Abstract

This paper presents outcomes from research studies conducted independently at Purdue University as part of a collaborative project with the staff of Pacific Northwest National Laboratory (PNNL). Research work focused on assessments for meeting the challenge of monitoring actinide content in spent nuclear fuel (SNF) via characteristic neutron emissions [from spontaneous fission and (α,n) reactions] using the centrifugally tensioned metastable fluid detector (CTMFD) sensor technology using an inert organic decafluoropentane (DFP)(C5H2F10) sensing fluid. Traditional detectors readily saturate and/or cannot monitor neutron emissions under the expected 1012:1 gamma to neutron radiation environment. A challenge problem was posed to examine if a CTMFD could operate reliably over 1 h for conducting neutron spectroscopy at a 1 m standoff from a 30-y cooled SNF, in a ∼1012:1 gamma:neutron intensity environment resulting in a 150 Gy (15 kRad) accumulated dose for the CTMFD. The impacts on reliable operability were studied separately under expected gamma radiation energy and intensity for possible effects of: (i) radiolysis in the CTMFD sensing fluid from absorbed (<1.5 MeV) gamma radiation; (ii) photoneutron contamination signals from < 3 MeV high energy gamma photons interacting with the sensing fluid; and, (iii) malfunction of CTMFD component electronics from the absorbed gamma radiation. A Co-60 gamma irradiator was used for dose accumulation in the CTMFD electronic components and sensing fluids. A 14 MeV DT accelerator was used with a NaCl target to produce 3–4 MeV photons from activated 37S (via. neutron absorption in 37Cl) at SNF-commensurate intensities from SNF at 1-m standoff. Our examinations revealed the absence of any significant impact on CTMFD performance for meeting and exceeding the challenge problem metric. That is, we validated for no discernible impact of: 3–4 MeV gamma-produced photoneutrons when combined with a fission neutron source and radiolysis in the DFP sensing fluid through a 150 Gy absorbed dose. Past research results at Purdue University have validated for survivability of the key electronic components for absorbed gamma doses above the targeted 150 Gy level. This paper also provides extended evidence for survivability (from radiolysis) at higher gamma doses through 750 Gy with a borated DFP-sensing fluid formulation-based CTMFD.

Introduction

Conventional neutron sensor systems [1,2] to detect the diversion of transuranic elements in SNF have a well-known deficiency in their lack of ability to provide real-time assessments. Material accountability using such techniques [38] for neutron signal monitoring are either too low in neutron detection efficiency (e.g., ≪ 1% for fission chambers) or others like moderated proportional/ionization chambers like He-3 detectors can quickly become saturated at >0.1 Gy/h (10 Rad/h) fields within the extreme γ/β environment expected from SNF, or require time-consuming, off-site laboratory analysis. It is well-known that considerable uncertainty exists for actinide content (esp., Pu-239, U-235, Cm-242, etc.) in SNF discharged from a conventional 3 GWt light water reactor (LWR) [9]. From a safeguards-security standpoint (i.e., diversion potential), it is important to assess the actinide content in SNF that is either intended for storage or reprocessing. The challenge in monitoring neutron emissions from SNF (MTU/SF) at the intensity of ∼106 n/s is complicated by the relatively huge (∼1019 γ/s) gamma radiation emissions, which can create radiation exposures in the 100 Gy/h (104 Rad/h) range.

Our past studies have revealed that the tensioned metastable fluid detector (TMFD) sensor technology presents a promising candidate for addressing such and related problems [924]. Table 1 summarizes the salient features of the TMFD architecture, including references to past publications supporting the claimed capabilities. Concerning the present application for actinide neutron emission-based identification, it is noted that CTMFDs can offer up to 80% (intrinsic neutron detection efficiency) alongside offering spectroscopic information with potential 100% gamma-blind operability even under 150 Gy/h (15,000 Rad/h) accelerator photon fields. In contrast to conventional sensor systems, TMFDs do not rely on components such as pre-amplifiers, high voltage sources, and PMTs for light flash or charge collection and extensive shock-sensitive electronic trains.

Table 1

Key enabling attributes of tensioned metastable fluid (TMFD) sensor technology

ParameterDescription
Versatility re: radiation detectionSingle intuitive system enabling multiple radiation types (alpha, neutron, cosmics, fission) monitoring; Enables physically “Hearing-Seeing-Recording” of various radiation particle interaction effects [10,11].
In-air (or fluid borne) actinide monitoringAbility to monitor for ultratrace (mBq/mL) key nuclides with 1.4 keV energy resolution in air-fluids-solid enclosures with under 2 min. sampling – including for 100% Rn/progeny rejection.[9,14,17]
Neutron energy rangeThermal (0.02 eV) to Fast (0.02–10 MeV) neutron detection with single system [15,18].
Intrinsic detection efficiencyUp to ∼60–80% (neutrons); ∼95%+ (alpha-fission) [915].
Gamma-beta rejection100% gamma-beta-muon blindness [tested to ∼100 Gy/h (104Rad/h) fields] [12,16,19,22,24].
Spectroscopic capabilitiesNeutron-alpha spectroscopy with keV energy resolution [9,20,23].
External environment effectsAuto-adjusted for temperature (273–323+ °K); to 95% relative humidity including condensing atmospheres; shock tolerance.
Incoming neutron radiation directionalitySingle ATMFD (for directionality); 2 ATMFD (directionality and source position tracking) [13].
Cost/Safety/WeightLow cost; sensing material: safe [0/0/0—NFPA); <$0.001/mg]; <2–3 kg/unit.
Nonflammable—no need for moderators (e.g., Paraffin/Polyethylene) or photomultiplier tubes (PMTs).
Overall SNM detection enablementReal-time, standoff detection of SNMs via active and passive inter-rogation [15,21].
ParameterDescription
Versatility re: radiation detectionSingle intuitive system enabling multiple radiation types (alpha, neutron, cosmics, fission) monitoring; Enables physically “Hearing-Seeing-Recording” of various radiation particle interaction effects [10,11].
In-air (or fluid borne) actinide monitoringAbility to monitor for ultratrace (mBq/mL) key nuclides with 1.4 keV energy resolution in air-fluids-solid enclosures with under 2 min. sampling – including for 100% Rn/progeny rejection.[9,14,17]
Neutron energy rangeThermal (0.02 eV) to Fast (0.02–10 MeV) neutron detection with single system [15,18].
Intrinsic detection efficiencyUp to ∼60–80% (neutrons); ∼95%+ (alpha-fission) [915].
Gamma-beta rejection100% gamma-beta-muon blindness [tested to ∼100 Gy/h (104Rad/h) fields] [12,16,19,22,24].
Spectroscopic capabilitiesNeutron-alpha spectroscopy with keV energy resolution [9,20,23].
External environment effectsAuto-adjusted for temperature (273–323+ °K); to 95% relative humidity including condensing atmospheres; shock tolerance.
Incoming neutron radiation directionalitySingle ATMFD (for directionality); 2 ATMFD (directionality and source position tracking) [13].
Cost/Safety/WeightLow cost; sensing material: safe [0/0/0—NFPA); <$0.001/mg]; <2–3 kg/unit.
Nonflammable—no need for moderators (e.g., Paraffin/Polyethylene) or photomultiplier tubes (PMTs).
Overall SNM detection enablementReal-time, standoff detection of SNMs via active and passive inter-rogation [15,21].

For completeness, we first provide a brief overview of the TMFD technology, and then present studies and results about qualifying CTMFDs for front-end SNF monitoring of actinide from their characteristic neutron emission signals.

Background on Tensioned Metastable Fluid Detector Underlying Science and Technology

It is not well-known that fluids like solids can also be placed under tensioned (below vacuum) negative pressure (Pneg) states—progressively weakening the intermolecular bonds to the point at which a femtoscale incoming ionizing particle (e.g., MeV neutron interaction) can rupture the bonds resulting in a cavitation detection event (CDE); indeed, a CDE starting at the nm scale, which quickly within microseconds can amazingly grow to ordinary human visible-audible-recordable scales. A variety of methods to cause Pneg states in ordinary inorganic and organic fluids have been developed as candidates for TMFDs [10,18]. One such method which was used for the present study is the CTMFD shown schematically in Fig. 1(a). Figure 1(b) provides a pictorial view of the CTMFD system used for this study, including key components.

Fig. 1
(a) Schematic of CTMFD system and (b) pictorial of CTMFD showing key components
Fig. 1
(a) Schematic of CTMFD system and (b) pictorial of CTMFD showing key components
Close modal

At its core, the typical CTMFD comprises a diamond-shaped glass enclosure filled with sensing fluid (Fig. 1(a)), which is connected to a variable-speed remotely controlled drive motor. The diamond-shaped glass piece is spun about a central axis. As the glass piece rotates, centrifugal forces stretch the fluid along the centerline, weakening the intermolecular bonds holding the fluid together and placing the fluid in the central volume in as-desired tensioned metastable negative pressure (Pneg) states. An incident neutron strike onto the atoms of the sensing fluid creates high (∼106 MeV/m) linear energy transfer (dE/dx) recoil ions, which deposit their energy within nanometers and under the right nucleation conditions, which can lead to a fast-growing CDE. In contrast, low dE/dx radiation (e.g., ∼1 MeV/cm gamma-beta radiation) deposits radiation energy over much larger length scales such that nucleation of a CDE is physically impossible for Pneg states used in TMFDs. This aspect allows the TMFD sensor to offer 100% gamma-beta radiation blindness while offering 80–99% intrinsic efficiency for detecting neutrons, alpha, and fission fragments [9,20].

The degree of tension (Pneg) state within the fluid along the central axis can be increased or decreased by simply raising or lowering the rotational frequency of the glass piece. Doing so not only alters the negative pressure state at the centerline but also changes the sensitivity of the detector to incident radiation, enabling spectroscopic capabilities for both neutrons [18,20]. The degree of tension along the centerline is given by the following equation [10]:
(1)

where ρ is the fluid density, r is the meniscus separation, f is the rotational frequency, and Pamb is the ambient pressure. For a given “ρ” and “r,” the Pneg can be controlled by manipulating the rotational frequency (f), allowing for selective energy discrimination. The CTMFD control software accounts for dynamic temperature compensation.

Figure 2(a) summarizes intrinsic neutron detection efficiency for CTMFDs (on a sensitive volume normalized basis) versus conventional fast and thermal neutron detectors. The used for this study comprised a 40 cm3 sensitive volume (SV) and utilized the inert (0,0,0 on the NFPA scale) organic liquid DFP with the molecular formula C5H2F10. As noted, the efficiency gains can range from over 75 versus moderated BF3 detectors to over 1000× over superheated drop detectors. Figure 2(b) presents evidence for the unique ability for CTMFDs to tailor the intrinsic detection efficiency over 104× by varying the degree of tension Pneg states—approaching the theoretical 100% interaction rates.

Fig. 2
Salient neutron detection characteristics of CTMFD versus conventional detectors
Fig. 2
Salient neutron detection characteristics of CTMFD versus conventional detectors
Close modal

Identifying Key Challenges for Guiding Experimental-Analytical Assessments

We have analytically shown [9] that information on key actinide content in SNF can be derived from external monitoring of the characteristic neutron intensity and energy spectra emissions. Since alpha and beta radiation are readily shielded within the SNF structure, the penetrating background radiation impacting the externally positioned neutron sensor next to an SNF will be dominated by gamma photons—both for intensity and energy spectrum-based effects. The photon energy comes into importance because of possible photoneutron production. Since the sensing fluid in DFP includes “H” atoms for which a 1:6000 are expected to be “D” atoms for which the photoneutron energy threshold is 2.2 MeV, any incoming photon of energy (Eγ) above 2.2 MeV can be expected to result in photoneutron-induced counts in the CTMFD—constituting a contamination signal, which must be accounted for as an additional technical challenge, beyond the expected impact of absorbed dose on production of significant radiolysis gases in DFP that may lead to spurious signals as well.

Since the gamma radiation emission is strongly dependent on decay of constituent fission products in SNF, and to narrow the scope of the challenges involved, it was decided to focus on the state of legacy SNF inventory built up in the U.S.A. This legacy SNF is dominated by fuel assemblies that have experienced a 30-y cooldown period.

Analysis of Gamma versus Neutron Intensity and Energy Spectra From 30-y Cooldown Spent Nuclear Fuel.

Figure 3(a) shows the expected photon intensity and energy distribution estimated using the well-established ORIGEN code [25]. As noted, the highest intensity (∼1015 γ/s) occurs toward the front end of the spectrum, with a steep drop in photon intensity once the photon energy exceeds ∼1.5 MeV. A prominent peak is observed at ∼0.6 MeV due mostly from the decay of Cs-137, a beta emitter with a half-life of 30.1 years. Figure 3(b) displays the neutron output from 30-y cooldown SNF with most neutron emissions derived from spontaneous fission (SF) with an emission intensity of about 107 n/s.

Fig. 3
30-y cooldown SNF gamma and neutron emission spectra calculated via ORIGEN code [25]
Fig. 3
30-y cooldown SNF gamma and neutron emission spectra calculated via ORIGEN code [25]
Close modal

These results indicate that the gamma-to-neutron intensity can be as high as: ∼1011:1 (for Eγ < 1.5 MeV), ∼10:1 (for Eγ∼ 2–3 MeV), and ∼ 1:1 (Eγ > 6 MeV). Consequently, it is clear that for the impact of radiolysis and radiation dose-related negative effect on CTMFD performance, the absorbed dose effect will be dominated by Eγ < 1.5 MeV gamma photons. In contrast, the potential for photoneutron contamination effects needs to be assessed for possible impact from Eγ ∼ 3 MeV and ∼ 7 MeV photons, respectively.

Developing the Problem Statement & Metrics for Investigation.

From a practical perspective, for standoff monitoring of neutron emissions from SNF (with a length span of ∼3.3 m (13–14 ft), a reasonable field of view coupled with conservatism would need a standoff of about 1 m—with the CTMFD positioned midway between the length of a typical LWR SNF. While CTMFDs with SV ranging from 1 mL to 80 mL have been developed, for this study a CTMFD with SV = 15 mL was deployed; such a CTMFD reaches an intrinsic detection efficiency of ∼30% at Pneg >10 bar.

Calculations were conducted to assess the situation for the gamma dose/exposure rate which indicated ∼ 150 Gy/h (∼15 kRad/h) expected dose rate. At a 1 m standoff, and a neutron source strength of ∼106 n/s, the neutron rate entering the CTMFD (SV = 15 mL) can be readily estimated (assuming 4π reduction with distance) to be = ∼106. 10/(4π.104) = ∼102 n/s. At this neutron rate, the 15 mL CTMFD would readily detect the incoming neutrons at a rate exceeding 50–100 cps (Note: The cosmic background count rate in the 15 cm3 CTMFD operating at a 7 bar Pneg state is ∼ 0.02 cps). For determining the neutron energy spectrum requires more time since this requires the acquisition of detection rates for at least 3–4 Pneg states [18]—estimated to require 15–30 min. We conservatively set the goal to be 1 h.

Resulting Challenge Metrics.

Based on the aforementioned discussion and analyses, the challenge goal performance metrics for CTMFDs were set as follows:

  • Metric 1: The CTMFD should function without spurious signals when subject to Eγ < 1.5 MeV for an accumulated dose < 150 Gy (15 kRad)—this metric includes spurious signals from radiolysis of DFP sensing fluid, and performance degradation of key electronic components used for CTMFD control.

  • Metric 2: The CTMFD should remain non-affected by high energy gammas, with Eγ in the 3–7 MeV range when placed in a photon-to-neutron field of 100:1 (for Eγ < 3 MeV) and 1:1 (for Eγ> 6 MeV).

Experiments & Results of Investigations to Assess versus Challenge Metrics

This section presents details on experiments and theoretical analyses to address the aforementioned two challenge metrics

Challenge Metric 1—Ability to Remain Blind to Radiolysis for Gamma Doses < 150 Gy (1.5 kRad).

The effect of high-rate gamma dose on the CTMD system was done using Purdue University's Nordion GammaCell 220TM Co-60 irradiator. Figure 4(a) shows an outside view of the irradiator, which is loaded internally with vertically positioned Co-60 source pencil-shaped elements surrounding the internal irradiation cavity for placement of samples. Figure 4(b) shows the relative distribution of gamma flux, the rate is strongest next to the Co-60 source, and is lower in the center. The CTMFD samples were placed and irradiated in the center of the irradiator, as depicted schematically in Fig. 4(c).

Fig. 4
Purdue University's GammaCellTM irradiator, relative dose rate map, and CTMFD sample positioning for irradiation dose accumulation
Fig. 4
Purdue University's GammaCellTM irradiator, relative dose rate map, and CTMFD sample positioning for irradiation dose accumulation
Close modal

Two formulations of CTMFD-sensing fluids were employed, the first was DFP only (which is sensitive only to fast > 0.1 MeV neutrons), and the second was a borated–DFP mixture (sensitive to 0.02 eV–to–MeV range neutrons). Unless otherwise noted, the sensing fluids were deployed in a sealed CTMFD without any prior degassing; under this condition, the first ∼15–20 detection events are caused by self-degassing of the predissolved air–after which the CTMFD is ready for detecting external neutrons. Prior degassing is conducted by acoustic agitation—a procedure we have developed that is readily accomplished within 1–2 min. Once predegassed, the CTMFD top stem (shown in Fig. 1(a)) is sealed shut to avoid air infiltration before deployment in the assemblage shown in Fig. 1(b).

Before and after gamma dose accumulation to a prescribed level, the CTMFD was examined for the possible impact of radiolysis gas buildup, which may lead to spurious neutron detection signals. Neutron detection signals were monitored under (i) normal background neutron conditions (from cosmic radiation and from neutron sources located in cabinets); and, (ii) from a certified Am-Be isotope neutron source emitting about 2 × 104 n/s at a 1 m standoff from the CTMFD.

Results of the investigations are shown in Fig. 5 through Fig. 7.

Fig. 5
Results of 150 Gy dose Irradiated 16 mL CTMFD (DFP filled, Pneg = 0.7 MPa with no predegassing) neutron detection performance with Am-Be neutron source – showing little to no impact
Fig. 5
Results of 150 Gy dose Irradiated 16 mL CTMFD (DFP filled, Pneg = 0.7 MPa with no predegassing) neutron detection performance with Am-Be neutron source – showing little to no impact
Close modal

Figure 5 shows detection results at Pneg = 0.7 MPa (7 bar) without predegassing—for 0 Gy and 150 Gy irradiation doses, respectively in the presence of a ∼2 × 104 n/s emission rate Am-Be isotope neutron source positioned 1 m away. As seen, the first 15–20 detection events occur at random during self-degassing. Still, after that, the count rate stabilizes to about 11 cpm for both 0 Gy and 150 Gy cases, respectively. This provides proof for having met Metric 1 requirements.

Figure 6(a) presents detection results at Pneg =0.7 MPa (7 bar) without predegassing (Option 1)—for 0 Gy and 450 Gy irradiation doses, respectively, but in a normal room neutron background condition. Considering the room background radiation is small, for 0 kGy (no irradiation) the count rate is < 1 cpm and is reached readily after the first few detection events. However, unlike for the case with 150 Gy gamma dose, at 450 Gy absorbed dose, there initially occurs a relatively large (20× higher than background) spurious count rate (cpm) signal, which clearly indicates the impact of significant radiolysis gas buildup, accompanied with simultaneous degassing as well since the count rate is seen to drop with each subsequent detection event (during which entrained gas is ejected out from the DFP)—the count rate gradually approaches the background count rate seen for the case without any prior irradiation. This result provides evidence for the need to examine the effect of predegassing (i.e., removal of radiolysis-caused gas pockets).

Fig. 6
Results of 450 Gy dose on CTMFD (DFP filled, Pneg = 0.7 MPa) ambient room radiation detection performance for, (a)Option 1—without predegassing and (b) Option 2—with predegassing.
Fig. 6
Results of 450 Gy dose on CTMFD (DFP filled, Pneg = 0.7 MPa) ambient room radiation detection performance for, (a)Option 1—without predegassing and (b) Option 2—with predegassing.
Close modal

Figure 6(b) presents the analogous results for Fig. 6(a), but now with predegassing (Option 2) of the DFP sensing fluid after receiving 450 Gy (4.5 kRad) gamma dose. The results are remarkable in that we now obtain a 100% removal of the radiolysis gas buildup effect of the 450 Gy (45 kRad) irradiation. In reality, for SNF, simultaneous neutron monitoring under radiolysis would continually purge any radiolysis gas buildup; however, this aspect needs to be confirmed in an integral test environment involving a 1010:1 gamma:neutron source rate environment.

Figure 7 presents exciting results on the null effect of irradiation with 150–750 Gy gamma doses on borated-DFP filled CTMFDs, and without requiring any predegassing (Option 1). Results are striking in that the borated formulation evidently changes the radiochemistry nature of the CTMFD sensing fluid to permit us to 100% overcome the impact of radiolysis. The count rates obtained with and without an external neutron source are within 1 SD error of the cases with and without gamma dose levels even as high as 750 Gy. Importantly, this result is achieved without any resort to intentional predegassing. Therefore, it appears reasonable to claim that Metric 1 is met and exceeded by 3x—when the sensing fluid is borated DFP. The interesting combined response to irradiation-induced chemical changes and detection of interactions with neutrons await further investigation.

Fig. 7
Results of 150,450,750 Gy doses on CTMFD (borated DFP without predegassing – Option 1). (a) Neutron detection performance with Am-Be (2 x 104 n/s) isotope neutron source count rate versus Pneg (bar) for 150 Gy dose and (b) Ambient count rate versus detection number and no predegassing for Pneg = 0.7 MPa. Note: 1 bar = 0.1 MPa.
Fig. 7
Results of 150,450,750 Gy doses on CTMFD (borated DFP without predegassing – Option 1). (a) Neutron detection performance with Am-Be (2 x 104 n/s) isotope neutron source count rate versus Pneg (bar) for 150 Gy dose and (b) Ambient count rate versus detection number and no predegassing for Pneg = 0.7 MPa. Note: 1 bar = 0.1 MPa.
Close modal

Challenge Metric 1—Functionality of Centrifugally Tensioned Metastable Fluid Detector Sensor Electronics for Gamma Doses < 150 Gy (1.5 kRad)

This aspect has been studied at Purdue University in the past [12]—the results are summarized herein for completeness. The CTMFD system (Fig. 1(b)) includes three key sensors: two IR sensors, one for monitoring the rotational speed and the other for monitoring the temperature of the CTMFD's sensing fluid, and one thermocouple (TC) for monitoring the incoming air and integrated with the IR temperature sensor for enabling dynamic temperature compensation. These three sensors were placed inside Purdue University's gamma irradiation chamber and connected to an external computer to monitor the output of the sensors over time. The sensors, each tested separately, were irradiated at a rate of 150 Gy/h for a total dose of ∼2750 Gy. Results are reproduced in Fig. 8 from the original data of Ref. [12].

Fig. 8
Results of CTMFD electronic sensors survivability versus dose: (a) infrared (bubble) detection sensor and (b) infrared speed & thermocouple sensors
Fig. 8
Results of CTMFD electronic sensors survivability versus dose: (a) infrared (bubble) detection sensor and (b) infrared speed & thermocouple sensors
Close modal

The IR bubble detection sensor shines an IR beam through the central bulk of the fluid and is a key to detecting radiation-induced cavitation events. The signal from this sensor is read as a value from 0 (no signal) to 1024 (max signal). From experience, the as-built CTMFD functions if the signal value is over 100. Figure 8(a) shows the drop of the IR beam signal with increased dose, indicating functionality retention through an accumulated dose of over 2750 Gy (275 kRad), which is ∼18× greater than needed for Metric 1. While not as high for survivability, the other two temperature-related sensors indicate functionality for < 250 Gy conditions, as seen in Fig. 8(b), and are readily and economically replaceable (∼$1–10).

Challenge Metric 2—Ability to Remain Blind to 3–4 MeV Gamma Photoneutron

From Fig. 3, it is noted that the more influential higher energy photons (which could lead to photoneutron contamination) exponentially decrease with increasing photon energy, with a reduction of 105 photons/sec/MTU from 1 MeV to 3 MeV and another 102 times reduction from 3 MeV to 7 MeV. Energetic photons above 2.2 MeV are above the (γ,n) threshold for de-uterium, a naturally occurring isotope of hydrogen within the DFP sensing fluid. The relative potential impact of 7 MeV gamma photons was assessed in an independent study at PNNL and is presented in a companion paper [26]. In tandem, confirmatory experiments for gaging potential contamination at a lower yet significant gamma energy of 3 MeV (which is above the photoneutron threshold for D atoms) were conducted at Purdue University.

The Purdue-based confirmatory experiment (Fig. 9(a)) used a 14 MeV D-T accelerator to target neutrons incident on a 9.1 kg (20 lb) NaCl target to activate Na atoms to produce the expected rate of photons at 3.1 MeV for verification of any interference from photoneutron contamination as may occur next to a SNF in a hot cell. Figure 9(b) shows a schematic of the GEANT code model. The expected photon emission rate from SNF at 3 MeV is 105 times reduced compared to 1 MeV intensities. To achieve the desired conditions, 14 MeV neutrons at a rate of ∼1.7 × 107 n/s were utilized. The D-T neutron generator head was enclosed within a NaCl-filled box and run for 15 min to produce 37S via the 37Cl(n,p)37S reaction, with a cross section of 24 mb at 14 MeV.37S beta decays to 37Cl with a 5.05-min half-life, simultaneously emitting a 3.1 MeV gamma and consequently creating a photon environment above the 2.2 MeV photoneutron threshold. The resulting potential for photoneutron-based contamination was adjudicated by comparing the CTMFD count rates resulting from neutron interactions from fission (using a Cf-252 source of suitable emission rate at the appropriate standoff). The following sections discuss estimations for 3 MeV photon emission rate resulting from activation by 14 MeV neutrons and experimental results for combined effects of fission neutron detection with and without the 3 MeV photon source present.

Fig. 9
14 MeV DT accelerator-driven system for 3 MeV activated gamma production
Fig. 9
14 MeV DT accelerator-driven system for 3 MeV activated gamma production
Close modal

Analytical Estimations of 3.1 MeV Photon Yield From 14 MeV Neutron Activation of NaCl.

An analytical estimate of the expected 3.1 MeV photon yield from D-T irradiation of NaCl was approximated by solving the well-known Bateman equations for Ni(t) atoms of isotope i that decay into isotope i+1, and, solving in relation to the 37Cl(n,p)37S reaction, the analytical Eq. (2) below is obtained
(2)

where σ represents the microscopic neutron absorption cross section, ϕ represents the incident neutron flux (n/cm2/s), N(0) represents the initial atom population, λ represents the decay constant (1/s), t represents the elapsed run time of the D-T neutron generator, and the subscripts 1 and 2 represent the target atom (37Cl) and the product atom (37S), respectively. The estimated 37S population, shown in Fig. 10(a), quickly reaches an equilibrium state within a few minutes and peaks slightly above 106 atoms, after which the D-T generator is turned off. Though not shown in the figure, the 37S population would decay with the characteristic 5.05-min half-life.

Fig. 10
Estimations of activated 3 MeV gamma production from 37S, and La-Br detector gamma spectra [Note: Analytically derived 37S population using the ∼1.7×107 n/s D-T source buried within 0.28 m × 0.23 m × 0.25 m (11″ × 9″ × 10″) NaCl target. The neutron absorption cross sections of 37Cl and 37S at Eneutron=14 MeV are 24 mb and 1 mb, respectively].Estimations of activated 3 MeV gamma production from 37S, and La-Br detector gamma spectra [Note: Analytically derived 37S population using the ∼1.7×107 n/s D-T source buried within 0.28 m × 0.23 m × 0.25 m (11″ × 9″ × 10″) NaCl target. The neutron absorption cross sections of 37Cl and 37S at Eneutron=14 MeV are 24 mb and 1 mb, respectively].
Fig. 10
Estimations of activated 3 MeV gamma production from 37S, and La-Br detector gamma spectra [Note: Analytically derived 37S population using the ∼1.7×107 n/s D-T source buried within 0.28 m × 0.23 m × 0.25 m (11″ × 9″ × 10″) NaCl target. The neutron absorption cross sections of 37Cl and 37S at Eneutron=14 MeV are 24 mb and 1 mb, respectively].Estimations of activated 3 MeV gamma production from 37S, and La-Br detector gamma spectra [Note: Analytically derived 37S population using the ∼1.7×107 n/s D-T source buried within 0.28 m × 0.23 m × 0.25 m (11″ × 9″ × 10″) NaCl target. The neutron absorption cross sections of 37Cl and 37S at Eneutron=14 MeV are 24 mb and 1 mb, respectively].
Close modal

The 3 MeV photon emission rate from SNF is ∼108 s−1 versus ∼107–8 n/s emanating from spontaneous fission. We simulated the relative intensities of 3 MeV photons versus neutrons from SF entering the CTMFD, so as to ensure the ratio of gammas to neutrons is > 10, as is discussed later.

Monte Carlo Simulation via GEANT4 Software Platform.

A second, independent theoretical analysis of the expected 37S population (and hence, for 3 MeV gamma photon generation) was performed with the well-known GEANT4 software toolkit, a Monte Carlo-type platform for simulating particles through matter. The simulated setup is shown in Fig. 9(b).

The GEANT4 software toolkit tracks the 37Cl(n,p)37S reaction within the NaCl target, giving an estimate to the 37S population over time. This serves as a confirmatory analysis to the expected 3.1 MeV photon emission rate deduced previously via the Bateman equations. The two analyses both yielded expected 37S populations of approximately 4×106 atoms, thus validating one another and serving as independent cross-checks. Once the D-T accelerator is shut off after 900 s of irradiation, the 37S population decays with a 5.05-min half-life shown in Fig. 10(b). The associated 3.1 MeV photon emission rate commensurate with the 4 × 106 37S atoms is thus ∼9109 Bq. Assuming as shown in Fig. 9, the standoff from the CTMFD is ∼11.5 cm (4.5″) and a 1/r2 variation of flux, the 3.1 MeV gamma photon emission rate entering the CTMFD is estimated to be ∼ 56 γ/s. In reality, the number of activation gammas produced from the 14 MeV neutrons can be expected to be significantly higher—albeit, of lower energy below the de-uterium photoneutron threshold of 2.2 MeV. The expected photoneutron production rate from ∼ 56 γ/s interactions with D atoms in DFP is discussed later in the last two subsections.

Experimental Analysis of 14 MeV Neutron Interactions With NaCl.

Figure 9(a) shows the experimental setup, including the CTMFD and position of the Cf-252 source of SF neutrons. DFP was used as the sensing fluid. A LaBr3(Ce) scintillation-based detection system (operating voltage = 470 V; Coarse gain = 8; Fine gain = 1.2) was used for spectroscopic monitoring of gamma-ray signals from the NaCl target. The 252Cf SF neutron source offered an emission rate of 104 n/s and as positioned, created the desired neutron to 3 MeV gamma emission rates of ∼10×.

As seen in Fig. 9(a), the 15 mL DFP-filled CTMFD was placed adjacent to the middle of the NaCl target, with the central cavity of the bulb ∼0.115 m (4.5″) from the target's outer edge. The LaBr3(Ce) scintillation detector was placed adjacent to the CTMFD with the scintillation crystal ∼0.114 m (4.5″) from the target's outer edge. The D-T head was buried ∼0.1 m (4″) within the NaCl target – 0.114 m (∼4.5″) from the target base and ∼0.076 m (3″) from the closest edge. The 252Cf spontaneous fission neutron source was placed ∼0.3 m (12″) from the central cavity of the CTMFD bulb and diametrically opposite the LaBr3(Ce) detector. The experiment station was elevated at ∼0.76 m (30″) above the floor.

The LaBr3(Ce) scintillation detector was calibrated using a ∼3000 Bq (0.08 μCi) 60Co check source, and further verified with a ∼25,000 Bq (0.65 μCi) 137Cs check source results, which are shown in Fig. 10(c). After calibration, a background measurement was taken with both detectors, immediately followed by a second measurement with a 252Cf source for which the results are presented in Fig. 10(d). Once both measurements were completed, the two detectors were stopped. The D-T generator was run 900 s with an average 4π neutron output of 1.7×107 n/s. After 900 s, the D-T generator was shut off, and a third measurement was taken with the 252Cf source present to demonstrate the CTMFD's ability to measure the SF neutrons at the same rate as before, despite the presence of 3+ MeV photons emanating from the activated NaCl target.

For all three measurements, the sum counts of the LaBr3(Ce) detector were totaled, including accounting for the 3.1 MeV photon peak expected from the 37S decay. The counts, shown in Table 2, show a 10× higher count for the activated NaCl with the 252Cf source present, versus with the 252Cf source without the activated NaCl target. The average excess count rate is ∼66 γ/s recorded by the LaBr detector. While this rough estimation does not consider the details re: detector efficiency and contributions from lower energy activation gammas (from 14 MeV interactions), it is of the same order of magnitude as that estimated from the aforementioned GEANT code-based calculated estimate of ∼56 γ/s.

Table 2

3.1 MeV photon counts

SourceTotal counts
252Cf (and background w/o activated NaCl)28,538
Activated NaCl and 252Cf266,433
SourceTotal counts
252Cf (and background w/o activated NaCl)28,538
Activated NaCl and 252Cf266,433

Theoretically Estimated versus Measured Centrifugally Tensioned Metastable Fluid Detector Count Rate for Experiments

As noted from Table 2, the gamma photon population measured by the LaBr detector is 10× higher for the case when the 14 MeV neutron-activated target is included – versus for the photon count rate with the Cf-252 source alone. A theoretical estimate for the photoneutron production rate from 3.1 MeV photons interacting with D atoms in the CTMFD's DFP (C5H2F12) sensing fluid was performed. Assuming DFP density = 1600 kg/m3, 1:6000 ratio of D:H atoms, 2.5 mb photoneutron cross section, and a 16 mL sensitive volume, the expected (barring unforeseen effects) photoneutron production rate is calculated to be negligibly small at ∼10−7 n/s. The confirmatory response of the CTMFD to the Cf-252 source neutrons with and without the 3.1 MeV-activated gammas is summarized in Table 3, and in Fig. 11, respectively.

Fig. 11
CTMFD (15 mL, DFP filled and predegassed) detection rate for monitoring spontaneous fission neutrons from a ∼1×104 n/s 252Cf source at ∼0.3 m standoff (Notes: The activated NaCl target was ∼0.114 m from the CTMFD bulb. The CTMFD bulb was filled with DFP and acoustically degassed before operation. Both measurements were conducted at Pneg=5 bar).
Fig. 11
CTMFD (15 mL, DFP filled and predegassed) detection rate for monitoring spontaneous fission neutrons from a ∼1×104 n/s 252Cf source at ∼0.3 m standoff (Notes: The activated NaCl target was ∼0.114 m from the CTMFD bulb. The CTMFD bulb was filled with DFP and acoustically degassed before operation. Both measurements were conducted at Pneg=5 bar).
Close modal
Table 3

Summary of results for lack of influence from 3 MeV photoneutron on Cf-252 fission neutron source monitoring

SourceAverage count rate (CPM)1 σ (CPM)
252Cf SF neutron source only10.71.49
Activated NaCl w/252Cf SF neutron source11.51.55
SourceAverage count rate (CPM)1 σ (CPM)
252Cf SF neutron source only10.71.49
Activated NaCl w/252Cf SF neutron source11.51.55

The CTMFD detection rate history for incoming SF neutrons from Cf-252 over time is shown in Fig. 11 for the cases with and without 3 MeV photons. Despite the 3+ MeV photon presence, no difference was observed in the time-averaged CTMFD count rate when monitoring the 252Cf source with and without the activated NaCl as summarized in Table 3. Thus, the 3.1 MeV photons observed via the LaBr3(Ce) scintillation detector did not constitute an observable hindrance on the CTMFD's detection capability via photoneutron interference. These results complement the companion results obtained independently in a separate study using 7 MeV-activated photons by researchers at PNNL [26]. As such, it appears that photoneutron-induced contamination remains negligible when using CTMFDs for examining SNF assemblies for their actinide inventory based on their unique neutron emission signature, even when in an intense gamma background.

Extension of Results to Real-Life Spent Nuclear Fuel Actinide Monitoring for Photoneutron Contamination

From Fig. 3, we have noted that the actual 3 MeV gamma emission rate from SNF is ∼108 γ/s versus a neutron emission rate of ∼107-8 n/s from spontaneous emission. At a 1-m standoff, the expected photoneutron production rate in the 16 mL CTMFD can be calculated to be ∼0.3 n/s; however, this value is insignificant in relation to the ∼104–5 higher neutron emission rate from SNF fission neutron rate.

Summary and Conclusions

This paper presents a study on assessing the CTMFD sensor technology for its ability to externally monitor for spontaneous and random (α,n) neutrons while remaining blind to background gamma radiation from 30-y cooldown SNF assemblies.

A staged approach was undertaken with ORIGEN code-based estimations of the gamma and neutron energy spectra and relative intensities. Two key challenge metrics were developed to estimate the feasibility of using CTMFDs in the expected neutron-to-gamma environment at a 1-m standoff from a typical LWR SNF assembly.

The first metric focused on the impact of < 1.5 MeV photon dose on radiolysis and potential malfunction of CTMFD electronic components for enabling neutron spectroscopy within 1 h of irradiation leading to ∼150 Gy (15 kRad) absorbed dose. Metric 1 was successfully met and exceeded.

The second metric focused on the possible impact of photoneutrons resulting from gamma photons with Eγ = 3 MeV interacting with D atoms in CTMFDs, in emission rate levels proportion to expected gamma-to-neutron radiation encountered by a CTMFD positioned at 1 m standoff from 30-y cooldown SNF. A 14 MeV neutron DT accelerator system was used with a NaCl source to produce 3.1 MeV activation gamma rays targeted onto a CTMFD with and without external neutrons from a Cf-252 source. While the Cf-252 neutron source was readily detected, the 3.1 MeV photons did not produce any noticeable difference nor impact. Therefore, Metric 2 is also deemed to be successfully met.

Acknowledgment

Numerous Professor Taleyarkhan's research group students, past and present, are duly acknowledged for their valuable contributions leading to the development of the TMFD sensor technology as also collaborators at various external institutions, including Oak Ridge National Laboratory, PNNL, and Savannah River National Laboratory. Past student J. A. Webster obtained the results on gamma dose on CTMFD electronics as part of his Ph.D dissertation (credited as Ref.12). The research work presented in this paper represents the work of Purdue University co-authors with project coordination for the separate complementary study at PNNL by A. Hagen of PNNL (credited as Ref. 26). The research at Purdue University was conceived, directed, and coordinated by the corresponding author, Professor R. P. Taleyarkhan of Purdue University. The timely support and assistance from Purdue University's REMS organization are duly acknowledged and appreciated.

Funding Data

  • Department of Energy (U.S.DOE) – Nuclear Safety R&D Program Office with Patrick Frias as DOE-HQ Program Manager, via PNNL (Grant No. 1400090).

Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

Nomenclature

Bq =

Becquerel

cc =

cubic centimeter (=mL)

C =

Celsius

Cf =

Californium

Ci =

Curie (= 3.7 × 1010 Bq)

CPM =

counts per minute

CTMFD =

centrifugally tensioned metastable fluid detector

eV =

electron volt

E =

energy

f =

frequency (Hz)

g =

gram

Gy =

Gray

h =

hour

L =

Liter

LaBr =

Lanthanum bromide

LWR =

light water reactor

m =

meter

min =

minute

mL =

milliliter

NaCl =

sodium chloride

NaI =

sodium iodide

n =

neutron

P =

pressure

Pa =

pascal

Pamb =

ambient pressure

Pneg =

negative pressure

PWR =

pressurized water reactor

r =

meniscus radius

Rad =

absorbed dose (=0.01 Gy)

SNF =

spent nuclear fuel

T =

temperature

TMFD =

tensioned metastable fluid detector

α =

alpha particle

β =

beta particle

γ =

gamma photon

σ =

microscopic cross section (barn)

References

1.
Knolls
,
G. F.
,
2000
,
Radiation Detection and Measurement
, 3rd ed.,
Wiley. Inc.
,
Hoboken, NJ
.
2.
Tsoufinidis
,
N.
, and
Landsberger
,
S.
,
2015
,
Measurement and Detection of Radiation
, 4th ed.,
CRC Press Taylor and Francis Group
,
Milton Park, UK
.
3.
Bean
,
R.
,
2007
, “
Aqueous Processing Material Accountability Instrumentation
,”
Idaho National Laboratory
, Report No. INL/EXT-07-13431.
4.
Cipiti
,
B. B.
,
2005
, “
Advanced Instrumentation for Reprocessing
,”
Sandia National Laboratories
,
Albuquerque
, Report No. SAND2005.
5.
Durst
,
P. C.
,
2007
, “
Advanced Safeguards Approaches for New Reprocessing Facilities
,”
Pacific Northwest National Laboratory
,
Richland, WA
, Report No. PNNL-16674.
6.
Guenther
,
R. J.
,
Blahnik
,
D.
,
Campbell
,
T.
,
Jenquin
,
T.
,
Mendel
,
J.
,
Thomas
,
L.
, and
Thornhill
,
C.
,
1988a
, “
Characterization of Spent Fuel Approved Testing material-ATM-103
,”
Pacific Northwest National Laboratory
,
Richland, WA
, Report No. PNNL-5109-103.
7.
Guenther
,
R. J.
,
Blahnik
,
D.
,
Campbell
,
T.
,
Jenquin
,
T.
,
Mendel
,
J.
,
Thomas
,
L.
, and
Thornhill
,
C.
,
1988b
, “
Characterization of Spent Fuel Approved Testing material-ATM-106
,”
Pacific Northwest National Laboratory
,
Richland, WA
, Report No. PNNL-5109-103.
8.
IAEA
,
2002
,
IAEA Safeguards Glossary
, 2001 ed., (International nuclear verification series No. 3),
International Atomic Energy Agency
,
Vienna, Austria
.
9.
Taleyarkhan
,
R. P.
,
Lapinskas
,
J.
,
Archambault
,
B.
,
Webster
,
J. A.
,
Grimes
,
T. F.
,
Hagen
,
A.
,
Fisher
,
K.
,
McDeavitt
,
S.
, and
Charlton
,
W.
,
2013
, “
Real-Time Monitoring of Actinides in Chemical Nuclear Fuel Reprocessing Plants
,”
Chem. Engr. Res. Des.
,
91
(
4
), pp.
688
702
.10.1016/j.cherd.2013.02.010
10.
Taleyarkhan
,
R. P.
,
Lapinskas
,
J.
, and
Xu
,
Y.
,
2008
, “
Tension Metastable Fluids and Nanoscale Interactions With External Stimuli – Theoretical-Cum-Experimental Assessments and Nuclear Engineering Applications
,”
Nucl. Eng. Des.
,
238
(
7
), pp.
1820
1827
.10.1016/j.nucengdes.2007.10.019
11.
Taleyarkhan
,
R. P.
,
Hagen
,
A.
,
Sansone
,
A.
, and
Archambault
,
B.
,
2016
, “
Femto-to-Macro Scale Interdisciplinary Sensing With Tensioned Metastable Fluid Detectors
,”
IEEE-SENSORS
, Orlando, FL, Oct. 30–Nov. 3, pp.
1
1
.10.1109/ICSENS.2016.7808563
12.
Webster
,
J. A.
,
Perez-Nunez
,
D.
, and
Taleyarkhan
,
R. P.
,
2016
, “
Qualification of CTMFD Sensors for Gamma-Beta Blind Functionality in SNF Reprocessing Facilities
,”
Proceedings of American Nuclear Soc. Adv. Non-Proliferation Tech. and Policy
, Santa Fe, NM, Sept. 25–30, pp.
122
125
.
13.
Archambault
,
B. C.
,
Webster
,
J. A.
,
Grimes
,
T. F.
,
Fischer
,
K. F.
,
Hagen
,
A. R.
, and
Taleyakhan
,
R. P.
,
2015
, “
Advancements in the Development of a Directional-Position Sensing Fast Neutron Detector Using Acoustically Tensioned Metastable Fluids
,”
Nucl. Instrum. Methods Res. Phys. A
,
784
, pp.
176
183
.10.1016/j.nima.2014.10.051
14.
Boyle
,
N.
,
Archambault
,
B.
,
Hemesath
,
M.
, and
Taleyarkhan
,
R. P.
,
2019
, “
Radon and Progeny Detection Using TMFDs
,”
Health Phys.
,
117
(
4
), pp.
434
442
.10.1097/HP.0000000000001066
15.
Archambault
,
B.
,
Hagen
,
A.
,
Grimes
,
T.
, and
Taleyarkhan
,
R. P.
,
2018
, “
Large-Array Special Nuclear Material Sensing With TMFDs
,”
IEEE Sens.
,
18
(
19
), pp.
7868
7874
.10.1109/JSEN.2018.2845344
16.
Hume
,
N.
,
Hagen
,
A.
,
Grimes
,
T.
,
Archambault
,
B.
,
Bakken
,
A.
, and
Taleyarkhan
,
R. P.
,
2020
, “
The MAC-TMFD: Novel Multi-Armed Centrifugally Tensioned Metastable Fluid Detector (Gamma-Blind) – Neutron-Alpha Recoil Spectrometer
,”
Nucl. Inst. Methods Phys. Res., A
,
949
(
2020
), p.
162869
.10.1016/j.nima.2019.162869
17.
Hemesath
,
M.
,
Boyle
,
N.
,
Archambault
,
B.
,
Lorier
,
T.
,
DiPrete
,
D.
, and
Taleyarkhan
,
R. P.
,
2022
, “
Actinide in Air (Rn-Progeny Rejected) Alpha Spectroscopy With Tensioned Metastable Fluid Detector
,”
ASME J. Nucl. Eng. Radiat. Sci.
,
8
(
2
), p.
022001
.10.1115/1.4049729
18.
Taleyarkhan
,
R. P.
,
Archambault
,
B.
,
Sansone
,
A.
,
Grimes
,
T.
, and
Hagen
,
A.
,
2020
, “
Neutron Spectroscopy and H*10 Dosimetry With Tensioned Metastable Fluid Detectors
,”
Nucl. Inst. Methods Phys. Res., A
,
959
(
2020
), p.
163278
.10.1016/j.nima.2019.163278
19.
Taleyarkhan
,
R. P.
,
2020
, “
Monitoring Neutron Radiation in Extreme Gamma/X-Ray Radiation Fields
,”
Sensors
,
20
(
3
), p.
640
.10.3390/s20030640
20.
Harabagiu
,
C.
,
Boyle
,
N.
,
Archambault
,
B.
,
DiPrete
,
D.
, and
Taleyarkhan
,
R. P.
,
2022
, “
High Resolution Pu-239/240 Mixture Alpha Spectroscopy Using Centrifugally Tensioned Metastable Fluid Detector Sensor Technology
,”
J. Anal. At. Spectrom.
,
37
(
2
), pp.
264
277
.10.1039/D1JA00285F
21.
Ozerov
,
S.
,
Boyle
,
N.
,
Hoiughtalen
,
N.
, and
Taleyarkhan
,
R. P.
,
2022
, “
Real-Time Shielded and Unshielded Moving SNM Detection Using Large Array TMFDs
,”
IEEE Trans. Nucl. Sci.
,
69
(
8
), pp.
1945
1952
.10.1109/TNS.2022.3184844
22.
Ozerov
,
S.
,
Hagen
,
A.
,
Archambault
,
B.
,
Sansone
,
A.
,
Boyle
,
N.
,
Grimes
,
T.
,
Rancilio
,
N.
,
Plantenga
,
J.
, and
Taleyarkhan
,
R. P.
,
2022
, “
Clinac 6 MV X-Ray Facility Photo-Neutron/Fission Interrogations With TMFD Sensors
,”
Nucl. Inst. Methods Phys. Res. A
,
1029
(
2022
), p.
166395
.10.1016/j.nima.2022.166395
23.
Ozerov
,
S.
,
Boyle
,
N.
,
Harabagiu
,
C.
,
DiPrete
,
D.
,
Whiteside
,
T.
,
Boone
,
A.
,
Hadlock
,
D.
, et al.,
2022
, “
Ultra-Low to Moderate Intensity Spectrometric Neutron Dosimetry With H*10-TMFD vs ROSPEC, Eberline and Ludlum Detector Systems
,”
Proceedings of 65th Radiobioassy and Radiochemical Measurements Conference
, Atlanta, GA, Oct. 31–Nov. 4.
24.
Boyle
,
N.
,
Archambault
,
B.
, and
Taleyarkhan
,
R. P.
,
2020
, “
High Energy Photo-Neutron Interrogation of Uranium With TMFDs
,”
Sens. Transducers J.
,
245
(
6
), pp.
36
40
.https://www.sensorsportal.com/HTML/DIGEST/october_2020/Vol_245/P_3170.pdf
25.
Gauld
,
I. C.
,
Herman
,
G. W.
, and
Westfall
,
R. M.
,
2009
, “
ORIGEN-S: SCALE System Module to Calculate Fuel Depletion, Actinide Transmutation, Fission Product Buildup and Decay and Associated Radiation Source Terms
,”
Oak Ridge National Laboratory
,
Oak Ridge, TN
, Report No. ORNL/TM-2005/39.
26.
Hagen
,
A.
,
Archambault
,
B.
, and
Garcia
,
I.
,
2023
, “
Further Experimental Evidence of the Photon Insensitivity and Robustness of TMFDs in High Intensity or High Energy Photon Fields
,”
ASME J. Nucl. Eng. Radiat. Sci.
(accepted).