very large, and that this may simply be a measurement outlier. 241
Fig. 3. Geometry factors for a Studsvik detector irradiated by 252Cf neutrons calculated using MCNP (solid circles), compared to measurement data (open symbols). The measurement data have been arbitrarily scaled to see if it follows the general trend of the calculated data, which has been fitted by the expression Y= X/(X 1.74) +0.0034. Also shown are data for the spherical Mk7 NRM detector (solid diamonds) which has a 10.4 cm radius, together with the theoretical geometry factor (dash-dotted line) as calculated using Eq. (2).
eliminate uncertainties in the source emission rate. Each detector response then had removed any geometry correction that may have been applied at the time (based on the algorithm for spherical detectors: any correction being better than none). The results in each measurement group were then compared in order to see if there was any trend with measurement distance. The possibility of there being an inherent flaw in any of the corrections applied to calibration measurements at NPL, manifesting as a systematic variation with distance, was tested by analysing data for a spherical instrument (a Mk7 NRM) in the same way. The results for 252Cf irradiations of a Studsvik are shown in Fig. 3 (open symbols), together with some results for a Mk7 NRM (solid diamonds). Each measurement group has been arbitrarily scaled in order to facilitate comparison with either the MCNPcalculated values (solid circles) or the standard spherical geometry correction (dash-dotted line). A slightly modified function, which now includes a constant term, has been used to fit the data, of the form Y = X/(X 1.74)+0.0034 (solid line). No underlying mechanism can be attributed to this form, it just fits the data reasonably well.
Fig. 4. Geometry factors for a NM2B detector irradiated by 241Am–Be neutrons calculated using MCNP (solid circles), compared to measurement data (open symbols). The measurement data have been arbitrarily scaled to see if it follows the general trend of the calculated data, which has been fitted by the expression Y= X/(X 2.1480)+ 0.0040. The discrepancy between the two data sets is most probably due to differences in the source encapsulation.
ARTICLE IN PRESS G.C. Taylor / Applied Radiation and Isotopes 68 (2010) 546–549
549
meters at source–detector distances beyond 1 m. Whether this is due to an off-axis effective centre or to some other mechanism is an interesting question, but it is secondary the apparent presence of the effect whatever the cause. Monte Carlo calculations, backed up to some extent by experimental data point to the fact that even calibrations performed at distances beyond 1 m may be wrong by 1% or more: not a critical amount for a simple pass/fail test to 30%, but significant enough for standards laboratories to consider. Further measurements need to be performed with much higher statistical precision in order to confirm the presence of this effect: although many checks have been performed on the Monte Carlo models, only by experiment can the true scale of this effect be quantified. Such measurements are planned for the near future at NPL.
Acknowledgements
Fig. 5. Schematic representation of cylindrical and spherical detectors undergoing irradiation by plane-parallel and divergent neutron fields.
The author wishes to thank Dr. Hamid Tagziria of the JRC, Ispra, Italy, for the development of the original models used in this study while working at NPL. This work was carried out as part of the National Metrology System research programme funded by the UK Department for Innovation, Universities, & Skills.
4. Discussion 4.1. The feasibility of off-axis effectives centre in cylindrical detectors
References
Although it may appear counter-intuitive for the effective centre of a cylindrical detector to be displaced from the axis of cylindrical symmetry, there are physical reasons why this may be possible. Fig. 5 shows schematics of cylindrical and spherical detectors being irradiated by divergent and plane-parallel neutron fields. Two points become apparent when comparing the different configurations. Firstly, for the plane-parallel beam cases, the path length through the cylindrical detector remains constant regardless of the vertical displacement of the neutron field, whereas for the spherical detector the path length shortens away from the axis of irradiation. Secondly, for the divergent beam cases, the path length through the cylindrical detector actually increases with angle, whereas for the spherical detector, the path length decreases. These differences may be sufficient to result in the cylindrical detector having an effective centre displaced from the cylindrical axis.
¨ ., Braun, J., 1963. A neutron rem counter with uniform sensitivity Andersson, I.O from 0.025 eV to 10 MeV. In: Proceedings of the Symposium on Neutron Dosimetry, vol. 2, Harwell, UK, 1962 (Vienna: IAEA), pp. 85–89. ¨ ., Braun, J., 1964. A neutron rem counter. Nucleonik 6, 237–241. Andersson, I.O Axton, E.J., 1972. The effective centre of a moderating sphere when used as an instrument for fast neutron flux measurement. J. Nucl. Energy 26, 581–583. Briesmeister, J.F. (Ed.) 2000. MCNP—a general Monte Carlo N-particle transport code, Version 4C. LANL Report LA-13709-M. Health and Safety Commission, 2000. Working with ionising radiation: ionising radiations regulations 1999 approved code of practice. ISBN 0-7176-1746-7. Hunt, J.B., 1984. The calibration of neutron sensitive spherical devices. Radiat. Prot. Dosim. 8, 239–251. International Organisation for Standardisation, 2000. Reference neutron radiations—Part 2: calibration fundamentals of radiation protection devices related to the basic quantities characterizing the radiation field. International Standard ISO 8529-2. Kluge, H., Weise, K., Hunt, J.B., 1990. Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes. Radiat. Prot. Dosim. 32, 233–244. Pulpa´n, J., Kra´lik, M., 1991. Geometrical correction factor. Radiat. Prot. Dosim. 35, 159–165. Tanner, R.J., Molinos, C., Roberts, N.J., Bartlett, D.T., Hager, L.G., Jones, L.N., Taylor, G.C., Thomas, D.J., 2006. Practical implications of neutron survey instrument performance. HPA Report HPA-RPD-016. Widell, C.-O., Svansson, L., 1973. A neutron monitor for radiation protection. In: Proceedings of the Symposium on Neutron Monitoring for Radiation Protection Purposes, Vienna, 1972 (Vienna: IAEA), pp. 225–230.
5. Conclusions There is strong evidence for a significant geometry effect being present in the irradiation of cylindrical neutron area survey