NEW DEVELOPMENTS AND APPLICATIONS OF SUPERHEATED EMULSIONS: WARHEAD VERIFICATION AND SPECIAL NUCLEAR MATERIAL INTERDICTION

NEW DEVELOPMENTS AND APPLICATIONS OF SUPERHEATED EMULSIONS: WARHEAD VERIFICATION AND SPECIAL... Abstract In recent years, neutron detection with superheated emulsions has received renewed attention thanks to improved detector manufacturing and read-out techniques, and thanks to successful applications in warhead verification and special nuclear material (SNM) interdiction. Detectors are currently manufactured with methods allowing high uniformity of the drop sizes, which in turn allows the use of optical read-out techniques based on dynamic light scattering. Small detector cartridges arranged in 2D matrices are developed for the verification of a declared warhead without revealing its design. For this application, the enabling features of the emulsions are that bubbles formed at different times cannot be distinguished from each other, while the passive nature of the detectors avoids the susceptibility to electronic snooping and tampering. Large modules of emulsions are developed to detect the presence of shielded special nuclear materials hidden in cargo containers ‘interrogated’ with high energy X-rays. In this case, the enabling features of the emulsions are photon discrimination, a neutron detection threshold close to 3 MeV and a rate-insensitive read-out. INTRODUCTION The verification of nuclear warheads and the interdiction of weapons grade ‘special nuclear materials’ (SNM) are two active areas of research with national and global security implications. Warhead verification methods are required for the next generation of arms control agreements. They must give inspectors high confidence in the authenticity of examined items while revealing nothing about their design. Past inspection systems relied on ‘information barriers’ to check the authenticity of an item and hide sensitive data recorded by electronic detectors, but they were found to be susceptible to tampering. Recently, Glaser et al.(1) proposed an approach to nuclear warhead verification based on a cryptographic zero-knowledge protocol whereby sensitive information is never measured and so does not need to be hidden. The approach uses a 2D neutron detector matrix that can be preloaded with the radiographic complement of an inspected warhead. The warhead is scanned with fast neutrons and the scan is recorded over the preload. If the superimposed weapon scan and preload match, the outcome is a uniform signal conveying no details of the weapon itself. Experiments with non-fissile objects confirmed the viability of this approach and its ability to detect various geometric and material diversions(2). A critical element in the implementation of the approach is the detector technology. The detectors must have the capability to be preloaded with a desired neutron count before the inspection. This preload must be stable, with minimal and well-characterized fading or sensitivity to background. The preloaded signal must be indistinguishable from the signal accumulated during the irradiation of the test items. The detectors must be insensitive to gamma-rays, while having high efficiency to neutrons in order to yield adequate statistics. Additionally, detectors must have a threshold behavior to minimize the detection of low energy neutrons returning from room walls. Finally, the detectors should be passive devices: relying on a non-electronic detection mechanism is highly desirable given that complex electronic components and circuits are potentially vulnerable to tampering and snooping. The interdiction of SNM also places heavy performance requirements on the detector systems. The goal here is to detect the presence in shipping containers of weapon components containing SNM, such as Pu-239 and highly enriched U-235 (HEU). These are extremely difficult to detect through their faint spontaneous radiation emission (especially for HEU, which can easily be shielded). Active interrogation techniques are considered the only viable option to detect shielded SNM. Radiation beams are used to trigger fission reactions, then prompt and/or delayed fission neutrons and/or gamma-rays are detected(3, 4). Among the favored active interrogation approaches is using X-rays from 9 MV electron linear accelerators. These X-rays have an effective energy causing adequate photofission in SNM, while avoiding neutron production in most ‘innocent’ materials, such as shipping container structures and legitimate contents. An exception is the production of photo-neutrons in naturally occurring deuterium; these neutrons can reach 3 MeV when produced by 9 MV X-rays. Therefore, in order to record the intense prompt neutron emission, an ideal detector should not only discriminate X-rays but also neutrons below ~3 MeV. Since the scan must be acquired and evaluated in real time, the detectors must be active and offer a rate-insensitive read out. This work describes the design and characterization of superheated emulsions(5) for applications in warhead verification and SNM interdiction. Superheated emulsions have become well-established among radiation detectors and they are included in recent standards issued by ISO(6) and ANSI(7). Several laboratories manufacture these detectors worldwide(5), and some make them available commercially(8) or within research collaborations(9). MATERIALS AND METHODS Detectors were manufactured in the form of emulsions placed inside glass containers, ranging from few-milliliter cartridges to several-liter tempered glass vessels. The metastable state of a superheated liquid is normally fragile and short-lived due to the microscopic particles and/or gas pockets present at the interface with container surfaces. However, fractionating a liquid into droplets and dispersing them in an immiscible fluid creates perfectly smooth spherical interfaces, free of nucleating impurities or irregularities. Thus an emulsified superheated liquid may be kept in steady-state metastable conditions. The emulsification of metastable superheated liquids in another fluid is rather complex, and the complexity increases when a mono-dispersed emulsion is sought, i.e. a dispersion of droplets of the same size. Magnetic stirrers, ultrasound fractionation and, in our case, coaxial flow proprietary techniques are employed. The latter allow the production of mono-dispersed emulsions containing droplets within 10% of any desired diameter between 50 and 200 μm (Figure 1). Figure 1. View largeDownload slide Micrograph of mono-dispersed, 100 μm diameter superheated drops of octafuorocyclobutane. Figure 1. View largeDownload slide Micrograph of mono-dispersed, 100 μm diameter superheated drops of octafuorocyclobutane. The emulsifier material must be clean and de-gassed, i.e. free of heterogeneous nucleation sites; it must also be immiscible and inert, so that droplets neither dissolve nor lose their properties through chemical reactions. In addition, the matrix must present either elevated viscosity or a close density match with the droplets to keep them suspended in the gel during and after manufacture. The matrix must also immobilize the radiation-induced bubbles and prevent their ‘explosive’ formation from triggering the boiling of adjacent drops. Number, size and composition of the droplets can be varied in the formulation of the detectors, and this permits a wide range of applications(5). For example, highly superheated halocarbons can be used for the detection of sparsely ionizing radiations, such as photons and electrons. In this work, halocarbons with a moderate degree of superheat were used (Table 1), since they are only nucleated by energetic heavy ions such as those released by fast neutron interactions. Table 1. Halocarbons used in the emulsions for nuclear warhead verification and for SNM interdiction. Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Table 1. Halocarbons used in the emulsions for nuclear warhead verification and for SNM interdiction. Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Performance results reported hereafter refer to octafluorocyclobutane emulsions manufactured as few-milliliter cartridges for warhead verification (Figure 2), or as several-liter modules for SNM interdiction. These detectors can be read out either post-exposure, e.g. with commercial image acquisition devices(8), or in real time, e.g. with dynamic light scattering techniques(4). Figure 2. View largeDownload slide Octafluorocyclobutane emulsions set up for ‘zero-knowledge’ nuclear warhead verification. Figure 2. View largeDownload slide Octafluorocyclobutane emulsions set up for ‘zero-knowledge’ nuclear warhead verification. A typical bubble read-out consists of counting bubbles from a 2D (y,z) projection of the volume perpendicular to the x axis (direction of light) and parallel to the vertical z axis of a cylindrical detector. This inherently introduces a non-linearity effect due to the fact that bubbles at the same (y,z) position but different x positions shadow or ‘occult’ one another. In a 2D projection, bubbles can overlap in a variety of ways, and the possibility of identifying or ‘segmenting’ them depends on the quality of the image analysis software. As the number of bubbles increases, the likelihood of occultation increases and eventually no algorithm can segment all bubbles from a single projection—similar to a saturation effect. To address this issue, we developed a bubble occultation model to correct data measured from a 2D projection and approximate the actual number of bubbles present in a cylindrical detector of radius, r(2). For an observer far away from the detector and looking in the x direction, every new bubble will be visible only if its image projection does not overlap the image of a pre-existing bubble. For every new bubble, the observer will see on average e−Σd bubbles, where, d is the mean chord of the cylinder along the line of sight (π/2r), and Σ is an effective macroscopic cross section. These parameters may be expressed as Σ=brσ/V, where, br is the real number of bubbles, σ is an effective (microscopic) occultation cross-section and V is the detector volume. As long as the number of bubbles in the detector corresponds to a small fraction of the total number of drops (~1%), we can assume the detector response to be linear. For every neutron n crossing the detector, on average ε bubbles will form (ε~10−4–10−3formLsizedetectors). If we assume that dbr/dn=ε, the observer will detect visible bubbles bv forming at a rate: dbvdn=εe−brσdV (1) Integrating Eq. (1) and using br=εn, we obtain: bv=Vσd(1−e−ϵnσdV) (2) This equation provides the number of visible bubbles as a function of real bubbles. It yields an efficiency ε at low fluences and saturates at bv=V/σd when br goes to infinity. To derive the number of true bubbles from the visible bubbles, we can rewrite Eq. (2) as follows: br=Vσdln((1−σdVbv)−1) (3) The parameters V/σd and ε can be obtained by fitting Eq. (2) to calibration data obtained for increasing neutron exposures. When the examined volume is smaller than the total detector volume, this procedure also compensates for other non-linear effects. Among the latter is the loss of counts occurring when the formation of bubbles displaces some detector material and other bubbles outside of the examined volume. RESULTS AND DISCUSSION All tests on the superheated emulsions were independently carried out at Princeton University, without any involvement of the manufacturing laboratory at Yale University. A batch homogeneity evaluation was first performed for the acceptance of the detectors. Detectors exposed 10 times to a fast neutron fluence producing ~120 bubbles were found to differ in sensitivity with a dispersion < 4% (1 standard deviation)(2). This is in agreement with the coefficient of variation reported earlier for superheated emulsions manufactured with the same technology(10). The previously described occultation model was applied to the calibration data. Figure 3 shows the observed data, both raw and corrected with Eq. (3). Data were compared to MCNP simulations of the experiment, performed simulating the irradiation field, folding neutron spectra with the known detector response function and assuming a linear behavior(2). The observed results (visible bubbles) follow a non-linear relationship correctly predicted by our model. When the data are corrected for the occultation phenomenon, the relationship between simulations and experimental results becomes linear, showing that our model captures most of the non-linearity of the data. Figure 3. View largeDownload slide Measured counts versus Monte-Carlo simulations of the irradiations. The occultation model captures adequately the non-linearity of the read-out technique. Figure 3. View largeDownload slide Measured counts versus Monte-Carlo simulations of the irradiations. The occultation model captures adequately the non-linearity of the read-out technique. As a further analysis of the response data, we verified that summed detector counts (preload and radiograph of an inspected item) follows Poisson statistics, i.e. that data obtained for all detectors have a variance equal to their bubble count. To verify that the count fluctuations of our detectors vary as √N, we generated synthetic data from our experimental results using the bootstrapping method(11). This method consists of estimating population parameters by randomly sampling with replacement from an approximating distribution—the empirical population obtained from our experimental data. Preloads and radiographs of various inspected items (the arrangements of materials hidden under the black box in Figure 2) were acquired with seven detectors and they were used as starting data sets. With these, we generated 1000 synthetic measurements for each case and obtained the bootstrapped mean and variance with their respective error bars. Results are reported in Figure 4 and demonstrate good agreement with the expected √N noise from Poisson statistics. Note that we used br deduced from the non-linear model. The good agreement indicates that the occultation process and its correction do not introduce significant additional noise at the level of non-linearity explored. Figure 4. View largeDownload slide Plot of the logarithm of the variance versus the logarithm of the average number of true (corrected) bubbles. Figure 4. View largeDownload slide Plot of the logarithm of the variance versus the logarithm of the average number of true (corrected) bubbles. Finally, the detectors were evaluated in terms of bubble size stability over a period of several months. The detectors were exposed to fast neutrons and then kept at room temperature and photographed periodically. As shown in Figure 5, bubbles remain quite stable over time. Only a minimal growth, due to gas/vapor entering the bubbles from the gel matrix, can be observed 2 months after the exposure. Figure 5. View largeDownload slide Photograph of bubbles in a superheated emulsion immediately after their formation (left), 2 weeks later (center) and 2 months later (right) [a few bubbles in the forefront appear larger due to magnification effects]. Figure 5. View largeDownload slide Photograph of bubbles in a superheated emulsion immediately after their formation (left), 2 weeks later (center) and 2 months later (right) [a few bubbles in the forefront appear larger due to magnification effects]. CONCLUSIONS Recent advances in the manufacturing and read-out of superheated emulsions enable new and advanced applications of this detector technology. The detectors present some features that are critical for a novel ‘zero knowledge’ warhead verification approach: bubbles formed at different times cannot be optically distinguished from each other, while the passive nature of the detectors prevents the susceptibility to electronic snooping and tampering. Superheated emulsions are also suitable to detect shielded SNM with active interrogation: they are insensitive to photons, they provide desirable neutron detection thresholds and can be read out in real time in a rate-insensitive manner. Optical bubble counting methods can be used with the detectors, either passive—based on image acquisitions, or active—based on dynamic light scattering. Both optical read-out methods are affected by non-linearities due to ‘occultation’ effects occurring for increasing numbers of bubbles. Careful modeling of these effects was done in order to achieve an accurate quantification of the number of bubbles. FUNDING Research supported by DHS grant (ARI 1038897) and DOE/NNSA grant (DE-NA 0002534). REFERENCES 1 Glaser , A. , Barak , B. and Goldston , R. A zero-knowledge protocol for nuclear warhead verification . Nature 510 , 497 – 502 ( 2014 ). Google Scholar CrossRef Search ADS PubMed 2 Philippe , S. , Glaser , A. , Goldston , R. and d’Errico , F. A physical zero-knowledge object-comparison system for nuclear warhead verification . Nat. Commun. 7 , 12890 ( 2016 ). Google Scholar CrossRef Search ADS PubMed 3 Medalia , J. E. Detection of Nuclear Weapons and Materials ( Washington, DC : Congressional Research Service ) ( 2010 ) 7-5700, R40154. 4 d’Errico , F. and Di Fulvio , A. Superheated emulsions for the detection of special nuclear material . Radiat. Meas. 46 ( 12 ), 1690 – 1693 ( 2011 ). Google Scholar CrossRef Search ADS 5 d’Errico , F. Radiation dosimetry and spectrometry with superheated emulsions . Nucl. Instrum. Methods B 184 , 229 – 254 ( 2001 ). Google Scholar CrossRef Search ADS 6 International Organization for Standardization . Passive Personal Neutron Dosimetry Systems. Performance and Test Requirements ( Geneva, CH : ISO ) ( 2002 ) 21909. 7 American National Standards Institute . Personnel Neutron Dosimeters (Neutron Energies Less Than 20 MeV) ( McLean, VA : HPS ) ( 2000 ) ANSI/HPS N13.52-1999. 8 Bubble Technology Industries . Chalk River, Ontario, Canada K0J 1J0. http://bubbletech.ca/. 9 Yale University . Office of Cooperative Research, New Haven, CT 06519, USA http://ocr.yale.edu/. 10 Vanhavere , F. and d’Errico , F. Standardisation of superheated drop and bubble detectors . Radiat. Prot. Dosim. 101 ( 1–4 ), 283 – 287 ( 2002 ). Google Scholar CrossRef Search ADS 11 Efron , B. and Tibshirani , R. J. An Introduction to the Bootstrap ( Boca Raton, FL : CRC Press ) ( 1994 ). © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Radiation Protection Dosimetry Oxford University Press

NEW DEVELOPMENTS AND APPLICATIONS OF SUPERHEATED EMULSIONS: WARHEAD VERIFICATION AND SPECIAL NUCLEAR MATERIAL INTERDICTION

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Abstract

Abstract In recent years, neutron detection with superheated emulsions has received renewed attention thanks to improved detector manufacturing and read-out techniques, and thanks to successful applications in warhead verification and special nuclear material (SNM) interdiction. Detectors are currently manufactured with methods allowing high uniformity of the drop sizes, which in turn allows the use of optical read-out techniques based on dynamic light scattering. Small detector cartridges arranged in 2D matrices are developed for the verification of a declared warhead without revealing its design. For this application, the enabling features of the emulsions are that bubbles formed at different times cannot be distinguished from each other, while the passive nature of the detectors avoids the susceptibility to electronic snooping and tampering. Large modules of emulsions are developed to detect the presence of shielded special nuclear materials hidden in cargo containers ‘interrogated’ with high energy X-rays. In this case, the enabling features of the emulsions are photon discrimination, a neutron detection threshold close to 3 MeV and a rate-insensitive read-out. INTRODUCTION The verification of nuclear warheads and the interdiction of weapons grade ‘special nuclear materials’ (SNM) are two active areas of research with national and global security implications. Warhead verification methods are required for the next generation of arms control agreements. They must give inspectors high confidence in the authenticity of examined items while revealing nothing about their design. Past inspection systems relied on ‘information barriers’ to check the authenticity of an item and hide sensitive data recorded by electronic detectors, but they were found to be susceptible to tampering. Recently, Glaser et al.(1) proposed an approach to nuclear warhead verification based on a cryptographic zero-knowledge protocol whereby sensitive information is never measured and so does not need to be hidden. The approach uses a 2D neutron detector matrix that can be preloaded with the radiographic complement of an inspected warhead. The warhead is scanned with fast neutrons and the scan is recorded over the preload. If the superimposed weapon scan and preload match, the outcome is a uniform signal conveying no details of the weapon itself. Experiments with non-fissile objects confirmed the viability of this approach and its ability to detect various geometric and material diversions(2). A critical element in the implementation of the approach is the detector technology. The detectors must have the capability to be preloaded with a desired neutron count before the inspection. This preload must be stable, with minimal and well-characterized fading or sensitivity to background. The preloaded signal must be indistinguishable from the signal accumulated during the irradiation of the test items. The detectors must be insensitive to gamma-rays, while having high efficiency to neutrons in order to yield adequate statistics. Additionally, detectors must have a threshold behavior to minimize the detection of low energy neutrons returning from room walls. Finally, the detectors should be passive devices: relying on a non-electronic detection mechanism is highly desirable given that complex electronic components and circuits are potentially vulnerable to tampering and snooping. The interdiction of SNM also places heavy performance requirements on the detector systems. The goal here is to detect the presence in shipping containers of weapon components containing SNM, such as Pu-239 and highly enriched U-235 (HEU). These are extremely difficult to detect through their faint spontaneous radiation emission (especially for HEU, which can easily be shielded). Active interrogation techniques are considered the only viable option to detect shielded SNM. Radiation beams are used to trigger fission reactions, then prompt and/or delayed fission neutrons and/or gamma-rays are detected(3, 4). Among the favored active interrogation approaches is using X-rays from 9 MV electron linear accelerators. These X-rays have an effective energy causing adequate photofission in SNM, while avoiding neutron production in most ‘innocent’ materials, such as shipping container structures and legitimate contents. An exception is the production of photo-neutrons in naturally occurring deuterium; these neutrons can reach 3 MeV when produced by 9 MV X-rays. Therefore, in order to record the intense prompt neutron emission, an ideal detector should not only discriminate X-rays but also neutrons below ~3 MeV. Since the scan must be acquired and evaluated in real time, the detectors must be active and offer a rate-insensitive read out. This work describes the design and characterization of superheated emulsions(5) for applications in warhead verification and SNM interdiction. Superheated emulsions have become well-established among radiation detectors and they are included in recent standards issued by ISO(6) and ANSI(7). Several laboratories manufacture these detectors worldwide(5), and some make them available commercially(8) or within research collaborations(9). MATERIALS AND METHODS Detectors were manufactured in the form of emulsions placed inside glass containers, ranging from few-milliliter cartridges to several-liter tempered glass vessels. The metastable state of a superheated liquid is normally fragile and short-lived due to the microscopic particles and/or gas pockets present at the interface with container surfaces. However, fractionating a liquid into droplets and dispersing them in an immiscible fluid creates perfectly smooth spherical interfaces, free of nucleating impurities or irregularities. Thus an emulsified superheated liquid may be kept in steady-state metastable conditions. The emulsification of metastable superheated liquids in another fluid is rather complex, and the complexity increases when a mono-dispersed emulsion is sought, i.e. a dispersion of droplets of the same size. Magnetic stirrers, ultrasound fractionation and, in our case, coaxial flow proprietary techniques are employed. The latter allow the production of mono-dispersed emulsions containing droplets within 10% of any desired diameter between 50 and 200 μm (Figure 1). Figure 1. View largeDownload slide Micrograph of mono-dispersed, 100 μm diameter superheated drops of octafuorocyclobutane. Figure 1. View largeDownload slide Micrograph of mono-dispersed, 100 μm diameter superheated drops of octafuorocyclobutane. The emulsifier material must be clean and de-gassed, i.e. free of heterogeneous nucleation sites; it must also be immiscible and inert, so that droplets neither dissolve nor lose their properties through chemical reactions. In addition, the matrix must present either elevated viscosity or a close density match with the droplets to keep them suspended in the gel during and after manufacture. The matrix must also immobilize the radiation-induced bubbles and prevent their ‘explosive’ formation from triggering the boiling of adjacent drops. Number, size and composition of the droplets can be varied in the formulation of the detectors, and this permits a wide range of applications(5). For example, highly superheated halocarbons can be used for the detection of sparsely ionizing radiations, such as photons and electrons. In this work, halocarbons with a moderate degree of superheat were used (Table 1), since they are only nucleated by energetic heavy ions such as those released by fast neutron interactions. Table 1. Halocarbons used in the emulsions for nuclear warhead verification and for SNM interdiction. Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Table 1. Halocarbons used in the emulsions for nuclear warhead verification and for SNM interdiction. Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Halocarbon name and code Chemical formula Boiling point (°C) Critical point (°C) Octafluorocyclobutane, C-318 C4F8 −7 115.2 Decafluorobutane, R-610 C4F10 −1.7 113.3 Performance results reported hereafter refer to octafluorocyclobutane emulsions manufactured as few-milliliter cartridges for warhead verification (Figure 2), or as several-liter modules for SNM interdiction. These detectors can be read out either post-exposure, e.g. with commercial image acquisition devices(8), or in real time, e.g. with dynamic light scattering techniques(4). Figure 2. View largeDownload slide Octafluorocyclobutane emulsions set up for ‘zero-knowledge’ nuclear warhead verification. Figure 2. View largeDownload slide Octafluorocyclobutane emulsions set up for ‘zero-knowledge’ nuclear warhead verification. A typical bubble read-out consists of counting bubbles from a 2D (y,z) projection of the volume perpendicular to the x axis (direction of light) and parallel to the vertical z axis of a cylindrical detector. This inherently introduces a non-linearity effect due to the fact that bubbles at the same (y,z) position but different x positions shadow or ‘occult’ one another. In a 2D projection, bubbles can overlap in a variety of ways, and the possibility of identifying or ‘segmenting’ them depends on the quality of the image analysis software. As the number of bubbles increases, the likelihood of occultation increases and eventually no algorithm can segment all bubbles from a single projection—similar to a saturation effect. To address this issue, we developed a bubble occultation model to correct data measured from a 2D projection and approximate the actual number of bubbles present in a cylindrical detector of radius, r(2). For an observer far away from the detector and looking in the x direction, every new bubble will be visible only if its image projection does not overlap the image of a pre-existing bubble. For every new bubble, the observer will see on average e−Σd bubbles, where, d is the mean chord of the cylinder along the line of sight (π/2r), and Σ is an effective macroscopic cross section. These parameters may be expressed as Σ=brσ/V, where, br is the real number of bubbles, σ is an effective (microscopic) occultation cross-section and V is the detector volume. As long as the number of bubbles in the detector corresponds to a small fraction of the total number of drops (~1%), we can assume the detector response to be linear. For every neutron n crossing the detector, on average ε bubbles will form (ε~10−4–10−3formLsizedetectors). If we assume that dbr/dn=ε, the observer will detect visible bubbles bv forming at a rate: dbvdn=εe−brσdV (1) Integrating Eq. (1) and using br=εn, we obtain: bv=Vσd(1−e−ϵnσdV) (2) This equation provides the number of visible bubbles as a function of real bubbles. It yields an efficiency ε at low fluences and saturates at bv=V/σd when br goes to infinity. To derive the number of true bubbles from the visible bubbles, we can rewrite Eq. (2) as follows: br=Vσdln((1−σdVbv)−1) (3) The parameters V/σd and ε can be obtained by fitting Eq. (2) to calibration data obtained for increasing neutron exposures. When the examined volume is smaller than the total detector volume, this procedure also compensates for other non-linear effects. Among the latter is the loss of counts occurring when the formation of bubbles displaces some detector material and other bubbles outside of the examined volume. RESULTS AND DISCUSSION All tests on the superheated emulsions were independently carried out at Princeton University, without any involvement of the manufacturing laboratory at Yale University. A batch homogeneity evaluation was first performed for the acceptance of the detectors. Detectors exposed 10 times to a fast neutron fluence producing ~120 bubbles were found to differ in sensitivity with a dispersion < 4% (1 standard deviation)(2). This is in agreement with the coefficient of variation reported earlier for superheated emulsions manufactured with the same technology(10). The previously described occultation model was applied to the calibration data. Figure 3 shows the observed data, both raw and corrected with Eq. (3). Data were compared to MCNP simulations of the experiment, performed simulating the irradiation field, folding neutron spectra with the known detector response function and assuming a linear behavior(2). The observed results (visible bubbles) follow a non-linear relationship correctly predicted by our model. When the data are corrected for the occultation phenomenon, the relationship between simulations and experimental results becomes linear, showing that our model captures most of the non-linearity of the data. Figure 3. View largeDownload slide Measured counts versus Monte-Carlo simulations of the irradiations. The occultation model captures adequately the non-linearity of the read-out technique. Figure 3. View largeDownload slide Measured counts versus Monte-Carlo simulations of the irradiations. The occultation model captures adequately the non-linearity of the read-out technique. As a further analysis of the response data, we verified that summed detector counts (preload and radiograph of an inspected item) follows Poisson statistics, i.e. that data obtained for all detectors have a variance equal to their bubble count. To verify that the count fluctuations of our detectors vary as √N, we generated synthetic data from our experimental results using the bootstrapping method(11). This method consists of estimating population parameters by randomly sampling with replacement from an approximating distribution—the empirical population obtained from our experimental data. Preloads and radiographs of various inspected items (the arrangements of materials hidden under the black box in Figure 2) were acquired with seven detectors and they were used as starting data sets. With these, we generated 1000 synthetic measurements for each case and obtained the bootstrapped mean and variance with their respective error bars. Results are reported in Figure 4 and demonstrate good agreement with the expected √N noise from Poisson statistics. Note that we used br deduced from the non-linear model. The good agreement indicates that the occultation process and its correction do not introduce significant additional noise at the level of non-linearity explored. Figure 4. View largeDownload slide Plot of the logarithm of the variance versus the logarithm of the average number of true (corrected) bubbles. Figure 4. View largeDownload slide Plot of the logarithm of the variance versus the logarithm of the average number of true (corrected) bubbles. Finally, the detectors were evaluated in terms of bubble size stability over a period of several months. The detectors were exposed to fast neutrons and then kept at room temperature and photographed periodically. As shown in Figure 5, bubbles remain quite stable over time. Only a minimal growth, due to gas/vapor entering the bubbles from the gel matrix, can be observed 2 months after the exposure. Figure 5. View largeDownload slide Photograph of bubbles in a superheated emulsion immediately after their formation (left), 2 weeks later (center) and 2 months later (right) [a few bubbles in the forefront appear larger due to magnification effects]. Figure 5. View largeDownload slide Photograph of bubbles in a superheated emulsion immediately after their formation (left), 2 weeks later (center) and 2 months later (right) [a few bubbles in the forefront appear larger due to magnification effects]. CONCLUSIONS Recent advances in the manufacturing and read-out of superheated emulsions enable new and advanced applications of this detector technology. The detectors present some features that are critical for a novel ‘zero knowledge’ warhead verification approach: bubbles formed at different times cannot be optically distinguished from each other, while the passive nature of the detectors prevents the susceptibility to electronic snooping and tampering. Superheated emulsions are also suitable to detect shielded SNM with active interrogation: they are insensitive to photons, they provide desirable neutron detection thresholds and can be read out in real time in a rate-insensitive manner. Optical bubble counting methods can be used with the detectors, either passive—based on image acquisitions, or active—based on dynamic light scattering. Both optical read-out methods are affected by non-linearities due to ‘occultation’ effects occurring for increasing numbers of bubbles. Careful modeling of these effects was done in order to achieve an accurate quantification of the number of bubbles. FUNDING Research supported by DHS grant (ARI 1038897) and DOE/NNSA grant (DE-NA 0002534). REFERENCES 1 Glaser , A. , Barak , B. and Goldston , R. A zero-knowledge protocol for nuclear warhead verification . Nature 510 , 497 – 502 ( 2014 ). Google Scholar CrossRef Search ADS PubMed 2 Philippe , S. , Glaser , A. , Goldston , R. and d’Errico , F. A physical zero-knowledge object-comparison system for nuclear warhead verification . Nat. Commun. 7 , 12890 ( 2016 ). Google Scholar CrossRef Search ADS PubMed 3 Medalia , J. E. Detection of Nuclear Weapons and Materials ( Washington, DC : Congressional Research Service ) ( 2010 ) 7-5700, R40154. 4 d’Errico , F. and Di Fulvio , A. Superheated emulsions for the detection of special nuclear material . Radiat. Meas. 46 ( 12 ), 1690 – 1693 ( 2011 ). Google Scholar CrossRef Search ADS 5 d’Errico , F. Radiation dosimetry and spectrometry with superheated emulsions . Nucl. Instrum. Methods B 184 , 229 – 254 ( 2001 ). Google Scholar CrossRef Search ADS 6 International Organization for Standardization . Passive Personal Neutron Dosimetry Systems. Performance and Test Requirements ( Geneva, CH : ISO ) ( 2002 ) 21909. 7 American National Standards Institute . Personnel Neutron Dosimeters (Neutron Energies Less Than 20 MeV) ( McLean, VA : HPS ) ( 2000 ) ANSI/HPS N13.52-1999. 8 Bubble Technology Industries . Chalk River, Ontario, Canada K0J 1J0. http://bubbletech.ca/. 9 Yale University . Office of Cooperative Research, New Haven, CT 06519, USA http://ocr.yale.edu/. 10 Vanhavere , F. and d’Errico , F. Standardisation of superheated drop and bubble detectors . Radiat. Prot. Dosim. 101 ( 1–4 ), 283 – 287 ( 2002 ). Google Scholar CrossRef Search ADS 11 Efron , B. and Tibshirani , R. J. An Introduction to the Bootstrap ( Boca Raton, FL : CRC Press ) ( 1994 ). © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Radiation Protection DosimetryOxford University Press

Published: Aug 1, 2018

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