Radiation Protection Dosimetry (2015), Vol. 164, No. 3, pp. 203 –209 Advance Access publication 16 September 2014
doi:10.1093/rpd/ncu288
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS OF VARIOUS ENERGIES M. B. Smith*, H. R. Andrews, H. Ing and M. R. Koslowsky Bubble Technology Industries, PO Box 100, Chalk River, Ontario K0J 1J0, Canada *Corresponding author: [email protected] Received 23 June 2014; revised 7 August 2014; accepted 18 August 2014
INTRODUCTION (1)
The bubble detector was first introduced 30 y ago to address an urgent need in the nuclear industry for a personal neutron dosemeter that would meet the requirements for safe radiation monitoring of personnel. In the intervening years, the bubble detector has been used in an enormous variety of venues including spacecraft, nuclear submarines, subterranean facilities, hospitals, high-energy physics laboratories, military operations, aircraft, movies, schools and the nuclear industry, encompassing power generation, fuel processing and calibration facilities. Numerous groups have assessed the performance of these detectors in relation to their particular applications. A few examples include studies by Chemtob et al.(2), Buckner et al.(3), Hoffman et al.(4), Nelson and Gordon(5), Olsen(6), Rosenstock et al.(7), Sawicki (8), Vanhavere et al.(9), Green et al.(10), Barnabe´-Heider et al.(11), McLean et al.(12), Matiullah et al.(13), Takada et al.(14), Andrews et al.(15) and Smith et al.(16). Essentially all of these studies were experimental because the theoretical basis for the processes behind the bubble detector is very complicated and not fully understood. These processes involve neutron interactions, charged-particle transport, energy transfer in gel and superheated media, liquid nucleation phenomena and gas diffusion. They include subatomic processes, molecular physics, mechanical engineering and chemical engineering and span time domains from 10214 s to weeks. Therefore, a full theoretical understanding of the physical processes behind the bubble detector is a significant technical challenge. Several groups, e.g. Buckner et al.(3), Barnabe´-Heider et al.(11) and Harper and Nelson(17), have studied some of the basic phenomena behind the bubble detector. These theoretical studies dealt mainly with the impact of temperature changes on the response of the
detector, effects that were important for earlier bubble detectors. Temperature effects are not so important for current detectors (Figure 1) because they are temperature-compensated, enabling them to be used for personnel monitoring in most work environments. The main emphasis of the current study is to understand the basic processes that are responsible for the dependence of the detector response on neutron energy. It should be mentioned that another type of detector, commonly called the superheated drop detector (SDD), bears close resemblance to the bubble detector in terms of the physics of bubble formation and is often confused with the bubble detector(18). However, the chemical formulation of the SDD is different from that of the bubble detector, and the SDD uses completely different approaches to account for its temperature dependence. Some theoretical interpretation of the fundamental properties of the SDD has been performed by groups involved with that technology(19). The work described in this paper should be interpreted as being applicable only to the bubble detector. The energy response of the SDD is expected to be different from that of the bubble detector because of its different chemical formulation. The current work was primarily driven by the need to better understand the energy dependence of the bubble detector for current and future applications in space. The use of the bubble detector in the monitoring of radiation exposure of astronauts is probably the most challenging of all applications for which the detector has been deployed. This is due to the fact that neutron radiation in space has a significant component with energy of .20 MeV. This is unlike radiation in most terrestrial environments, with the exception of high-energy physics laboratories. Monoenergetic neutron sources in this energy range (the Fermi energy domain) are non-existent, making calibration of detectors for the space environment difficult. A few
# The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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A series of Monte-Carlo simulations has been performed in order to investigate the response of the bubble detector to monoenergetic neutrons of various energies. The work was driven by the need to better understand the energy dependence of the detector for applications in space, where the neutron spectrum has a significant component with energy of >20 MeV. The response to neutrons in the range of a few keV to 500 MeV has been calculated, and good agreement between the simulations and experimental data is demonstrated over the entire energy range.
M. B. SMITH ET AL.
specialised laboratories can provide quasi-monoenergetic neutron beams with energies of 50 MeV and higher, but these beams are not well characterised. Thus, it is necessary to rely on good theoretical modelling in order to characterise the behaviour of the bubble detector, especially over this difficult energy region, to ensure that good dosimetric accuracy is maintained for space applications. Ground-based experiments have shown(14, 15) that the bubble detector responds to energetic charged particles as well as neutrons. However, in low Earth orbit (LEO), where most bubble-detector measurements in space have been performed, the relative abundance of charged particles and neutrons is such that bubble detectors provide reliable measurements of the neutron dose. The contribution of charged particles to the detector reading has been estimated(16) to be ,2 %. This is primarily because most of the protons in LEO are encountered during the short passes through the South Atlantic anomaly, where trapped protons are relatively low in energy (200 MeV) and are more efficient in producing neutrons than higher-energy protons from cosmic rays. However, for future expeditions beyond LEO (including flights to the moon and Mars), the mix of charged particles and neutrons will differ. For these missions, it will be necessary to re-evaluate the contribution of charged particles to the readings of bubble detectors. A good understanding of the response of the bubble detector from reliable modelling will be crucial to the correct interpretation of data from these environments.
NUCLEATION IN THE SUPERHEATED MEDIUM The formation of bubbles in the bubble detector is commonly interpreted using the thermal spike theory
Emin ¼
16ps3 ðDpÞ2
2 1 þ rv H=ðMDpÞ 3
ð1Þ
where s is the surface tension of the liquid, Dp is the superheat (defined as the difference between the vapour pressure of the superheated liquid at the ambient temperature and the externally applied pressure—usually atmospheric), rv is the density of the vapour, H is the molar heat of vaporisation and M is the molecular weight of the superheated liquid. Thus, for a particular formulation of the bubble detector, having a particular type of superheated droplets and used at a particular temperature and pressure, there is a minimum neutron energy required in order to produce the required Emin for producing bubbles in the detector. Therefore, inherently, bubble detectors are threshold detectors having no response to neutrons below a particular energy. For a chosen detector medium, the energy threshold of the detector can be controlled by the selection of a particular detector liquid having a particular superheat (i.e. boiling point) at a desired operating point (e.g. ambient temperature and pressure) for the detector. This property has been utilised to produce the bubble detector spectrometer (BDS), a set of six detectors with different energy thresholds, to enable the measurement of the energy spectrum of fast neutrons. A special version of the BDS, known as the space BDS or SBDS, has recently been developed(16) for use on the International Space Station. The energy required to form a vapour bubble with radius at least equal to the critical radius was calculated using thermodynamics by computing the work done to grow a vapour bubble from zero radius to the critical radius. For bubble detectors, the exact energy
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Figure 1. Temperature-compensated bubble detectors.
proposed by Seitz(20). This theory hypothesises that ionising particles, such as those produced by neutron interactions with the nucleus, create regions of plasmalike medium known as temperature spikes. When these spikes occur within one of the multitude of superheated liquid droplets in a bubble detector, the liquid explodes into nascent bubbles because of the energy stored in the superheated state. If one or more of these nascent bubbles is large enough to exceed the critical radius for bubble formation, the bubble will grow by consuming the superheated liquid in its vicinity. This growth stops when all the liquid in the superheated droplet is vaporised, giving rise to a visible bubble whose size is determined by the size of the original superheated droplet. If none of the nascent bubbles exceed the critical radius, the surface tension of the superheated liquid will recompress the bubbles back into the liquid phase, and no bubbles will result from the neutron interaction. Seitz provided a formula for the minimum amount of energy (Emin) required to create a critical bubble, which, assuming adiabatic conditions, can be written as follows:
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS
CALCULATION OF THE BUBBLE-DETECTOR RESPONSE The response of the bubble detector has been simulated using the Geant4(22) Monte-Carlo software toolkit (version 9.5, patch 1) (http://geant4.web.cern. ch/). Geant4 uses a physics list to define the processes included in the simulations. The physics list employed in the bubble-detector simulations was based on the built-in QBBC physics list, with the following modifications: NeutronHP physics was added for neutrons of ,20 MeV; standard electromagnetic (EM) physics was replaced with Penelope EM physics and neutron tracking cuts were not employed. The production cuts used were 3 mm for electrons and positrons (so that electrons and positrons that are produced and subsequently travel ,3 mm are ignored in the simulation) and 1 nm for other particles. The reason for the high production cut for electrons was to reduce the large number of free electrons generated by recoil protons. These electrons do not contribute to bubble formation, so a cut was set so that fewer electrons would be generated, thus reducing the time spent by the simulations in tracking unimportant particles. A shortcoming of the Geant4 NeutronHP physics model is that it does not model a handful of reactions, including the 12C(n, n0 )3a break-up reaction. While other Geant4 physics models do model this carbon break-up reaction, they are considered worse than the NeutronHP model in most other areas. A method to work around this deficiency was developed and is described later in this paper. Two different geometries were used in Geant4 to determine the neutron response of the bubble detector. The first geometry, used for neutron energies of ,20 MeV, was based on a single fluorocarbon droplet in a bubble detector. A sphere of fluorocarbon (with chemical composition representative of a droplet in a bubble detector) with radius of 10 mm was surrounded by a spherical shell of material similar to the polymer gel used in the bubble detector. The radius of the gel
surrounding the fluorocarbon droplet was equal to the mean range of a recoil proton with maximum energy from an incoming neutron. This radius was chosen with the aim of realistically modelling the effect of recoil particles from the gel reaching the droplet. The geometry was therefore dependent on the neutron energy chosen for the simulation. Neutrons were fired at this geometry in a cylindrical beam with radius equal to the outer radius of the gel. This geometry is referred to as the droplet geometry. For the second geometry, a 10 ` 10-cm layer of 20-mm-thick fluorocarbon was placed behind a 10` 10-cm layer of 1-cm-thick gel. The compositions of the fluorocarbon and gel were the same as those used for the droplet geometry. A line beam of neutrons was fired at the centre of the 10 ` 10-cm layers. This geometry is referred to as the block geometry. The advantage of the droplet geometry over the block geometry is that it more accurately reflects the scenario of a droplet inside a bubble detector. However, as the radius of the gel in the droplet model increases (for higher neutron energies), the cross-sectional area of the droplet quickly becomes a small fraction of the beam area, and collecting good counting statistics at higher energies becomes time-consuming. The block geometry does not suffer from this deficiency and was therefore used for investigations at energies of .20 MeV. Scoring, in both models, was approached in the following way. For secondary particles generated inside the fluorocarbon droplet, the initial energy of the particle was recorded, as was the energy of the particle as it exited the fluorocarbon (zero exit energy was recorded if it did not leave the droplet). Similarly, for secondary particles entering the fluorocarbon from the gel, the energy of the particle as it entered the droplet was recorded along with its exit energy. The data for each particle were output and read into a separate program that analysed the results to decide whether the LET of a given particle was high enough to cause nucleation, given the energy range with which the particle went through the fluorocarbon. The Stopping and Range of Ions in Matter code (http:// www.srim.org/) was used in this analysis. In this approach, the LET threshold (as described in the previous section) could be chosen during the data analysis without re-running the Monte-Carlo simulations. For the block geometry, events generating at least one ion above this LET threshold were scored. For the droplet geometry, the number of particles above the LET threshold was computed, and this number was scaled by the neutron fluence used in the simulation to calculate the response of a single droplet per unit fluence. In the case of the block geometry, the results were instead scaled by the number of primary neutrons used in the simulation. For both geometries, the resulting response curves were normalised so that they would produce one bubble if exposed to 1 mrem of radiation from an
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required is not of particular interest, except to note that it depends only on macroscopic properties of the superheated liquid used to form the droplets, and can therefore be treated as a function of external temperature and pressure. A particle traversing the superheated droplet will cause a bubble to form if it can deposit an amount of energy equal to the threshold energy within a short distance. A threshold energy E and a distance L, across which the energy transfer must occur, defines an energy transfer of E/L, which is commonly referred to as the linear energy transfer (LET) threshold. It is thus reasonable to assume that if a particle ever has LET in the droplet of at least the threshold LET, then a bubble is formed. This assumption is good as long as L is small (theoretically L is 20 nm)(21).
M. B. SMITH ET AL.
RESULTS AND DISCUSSION The investigation described in this paper concentrates on the SBDS-100 detector, although the method is extensible to the other detectors making up the SBDS, or to terrestrial bubble detectors such as the BD-PNDTM used for personal neutron dosimetry. Figure 2 presents the response curves created from the simulations using the droplet geometry. These results
are normalised to the neutron fluence and an AmBe source and include the correction for carbon break-up in the 12C(n, n0 )3a reaction. Several response curves are presented, corresponding to the different LET thresholds used in the data analysis, ranging from 40 to 150 keV/mm. Figure 3 shows the results of the simulations using the block geometry, analysed using the same LET thresholds. These response curves are normalised by the number of primary neutrons and to the AmBe source. It is evident that the simulations performed using the droplet and block geometries are in good agreement. The data were combined, using the droplet data up to 20 MeV and the block data above 20 MeV, to produce an overall set of response curves. These combined curves are presented in Figure 4 and span the energy range from a few keV up to 500 MeV. The Monte-Carlo data provided in Figure 4 have been compared with the empirical data used to generate the SBDS response matrix(16). These experimental data were measured using monoenergetic neutron beams produced by the Defence Research and Development Canada Van de Graaff accelerator facility in Ottawa (,20 MeV) and the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) in Faure, South Africa (.90 MeV). Comparison of the data indicated that the MonteCarlo calculations agree best with the experimental
Figure 2. Bubble-detector response calculated using the droplet geometry, corrected for carbon break-up and normalised to neutron fluence and an AmBe source.
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AmBe neutron source (equivalent to 10.7 mSv). This corresponds to the calibration procedure used for bubble detectors(16). For many applications, including those in space, the quantity reported by the bubble detector is considered to be the ambient dose equivalent, H*(10). In order to work around the 12C(n, n0 )3a reaction missing from the simulations, the following approach was used. First, the number of 15N ions in the droplet during the simulation was calculated. These ions were attributed to be products of the 19F(n, n0 )a reaction. The number of 15N ions was scaled by the ratio of the 19 F(n, n0 )a cross section to the 12C(n, n0 )3a cross section and then multiplied by 3 to estimate the number of alpha particles produced. This approach impacted the detector response from 5 to 20 MeV, increasing the response in this energy range by ,10 % for all LET thresholds considered in this work.
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS
Figure 4. Combined bubble-detector response from the droplet and block geometries.
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Figure 3. Bubble-detector response calculated using the block geometry, normalised to the total number of primary neutrons and an AmBe source.
M. B. SMITH ET AL.
data for the SBDS-100 detector using an LET threshold of 130 keV/mm. Other thresholds used in the response calculations are representative of the other detectors that comprise the SBDS. The calculations for the 130-keV/mm threshold are compared with the experimental SBDS-100 data in Figure 5. It should be noted that the simulated and empirical data are presented on an absolute scale, with no normalisation between the two. Reasonable agreement between the calculations and the empirical data is obtained over the entire energy range.
unfolding. The modelling capability enables rigorous analysis of the readings of bubble detectors deployed in space missions, including a variety of radiation environments that will be encountered in the future. FUNDING This work was supported by the Canadian Space Agency. REFERENCES
CONCLUSIONS The Monte-Carlo simulations presented in this work provide important insight into the processes responsible for bubble formation in a bubble detector. In particular, the LET required to create bubbles in the SBDS-100 detector has been elucidated. The Geant4 model described is expected to make major contributions to future work with bubble detectors, particularly for analysis of data from space. With this modelling capability established, it is possible to simulate the bubble-detector response due to any particle (neutrons, protons, heavy ions, pions, etc.) with any energy. The simulated response may also be employed to improve the empirical response matrix used in data 208
1. Ing, H. and Birnboim, H. C. A bubble-damage polymer detector for neutrons. Nucl. Tracks Radiat. Meas. 8, 285– 288 (1984). 2. Chemtob, M., Dollo, R., Coquema, C., Chary, J. and Ginisty, C. Essais de dosime`tres neutrons a` bulles, mode`le BD 100 R-PND et mode`le BDT. Radioprotection. 30(1), 61– 78 (1995). 3. Buckner, M. A., Noulty, R. A. and Cousins, T. The effect of temperature on the neutron energy thresholds of Bubble Technology Industries’ bubble detector spectrometer. Radiat. Prot. Dosim. 55(1), 23–30 (1994). 4. Hoffman, J. M., Harvey, W. F. and Foltyn, E. M. Bubble dosimetry experience at Los Alamos National Laboratory. Report LA-UR-92-3700, Los Alamos National Laboratory (1992). 5. Nelson, M. E. and Gordon, R. Comparison of neutron measurements at linacs using bubble dosemeters to other
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Figure 5. Comparison of experimental data for the SBDS-100 detector with the Monte-Carlo response calculated for a 130-keV/mm threshold.
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS
6. 7.
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of BD-100R bubble and CR-39 based neutron detectors for personnel neutron dosimetry. Radiat. Prot. Dosim. 47(1– 4), 555–558 (1993). Takada, M., Kitamura, H., Koi, T., Nakamura, T. and Fujitaka, K. Measured proton sensitivities of bubble detectors. Radiat. Prot. Dosim. 111(2), 181– 189 (2004). Andrews, H. R., Noulty, R. A., Ing, H., d’Errico, F., Lewis, B. J., Bennett, L. G. I. and Green, A. R. LET dependence of bubble detector response to heavy ions. Radiat. Prot. Dosim. 120(1– 4), 480– 484 (2006). Smith, M. B. et al. Measurements of the neutron dose and energy spectrum on the International Space Station during expeditions ISS-16 to ISS-21. Radiat. Prot. Dosim. 153(4), 509 –533 (2013). Harper, M. J. and Nelson, M. E. Experimental verification of a superheated liquid droplet (bubble) neutron detector theoretical model. Radiat. Prot. Dosim. 47(1–4), 535–542 (1993). Knoll, G. F. Radiation Detection and Measurement, fourth edn. Wiley (2010). ISBN: 978-0-470-13148-0. d’Errico, F. Fundamental properties of superheated drop (bubble) detectors. Radiat. Prot. Dosim. 84(1–4), 55–62 (1999). Seitz, F. On the theory of the bubble chamber. Phys. Fluids. 1(1), 2–13 (1958). Ing, H., McLean, T. D., Noulty, R. A. and Mortimer, A. Bubble detectors and the assessment of biological risk from space radiations. Radiat. Prot. Dosim. 65(1– 4), 421–424 (1996). Agostinelli, S. et al. Geant4 – a simulation toolkit. Nucl. Instrum. Meth. Phys. Res. A. 506(3), 250– 303 (2003).
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10.
neutron detectors. Radiat. Prot. Dosim. 47(1–4), 547–550 (1993). Olsen, R. G. Radiofrequency detection by bubble dosemeter technology. Radiat. Prot. Dosim. 34(1–4), 381–384 (1990). Rosenstock, W., Schulze, J., Ko¨ble, T., Kruzinski, G., Thesing, P., Jaunich, G. and Kronholz, H. L. Estimation of neutron energy spectra with bubble detectors: potential and limitations. Radiat. Prot. Dosim. 61(1–3), 133– 136 (1995). Sawicki, J. A. Longevity tests and background response of bubble neutron detectors. Nucl. Instrum. Meth. Phys. Res. A. 336(1–2), 215– 219 (1993). Vanhavere, F., Loos, M., Plompen, A. J. M., Wattecamps, E. and Thierens, H. A combined use of the BD-PND and BDT bubble detectors in neutron dosimetry. Radiat. Meas. 29(5), 573– 577 (1998). Green, A. R., Bennett, L. G. I., Lewis, B. J., Tume, P., Andrews, H. R., Noulty, R. A. and Ing, H. Characterisation of bubble detectors for aircrew and space radiation exposure. Radiat. Prot. Dosim. 120(1– 4), 485 –490 (2006). Barnabe´-Heider, M. et al. Response of superheated droplet detectors of the PICASSO dark matter search experiment. Nucl. Instrum. Meth. Phys. Res. A. 555, 184–204 (2005). McLean, T. D., Romero, L. L., Seagraves, D. T., Olsher, R. H. and Devine, R. T. Calibration and response of neutron bubble dosimeters from thermal energies to 60 MeV. Health Physics Society 50th Annual Meeting. Spokane, Washington, July 2005. LA-UR-05-5021 (2005). Matiullah, Kudo, K., Rashid, T., Takeda, N., Xiaoyun, Y. and Yamamoto, T. Comparative studies of the response
doi:10.1093/rpd/ncu288
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS OF VARIOUS ENERGIES M. B. Smith*, H. R. Andrews, H. Ing and M. R. Koslowsky Bubble Technology Industries, PO Box 100, Chalk River, Ontario K0J 1J0, Canada *Corresponding author: [email protected] Received 23 June 2014; revised 7 August 2014; accepted 18 August 2014
INTRODUCTION (1)
The bubble detector was first introduced 30 y ago to address an urgent need in the nuclear industry for a personal neutron dosemeter that would meet the requirements for safe radiation monitoring of personnel. In the intervening years, the bubble detector has been used in an enormous variety of venues including spacecraft, nuclear submarines, subterranean facilities, hospitals, high-energy physics laboratories, military operations, aircraft, movies, schools and the nuclear industry, encompassing power generation, fuel processing and calibration facilities. Numerous groups have assessed the performance of these detectors in relation to their particular applications. A few examples include studies by Chemtob et al.(2), Buckner et al.(3), Hoffman et al.(4), Nelson and Gordon(5), Olsen(6), Rosenstock et al.(7), Sawicki (8), Vanhavere et al.(9), Green et al.(10), Barnabe´-Heider et al.(11), McLean et al.(12), Matiullah et al.(13), Takada et al.(14), Andrews et al.(15) and Smith et al.(16). Essentially all of these studies were experimental because the theoretical basis for the processes behind the bubble detector is very complicated and not fully understood. These processes involve neutron interactions, charged-particle transport, energy transfer in gel and superheated media, liquid nucleation phenomena and gas diffusion. They include subatomic processes, molecular physics, mechanical engineering and chemical engineering and span time domains from 10214 s to weeks. Therefore, a full theoretical understanding of the physical processes behind the bubble detector is a significant technical challenge. Several groups, e.g. Buckner et al.(3), Barnabe´-Heider et al.(11) and Harper and Nelson(17), have studied some of the basic phenomena behind the bubble detector. These theoretical studies dealt mainly with the impact of temperature changes on the response of the
detector, effects that were important for earlier bubble detectors. Temperature effects are not so important for current detectors (Figure 1) because they are temperature-compensated, enabling them to be used for personnel monitoring in most work environments. The main emphasis of the current study is to understand the basic processes that are responsible for the dependence of the detector response on neutron energy. It should be mentioned that another type of detector, commonly called the superheated drop detector (SDD), bears close resemblance to the bubble detector in terms of the physics of bubble formation and is often confused with the bubble detector(18). However, the chemical formulation of the SDD is different from that of the bubble detector, and the SDD uses completely different approaches to account for its temperature dependence. Some theoretical interpretation of the fundamental properties of the SDD has been performed by groups involved with that technology(19). The work described in this paper should be interpreted as being applicable only to the bubble detector. The energy response of the SDD is expected to be different from that of the bubble detector because of its different chemical formulation. The current work was primarily driven by the need to better understand the energy dependence of the bubble detector for current and future applications in space. The use of the bubble detector in the monitoring of radiation exposure of astronauts is probably the most challenging of all applications for which the detector has been deployed. This is due to the fact that neutron radiation in space has a significant component with energy of .20 MeV. This is unlike radiation in most terrestrial environments, with the exception of high-energy physics laboratories. Monoenergetic neutron sources in this energy range (the Fermi energy domain) are non-existent, making calibration of detectors for the space environment difficult. A few
# The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
Downloaded from http://rpd.oxfordjournals.org/ at Stockholms Universitet on November 16, 2015
A series of Monte-Carlo simulations has been performed in order to investigate the response of the bubble detector to monoenergetic neutrons of various energies. The work was driven by the need to better understand the energy dependence of the detector for applications in space, where the neutron spectrum has a significant component with energy of >20 MeV. The response to neutrons in the range of a few keV to 500 MeV has been calculated, and good agreement between the simulations and experimental data is demonstrated over the entire energy range.
M. B. SMITH ET AL.
specialised laboratories can provide quasi-monoenergetic neutron beams with energies of 50 MeV and higher, but these beams are not well characterised. Thus, it is necessary to rely on good theoretical modelling in order to characterise the behaviour of the bubble detector, especially over this difficult energy region, to ensure that good dosimetric accuracy is maintained for space applications. Ground-based experiments have shown(14, 15) that the bubble detector responds to energetic charged particles as well as neutrons. However, in low Earth orbit (LEO), where most bubble-detector measurements in space have been performed, the relative abundance of charged particles and neutrons is such that bubble detectors provide reliable measurements of the neutron dose. The contribution of charged particles to the detector reading has been estimated(16) to be ,2 %. This is primarily because most of the protons in LEO are encountered during the short passes through the South Atlantic anomaly, where trapped protons are relatively low in energy (200 MeV) and are more efficient in producing neutrons than higher-energy protons from cosmic rays. However, for future expeditions beyond LEO (including flights to the moon and Mars), the mix of charged particles and neutrons will differ. For these missions, it will be necessary to re-evaluate the contribution of charged particles to the readings of bubble detectors. A good understanding of the response of the bubble detector from reliable modelling will be crucial to the correct interpretation of data from these environments.
NUCLEATION IN THE SUPERHEATED MEDIUM The formation of bubbles in the bubble detector is commonly interpreted using the thermal spike theory
Emin ¼
16ps3 ðDpÞ2
2 1 þ rv H=ðMDpÞ 3
ð1Þ
where s is the surface tension of the liquid, Dp is the superheat (defined as the difference between the vapour pressure of the superheated liquid at the ambient temperature and the externally applied pressure—usually atmospheric), rv is the density of the vapour, H is the molar heat of vaporisation and M is the molecular weight of the superheated liquid. Thus, for a particular formulation of the bubble detector, having a particular type of superheated droplets and used at a particular temperature and pressure, there is a minimum neutron energy required in order to produce the required Emin for producing bubbles in the detector. Therefore, inherently, bubble detectors are threshold detectors having no response to neutrons below a particular energy. For a chosen detector medium, the energy threshold of the detector can be controlled by the selection of a particular detector liquid having a particular superheat (i.e. boiling point) at a desired operating point (e.g. ambient temperature and pressure) for the detector. This property has been utilised to produce the bubble detector spectrometer (BDS), a set of six detectors with different energy thresholds, to enable the measurement of the energy spectrum of fast neutrons. A special version of the BDS, known as the space BDS or SBDS, has recently been developed(16) for use on the International Space Station. The energy required to form a vapour bubble with radius at least equal to the critical radius was calculated using thermodynamics by computing the work done to grow a vapour bubble from zero radius to the critical radius. For bubble detectors, the exact energy
204
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Figure 1. Temperature-compensated bubble detectors.
proposed by Seitz(20). This theory hypothesises that ionising particles, such as those produced by neutron interactions with the nucleus, create regions of plasmalike medium known as temperature spikes. When these spikes occur within one of the multitude of superheated liquid droplets in a bubble detector, the liquid explodes into nascent bubbles because of the energy stored in the superheated state. If one or more of these nascent bubbles is large enough to exceed the critical radius for bubble formation, the bubble will grow by consuming the superheated liquid in its vicinity. This growth stops when all the liquid in the superheated droplet is vaporised, giving rise to a visible bubble whose size is determined by the size of the original superheated droplet. If none of the nascent bubbles exceed the critical radius, the surface tension of the superheated liquid will recompress the bubbles back into the liquid phase, and no bubbles will result from the neutron interaction. Seitz provided a formula for the minimum amount of energy (Emin) required to create a critical bubble, which, assuming adiabatic conditions, can be written as follows:
RESPONSE OF THE BUBBLE DETECTOR TO NEUTRONS
CALCULATION OF THE BUBBLE-DETECTOR RESPONSE The response of the bubble detector has been simulated using the Geant4(22) Monte-Carlo software toolkit (version 9.5, patch 1) (http://geant4.web.cern. ch/). Geant4 uses a physics list to define the processes included in the simulations. The physics list employed in the bubble-detector simulations was based on the built-in QBBC physics list, with the following modifications: NeutronHP physics was added for neutrons of ,20 MeV; standard electromagnetic (EM) physics was replaced with Penelope EM physics and neutron tracking cuts were not employed. The production cuts used were 3 mm for electrons and positrons (so that electrons and positrons that are produced and subsequently travel ,3 mm are ignored in the simulation) and 1 nm for other particles. The reason for the high production cut for electrons was to reduce the large number of free electrons generated by recoil protons. These electrons do not contribute to bubble formation, so a cut was set so that fewer electrons would be generated, thus reducing the time spent by the simulations in tracking unimportant particles. A shortcoming of the Geant4 NeutronHP physics model is that it does not model a handful of reactions, including the 12C(n, n0 )3a break-up reaction. While other Geant4 physics models do model this carbon break-up reaction, they are considered worse than the NeutronHP model in most other areas. A method to work around this deficiency was developed and is described later in this paper. Two different geometries were used in Geant4 to determine the neutron response of the bubble detector. The first geometry, used for neutron energies of ,20 MeV, was based on a single fluorocarbon droplet in a bubble detector. A sphere of fluorocarbon (with chemical composition representative of a droplet in a bubble detector) with radius of 10 mm was surrounded by a spherical shell of material similar to the polymer gel used in the bubble detector. The radius of the gel
surrounding the fluorocarbon droplet was equal to the mean range of a recoil proton with maximum energy from an incoming neutron. This radius was chosen with the aim of realistically modelling the effect of recoil particles from the gel reaching the droplet. The geometry was therefore dependent on the neutron energy chosen for the simulation. Neutrons were fired at this geometry in a cylindrical beam with radius equal to the outer radius of the gel. This geometry is referred to as the droplet geometry. For the second geometry, a 10 ` 10-cm layer of 20-mm-thick fluorocarbon was placed behind a 10` 10-cm layer of 1-cm-thick gel. The compositions of the fluorocarbon and gel were the same as those used for the droplet geometry. A line beam of neutrons was fired at the centre of the 10 ` 10-cm layers. This geometry is referred to as the block geometry. The advantage of the droplet geometry over the block geometry is that it more accurately reflects the scenario of a droplet inside a bubble detector. However, as the radius of the gel in the droplet model increases (for higher neutron energies), the cross-sectional area of the droplet quickly becomes a small fraction of the beam area, and collecting good counting statistics at higher energies becomes time-consuming. The block geometry does not suffer from this deficiency and was therefore used for investigations at energies of .20 MeV. Scoring, in both models, was approached in the following way. For secondary particles generated inside the fluorocarbon droplet, the initial energy of the particle was recorded, as was the energy of the particle as it exited the fluorocarbon (zero exit energy was recorded if it did not leave the droplet). Similarly, for secondary particles entering the fluorocarbon from the gel, the energy of the particle as it entered the droplet was recorded along with its exit energy. The data for each particle were output and read into a separate program that analysed the results to decide whether the LET of a given particle was high enough to cause nucleation, given the energy range with which the particle went through the fluorocarbon. The Stopping and Range of Ions in Matter code (http:// www.srim.org/) was used in this analysis. In this approach, the LET threshold (as described in the previous section) could be chosen during the data analysis without re-running the Monte-Carlo simulations. For the block geometry, events generating at least one ion above this LET threshold were scored. For the droplet geometry, the number of particles above the LET threshold was computed, and this number was scaled by the neutron fluence used in the simulation to calculate the response of a single droplet per unit fluence. In the case of the block geometry, the results were instead scaled by the number of primary neutrons used in the simulation. For both geometries, the resulting response curves were normalised so that they would produce one bubble if exposed to 1 mrem of radiation from an
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required is not of particular interest, except to note that it depends only on macroscopic properties of the superheated liquid used to form the droplets, and can therefore be treated as a function of external temperature and pressure. A particle traversing the superheated droplet will cause a bubble to form if it can deposit an amount of energy equal to the threshold energy within a short distance. A threshold energy E and a distance L, across which the energy transfer must occur, defines an energy transfer of E/L, which is commonly referred to as the linear energy transfer (LET) threshold. It is thus reasonable to assume that if a particle ever has LET in the droplet of at least the threshold LET, then a bubble is formed. This assumption is good as long as L is small (theoretically L is 20 nm)(21).
M. B. SMITH ET AL.
RESULTS AND DISCUSSION The investigation described in this paper concentrates on the SBDS-100 detector, although the method is extensible to the other detectors making up the SBDS, or to terrestrial bubble detectors such as the BD-PNDTM used for personal neutron dosimetry. Figure 2 presents the response curves created from the simulations using the droplet geometry. These results
are normalised to the neutron fluence and an AmBe source and include the correction for carbon break-up in the 12C(n, n0 )3a reaction. Several response curves are presented, corresponding to the different LET thresholds used in the data analysis, ranging from 40 to 150 keV/mm. Figure 3 shows the results of the simulations using the block geometry, analysed using the same LET thresholds. These response curves are normalised by the number of primary neutrons and to the AmBe source. It is evident that the simulations performed using the droplet and block geometries are in good agreement. The data were combined, using the droplet data up to 20 MeV and the block data above 20 MeV, to produce an overall set of response curves. These combined curves are presented in Figure 4 and span the energy range from a few keV up to 500 MeV. The Monte-Carlo data provided in Figure 4 have been compared with the empirical data used to generate the SBDS response matrix(16). These experimental data were measured using monoenergetic neutron beams produced by the Defence Research and Development Canada Van de Graaff accelerator facility in Ottawa (,20 MeV) and the iThemba Laboratory for Accelerator Based Sciences (iThemba LABS) in Faure, South Africa (.90 MeV). Comparison of the data indicated that the MonteCarlo calculations agree best with the experimental
Figure 2. Bubble-detector response calculated using the droplet geometry, corrected for carbon break-up and normalised to neutron fluence and an AmBe source.
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AmBe neutron source (equivalent to 10.7 mSv). This corresponds to the calibration procedure used for bubble detectors(16). For many applications, including those in space, the quantity reported by the bubble detector is considered to be the ambient dose equivalent, H*(10). In order to work around the 12C(n, n0 )3a reaction missing from the simulations, the following approach was used. First, the number of 15N ions in the droplet during the simulation was calculated. These ions were attributed to be products of the 19F(n, n0 )a reaction. The number of 15N ions was scaled by the ratio of the 19 F(n, n0 )a cross section to the 12C(n, n0 )3a cross section and then multiplied by 3 to estimate the number of alpha particles produced. This approach impacted the detector response from 5 to 20 MeV, increasing the response in this energy range by ,10 % for all LET thresholds considered in this work.
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Figure 4. Combined bubble-detector response from the droplet and block geometries.
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Figure 3. Bubble-detector response calculated using the block geometry, normalised to the total number of primary neutrons and an AmBe source.
M. B. SMITH ET AL.
data for the SBDS-100 detector using an LET threshold of 130 keV/mm. Other thresholds used in the response calculations are representative of the other detectors that comprise the SBDS. The calculations for the 130-keV/mm threshold are compared with the experimental SBDS-100 data in Figure 5. It should be noted that the simulated and empirical data are presented on an absolute scale, with no normalisation between the two. Reasonable agreement between the calculations and the empirical data is obtained over the entire energy range.
unfolding. The modelling capability enables rigorous analysis of the readings of bubble detectors deployed in space missions, including a variety of radiation environments that will be encountered in the future. FUNDING This work was supported by the Canadian Space Agency. REFERENCES
CONCLUSIONS The Monte-Carlo simulations presented in this work provide important insight into the processes responsible for bubble formation in a bubble detector. In particular, the LET required to create bubbles in the SBDS-100 detector has been elucidated. The Geant4 model described is expected to make major contributions to future work with bubble detectors, particularly for analysis of data from space. With this modelling capability established, it is possible to simulate the bubble-detector response due to any particle (neutrons, protons, heavy ions, pions, etc.) with any energy. The simulated response may also be employed to improve the empirical response matrix used in data 208
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Figure 5. Comparison of experimental data for the SBDS-100 detector with the Monte-Carlo response calculated for a 130-keV/mm threshold.
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