Various groups have demonstrated that antineutrino monitoring can be successful in assessing the plutonium content in water-cooled nuclear reactors for nonproliferation applications. New reactor designs and concepts incorporate nontraditional fuel types and chemistry. Understanding how these properties affect the antineutrino emission from a reactor can extend the applicability of antineutrino monitoring. Thorium molten salt reactors breed 233U, that if diverted constitute a direct use material as defined by the International Atomic Energy Agency (IAEA). The antineutrino spectrum from the fission of 233U has been estimated for the first time, and the feasibility of detecting the diversion of 8 kg of 233U, within a 30 day timeliness goal has been evaluated. The antineutrino emission from a thorium reactor operating under normal conditions is compared to a diversion scenario by evaluating the daily antineutrino count rate and the energy spectrum of the detected antineutrinos at a 25 m standoff. It was found that the diversion of a significant quantity of 233U could not be detected within the current IAEA timeliness detection goal using either tests. A rate-time based analysis exceeded the timeliness goal by 23 days, while a spectral based analysis exceeds this goal by 31 days.

The accident that occurred at the Fukushima-Daiichi nuclear power plant following the 2011 earthquake and subsequent tsunami in Japan led to an international effort to increase the development of accident tolerant nuclear fuels specifically to withstand a core meltdown in the case of a beyond-design-basis event such as a loss of coolant. This has led to a revival in the interest in thorium molten salt reactor (MSR) designs. Despite the improvement to reactor safety, the production and online reprocessing of 233 Pa which decays into 233U creates a state-sponsored proliferation risk. Current International Atomic Energy Agency (IAEA) methods used to detect the divergence of nuclear material are relatively intrusive and cannot directly measure the fissile inventory of the reactor.1 Moreover, the safeguards approach for this new class of reactors has not yet been defined. Groups at Lawrence Livermore National Laboratory (LLNL) and Sandia National Laboratories (SNL) have shown that using antineutrino detectors provide a remote and non-intrusive method to observe the diversion of nuclear material.2 In this paper, the feasibility of using antineutrino monitoring to detect the diversion of 233U from a thorium MSR is evaluated.

Antineutrinos are weakly interacting neutral particles produced from the beta decay of neutron rich fission products. Unlike neutrons, beta particles, and gamma rays; antineutrinos can be detected from, well outside the reactor core because of their low interaction cross section. About six antineutrinos are produced from each fission resulting in an antineutrino flux of about 1021νe¯/s from a 1 GW reactor. Antineutrino monitoring of traditional nuclear reactors uses the varying spectral contributions of fission products from 235U and 239Pu over time to make the detection of materials diversion feasible. When these isotopes fission, they produce different beta emitters with various yields. The antineutrino spectrum for each fissile isotope is a combination of the antineutrino spectra of individual fission products, with each contribution fixed by the fission yield and branching ratio. As a result, each fissile isotope has a distinct antineutrino spectra shape and amplitude making its growth or depletion potentially accessible through antineutrino monitoring. For thorium reactors, the difference in antineutrino spectra from 233U and 235U, the most prominent fissile isotopes, allow for diversion detection.

Antineutrinos can be detected through their interactions with quasi-free protons in a liquid scintillating medium, using the inverse beta decay process shown in the following equation:

ν¯e+pe++nQ=1.804MeV.
(1)

The threshold for this reaction is 1.804 MeV, limiting detection of antineutrinos to those above that energy. In a liquid scintillator detector, the positron created from this reaction will slow in the detector and annihilate with an electron. The positron will deposit almost all of its energy at the end of its trajectory, and because subsequent annihilation occurs instantaneously, the energy of the positron and the gamma rays emitted from annihilation create an indistinguishable prompt signal. In a gadolinium-doped scintillator, the neutron captures on the Gd dopant within a few tens of microseconds, depending on the dopant concentration, a delayed signal from the resulting 8 MeV gamma ray cascade is formed. These two signals, detected in close time coincidence defines an antineutrino event.

TABLE I.

Summary of the detector parameters used in this analysis.

PropertyQuantity
Target Mass 3.6 Tons 
Efficiency 39.2 ± 4.7% 
Energy Resolution 20%E/(MeV) 
Fiducial Volume 100% 
Standoff 25 m 
Overburden 25 M.W.E 
Signal to Background 1262/200 
PropertyQuantity
Target Mass 3.6 Tons 
Efficiency 39.2 ± 4.7% 
Energy Resolution 20%E/(MeV) 
Fiducial Volume 100% 
Standoff 25 m 
Overburden 25 M.W.E 
Signal to Background 1262/200 

In the present work, the antineutrino emission from the reactor is studied using a design similar to that of a detector developed and tested at LLNL.3 The detector is assumed to be deployed at a 25 m standoff, 10 m below the surface, equivalent to a water overburden of about 25 m. At these depths, a previous iteration of this detector, SONGS1, experienced singles and delayed coincidence background count rate of 3725 and 105 counts a day, respectively, for a target mass of 0.64 tons.2 For a 3.6 ton detector, the uncorrelated daily background rate is assumed to be 21 000 counts. This uncorrelated background may be subtracted, thereby contributing a 150 count uncertainty on the signal. Due to significant improvements in background rejection from the muon veto system, larger fiducial volume and inter-event timing cuts, the correlated background is found to contribute to an additional 200 counts per day.3 It is assumed these counts are evenly distributed within 500 keV energy bins. While the backgrounds cannot be precisely known without an actual deployment, these estimates represent a reasonable extrapolation based on the measured properties of the 3.6 ton detector, and the known signal and background for the SONGS detector. Other experiments have shown similar signal to background ratios. The detector parameters used in this work can be found in Table I.4 

Although the antineutrino flux from the reactor is about 1021νe¯/s, the low interaction cross section for this reaction (σ=9.52E2×1044cm2) significantly reduces the number of events detected.5 Figure 1 gives a visual representation of the interaction cross section and antineutrino spectra effect on antineutrino detection for 235U and 233U fissions, as well as the ratio between the two. The falling antineutrino spectrum coupled with the quadratic increase in the interaction cross section results in a unique detection spectrum for each fissionable isotope.6 The sum of their antineutrino spectra can be used to estimate the inventory of fissionable content in a given reactor throughout the cycle.

FIG. 1.

(a) Visualization of antineutrino flux, (b)inverse beta decay cross section, and (c) detected antineutrino events from 235U and 233U fissions (top) shown with 1σ. Units for the inverse beta decay cross section and the detected antineutrino events are in arbitrary units to effectively communicate the effects of physical properties on the detected spectrum. Oscillation effects are neglected. Ratio of the 233U and 235U antineutrino spectra are shown (bottom). A detailed calculation of the 233U antineutrino spectrum shown above is discussed in Section III.

FIG. 1.

(a) Visualization of antineutrino flux, (b)inverse beta decay cross section, and (c) detected antineutrino events from 235U and 233U fissions (top) shown with 1σ. Units for the inverse beta decay cross section and the detected antineutrino events are in arbitrary units to effectively communicate the effects of physical properties on the detected spectrum. Oscillation effects are neglected. Ratio of the 233U and 235U antineutrino spectra are shown (bottom). A detailed calculation of the 233U antineutrino spectrum shown above is discussed in Section III.

Close modal

A thorium MSR core consists of a seed and blanket separated by a graphite moderator. Neutrons emitted from fissile material contained in the seed, converts 232Th in the blanket to 233U. At the beginning of the reactor lifetime, the seed is comprised of low enriched uranium (20% 235U); over time enough 233U is bred through the blanket to be used in the seed. 233U is formed from neutron capture by 232Th and subsequent beta decay chains shown below

Th232+n233Th22.3minβ233Pa26.97daysβ233U.
(2)

Online reprocessing occurs in the blanket to separate 233 Pa and 233U from 232Th. As shown in Figure 2, salt from the blanket undergoes flourination to re-inject uranium into the core, and minimize reactivity losses. 233 Pa is then extracted from the salt, and allowed to decay in a sub-critical storage containment. Another reduction process is used to extract 232Th and replace it in the blanket. After 233 Pa decays to 233U, it is reintroduced into the core.7 Because the conversion ratio for 232Th and 233U is less than one for this reactor, enriched uranium is also added to the seed as makeup fuel. If a state diverts 233 Pa before its daughter product can be reintroduced into the core, enough 233U could be proliferated to construct a nuclear device.

FIG. 2.

Flow diagram of a thorium MSR reprocessing unit showing the movement of fissile and fertile material. The introduction of thorium and enriched uranium come from external processes.

FIG. 2.

Flow diagram of a thorium MSR reprocessing unit showing the movement of fissile and fertile material. The introduction of thorium and enriched uranium come from external processes.

Close modal

The reactor used in this analysis is a 500 MWth thermal thorium MSR taken from the Sandia National Laboratories Nuclear Fuel Cycle Catalog.8 The fuel evolution was calculated using ORIGEN 2.2, a reactor neutronics software to simulate the isotopic inventory of nuclear systems.9 The fissile inventory of the core over the reactor's lifetime is shown in Figure 3. The inability to fully refuel the core and the material degradation from using molten salts reduces the lifetime of these reactors to a few decades.

FIG. 3.

Fission fraction of fissile isotopes throughout the reactor's lifetime with associated uncertainties from simulation. At the beginning of the reactor's lifetime, most of the fissions come from 235U. Over time, the contribution of 233U to the fission fraction increases until it reaches an equilibrium.

FIG. 3.

Fission fraction of fissile isotopes throughout the reactor's lifetime with associated uncertainties from simulation. At the beginning of the reactor's lifetime, most of the fissions come from 235U. Over time, the contribution of 233U to the fission fraction increases until it reaches an equilibrium.

Close modal

To determine the expected antineutrino emission from a thorium MSR, the antineutrino spectra for 233,235,238U and 239,241Pu must be evaluated. Because of the graphite moderator, the fast neutron flux in the blanket is negligible. As a result, fissile actinides such as 232Th and 233 Pa do not contribute to the antineutrino emission from the reactor. The antineutrino spectra from 235,238U and 239,241Pu have been previously determined by converting the measured electron emission following neutron irradiation at ILL and FRM II;10,11 while the antineutrino spectra from the fission of 233U is not available in open literature, and must be estimated through an aggregate summation method.

The antineutrino spectrum from the fission of an isotope, N(Ev¯),is a combination of spectra, Pv¯(Ev¯,E0i,Z), from its fission products. In this work, the fission yield and uncertainties were taken from ENDF-34912 

N(Ev¯)=nYn(Z,A,t)×ibn,i(E0i)Pv¯(Ev¯,E0i,Z),
(3)

where Yn(Z,A,t) is the number of beta decays per second for a given isotope (Z, A); bn,i(E0i) is the branching ratio to an excited state with the electron energy spectrum endpoint

E0i=QnEexi.
(4)

Here Qn is the Q value for the beta decay of isotope (Z, A), and Eexi is the excitation energy in the daughter nucleus (Z+1,A). The decay information for all the fission products was taken from the Evaluated Nuclear Structure Data Files.13 The fission products for which the decay data was absent were neglected because they only represented less than 10−6 of the cumulative fission yield, or had such large Q values that these nuclei would be beta delayed neutron candidates such that the antineutrinos emitted from their decay would be less than 3 MeV (below the energy range of this assessment).

The spectrum shape factor, Pv¯(Ev¯,E0,Z) shown in Equation (5) is derived from the phase space relationship between the electron and antineutrino and the normalization constant, k, for each branch; as well as the Fermi Coulomb function, F(E0,Z), which accounts for the Coulomb attraction between the emitted electron, and daughter nucleus is shown in Equation (6).14 An allowed Gamow-Teller spectral shape was assumed for all beta decays

Pv¯=kEv¯2(E0Ev¯)2F(E0,Z).
(5)

Additional corrections to the antineutrino spectra include both the electromagnetic and weak-interaction finite size correction, the radiative corrections, and the weak magnetism correction.6,10,15,16 Effects of the screening correction were neglected due to its small contribution to the antineutrino shape.10 Previous assessments show that multiple methods of evaluating the spectrum introduces disagreements in the antineutrino spectrum from fission.17 To quantify the systematic uncertainty in the aggregate spectra, the antineutrino spectra from 235,238U and 239,241Pu were calculated in the same manner and compared to the ILL and FRM II results.10,11 A comparison of the antineutrino spectra from the experiments at ILL and FRM II compared to those determined using the summation method is shown in Figure 4. The spectra evaluated in this work show a 10% deficit from 2–4 MeV, and an excess between 4–7 MeV. The resulting 233U antineutrino spectrum is shown in Figure 1 and presented in Table II.

FIG. 4.

Comparison of the antineutrino spectra from the fission of 235,238U and 239,241Pu determined from the summation method (blue) and the converted beta measurements at ILL and FRM II (black). The antineutrino spectra for 238U was only evaluated between 3–7.5 MeV.10,11

FIG. 4.

Comparison of the antineutrino spectra from the fission of 235,238U and 239,241Pu determined from the summation method (blue) and the converted beta measurements at ILL and FRM II (black). The antineutrino spectra for 238U was only evaluated between 3–7.5 MeV.10,11

Close modal
TABLE II.

Approximated 233U antineutrino spectra, and correlated uncertainties using the summation method.

Ev¯Nv¯σ
[MeV][ν fission−1 MeV−1][%]
2.00 9.45×101 9.03 
2.25 7.76×101 10.0 
2.50 6.34×101 6.85 
2.75 5.14×101 9.39 
3.00 4.10×101 11.6 
3.25 3.22×101 13.3 
3.50 2.54×101 14.6 
3.75 2.20×101 13.2 
4.00 1.58×101 11.6 
4.25 1.25×101 10.6 
4.50 9.90×102 7.52 
4.75 7.92×102 12.5 
5.00 6.25×102 16.5 
5.25 4.88×102 18.7 
5.50 3.77×102 23.8 
5.75 2.83×102 23.6 
6.00 2.07×102 27.1 
6.25 1.45×102 36.7 
6.50 9.62×103 23.5 
6.75 5.92×103 19.9 
7.00 3.53×103 19.6 
7.25 2.20×103 24.5 
7.50 1.36×103 22.1 
7.75 7.61×104 17.6 
8.00 3.91×104 19.9 
Ev¯Nv¯σ
[MeV][ν fission−1 MeV−1][%]
2.00 9.45×101 9.03 
2.25 7.76×101 10.0 
2.50 6.34×101 6.85 
2.75 5.14×101 9.39 
3.00 4.10×101 11.6 
3.25 3.22×101 13.3 
3.50 2.54×101 14.6 
3.75 2.20×101 13.2 
4.00 1.58×101 11.6 
4.25 1.25×101 10.6 
4.50 9.90×102 7.52 
4.75 7.92×102 12.5 
5.00 6.25×102 16.5 
5.25 4.88×102 18.7 
5.50 3.77×102 23.8 
5.75 2.83×102 23.6 
6.00 2.07×102 27.1 
6.25 1.45×102 36.7 
6.50 9.62×103 23.5 
6.75 5.92×103 19.9 
7.00 3.53×103 19.6 
7.25 2.20×103 24.5 
7.50 1.36×103 22.1 
7.75 7.61×104 17.6 
8.00 3.91×104 19.9 

Once the antineutrino spectra of fissile isotopes were calculated, the corresponding detection rate, D(Ev¯), was found using Equation (6). Here ρp is the proton density, V is the detection volume, ϵ is the detector efficiency, T is the counting time, r is the distance from the detector to the reactor core, and ϕ is the antineutrino rate derived from the fission rate in the reactor.2 The survival probability, Pee, which accounts for the oscillation of neutrino flavor is also accounted for. However, because the detector is located 25 m from the reactor core, the loss of antineutrinos due to oscillations was negligible

D(Ev¯)=TρpVϵ4πr2σ(Ev¯)ϕ(Ev¯)Pee(Ev¯,r).
(6)

Once the antineutrino is emitted, there is no way to determine which fissile isotope was responsible for its emission. Regardless of the count rate evolution and the overall detected antineutrino, energy spectrum will still reflect changes in inventory of fissile material in the reactor.

The IAEA set limits of concern for unaccounted nuclear material that can be used for the construction of a nuclear device. In the case of 233U, the IAEA defines a significant quantity to be 8 kg with a timeliness detection goal of 30 days. Two cases are compared in the diversion study: a baseline scenario in which the reactor is under standard operation, and an anomalous scenario in which a state is trying to divert 233U. The thorium molten salt reactor used in this analysis reaches a 233 Pa production equilibrium of about 330 g a day. In the anomalous scenario, the reactor has reached this equilibrium production and 330 g of 233U is diverted and replaced with 294.36 g of 235U each day until a significant quantity, 8 kg, is obtained. The addition of 235U compensates for the reactivity and power loss from diversion activity. The evaluation for the analysis takes place at 4500 effective full power days. For this diversion scenario, we assume that a proliferating party intends to minimize the amount of time needed to divert material in order to maximize the time between when a significant quantity is extracted and when the anomalous activity can be detected. In this scenario, t = 0 is when the diversion of 330 g of 233U begins. This continues for twenty-five days, at which point the IAEA timeliness detection goal for this material is thirty days.18 The antineutrino evolution for both the baseline and anomalous case will be evaluated for 55 days assuming a full power operation or until there is a 95% confidence that material was diverted.

A spectral based analysis was performed by comparing the detected antineutrino spectra from the baseline and anomalous scenarios defined in this Section, in order to determine the counting period required to achieve a 95% confidence that a significant quantity of material was diverted. This analysis observes the individual contributions of each fissioning isotope in the reactor to the overall detected antineutrino spectrum through an energy binned maximum likelihood analysis for correlated variables

p=1(2π)n/2det(Σ)exp(12AΣ1AT).
(7)

Here, A=[MiBi,,MnBn], compares the measured counts, M, in each energy bin, n, against the counts calculated in the baseline B; Σ represents the variance-covariance matrix for the measured spectra, and p defines the probability of an anomalous scenario. Applying the statistics test to the antineutrino spectra shown in Figure 5 resulted in an 87% confidence level for anomalous activity. A counting period of 86 days, 31 days past the IAEA timeliness detection goal, was required to meet the desired confidence level. The ROC (Receiver Operating Characteristic), curve shown in Figure 7 validates the strength of the test for the spectral analysis. Subsection IV B discusses the use of ROC in more detail.

FIG. 5.

Detected antineutrino energy spectra integrated for the anomalous and baseline scenario over an 86 day counting period (top). Energy binned differences between the anomalous and baseline scenario with statistical errors (bottom).

FIG. 5.

Detected antineutrino energy spectra integrated for the anomalous and baseline scenario over an 86 day counting period (top). Energy binned differences between the anomalous and baseline scenario with statistical errors (bottom).

Close modal

As shown in Fig. 1, the largest spectral difference between 233U and 235U occurs at higher energies where the uncertainties in the spectral shape are the largest. Recent results from the Daya Bay experiment indicate that a small number of beta-decay isotopes can explain the presence of an anomalous bump in the antineutrino spectrum around 6–7 MeV.19 In principle, this could have implications to antineutrino detection for nuclear safeguards if the “bump” was attributed to specific actinides. However, our results do not depend on the bump and that a higher resolution detector with higher statistics would be needed to exploit this still poorly understood feature.

Previous studies looking at the diversion of plutonium have shown an excess of counts at higher energies, and a deficit at lower energies due the shape of 239Pu and241Pu relative to 235U.20 Because the antineutrino spectrum of 233U lower than that of 235U at all energies, a spectral analysis shows an excess of counts in each energy bin. Additionally, results from this analysis can be improved if the uncertainties due to counting statistics and the predicted antineutrino emission were reduced.

In this analysis, the antineutrino count rate evolution in an anomalous scenario was compared to the expected antineutrino counts under standard operations (baseline) using a hypothesis testing procedure.4 Figure 6 shows the count rate evolution in both the baseline and anomalous scenarios along with the LS regression fit. The antineutrino count rate for this thorium MSR shows a smaller decline over time than that of the PWR seen in Reference 4. This MSR is refueled online with more frequency than a PWR, as a result the reactivity of a reactor, for a given thermal output, is primarily controlled by the makeup fuel; whereas, in a PWR the boron concentration of the coolant throughout a cycle indiscriminately affects the actinides fission rate.

FIG. 6.

Baseline (green) and anomalous scenario (blue) evolutions of the antineutrino count rate in counts per day over the fifty-five day period, along with the expected count rate in the case of operator malice (red). The associated errors in the count rates have been removed to show a direct comparison of the count rates and calculated fits.

FIG. 6.

Baseline (green) and anomalous scenario (blue) evolutions of the antineutrino count rate in counts per day over the fifty-five day period, along with the expected count rate in the case of operator malice (red). The associated errors in the count rates have been removed to show a direct comparison of the count rates and calculated fits.

Close modal

Once the antineutrino count rate was determined, a quadratic fit using least square (LS) regression was applied to the rate. To eliminate dependencies between the coefficients, the LS regression was performed on the sample mean (tt¯) as shown in the following equation:

Nv¯(B)=β0(B)+β1(B)(tt¯)+β2(B)(tt¯)2.
(8)

Here, the superscripts are consistent with those used in the spectral analysis. Comparing the coefficients β0, β1, and β2 between the measured and baseline fit will indicate if material has been diverted using the following hypothesis test

H0i:βi(M)=βi(B)vrsHai:βi(M)βi(B).
(9)

Equation (9) can be determined using the following test statistics:

si=βi(M)βi(B)σ2(βi(M))+σ2(βi(B))
(10)

and the corresponding p value

pi=2·P(S|si|).
(11)

Here, S has a Student's t distribution with 2·(n3) degrees of freedom, with n being the number of count rate measurements and σ referring to the uncertainties in the daily count rate. Although not included in this work, the systematic uncertainties in the detector response and antineutrino rate may be reduced if previous measurements on this reactor can allow for template matching.4 

When applying the test to the count rate evolution, two of the three coefficients reject the null hypothesis in favor of the alternative hypothesis. The one coefficient, β0, that showed no statistical difference was related to the absolute antineutrino rate emission. This shows that the test is not dependent on precise knowledge of the expected count rate, but observes general trends (i.e., is the count rate monotonically decreasing or not) in the rate evolution.

To determine the robustness of the hypothesis tests to statistical variations in LS coefficients, a Monte Carlo simulation was used to generate one hundred thousand anomalous and baseline detected antineutrino count rate evolutions assuming a Gaussian distribution. An ideal threshold for the true positive/false positive rate was identified as 95%/5%. A true positive result was identified as the test correctly identifying an anomalous scenario, while a false positive result indicated that the baseline was incorrectly identified as an anomalous scenario. Figure 7 shows the ROC curve for the rate analysis under a 55 day counting period as well as the counting time required to reach the desired TP/FP rate. Under the 55 day constraint, a 81%/5% TP/FP rate is achieved. The desired rate is achieved by increasing the counting time to 78 days (Table III).

FIG. 7.

ROC curve for the count rate evolution within the IAEA timeliness goal (blue) and when the target TP/FP rate is met for both the count rate evolution (green) and the spectral (purple) curve for the desired true positive and false positive rate is plotted with dotted lines.

FIG. 7.

ROC curve for the count rate evolution within the IAEA timeliness goal (blue) and when the target TP/FP rate is met for both the count rate evolution (green) and the spectral (purple) curve for the desired true positive and false positive rate is plotted with dotted lines.

Close modal
TABLE III.

Sensitivity of the count rate evolution test using Monte Carlo simulations. The results show the false positive rate that would incur for a 5% false positive rate for both the diversion scenario presented in the study, and a misreported power shift.

CountingDiversion ScenarioMisreported Power
TimeTP/FPTP/FP
55 Days 81%/5% 58%/5% 
78 Days 95%/5% 73% /5% 
114 Days 99% /2% 95%/5% 
CountingDiversion ScenarioMisreported Power
TimeTP/FPTP/FP
55 Days 81%/5% 58%/5% 
78 Days 95%/5% 73% /5% 
114 Days 99% /2% 95%/5% 

When this procedure was applied to pressurized water reactors to observe the diversion of plutonium, it could not identify anomalous activity as quickly if the operator misreported the thermal power output.4 Because of the transient growth of the antineutrino spectra caused by the diversion of 233U, misreporting the reactor power would not mask proliferation. Figure 6 shows the expected antineutrino count rate if the reactor was operating at a 7 MW excess. Here the β0 coefficients are matched, requiring more time to detect material diversion. After applying the same procedure, as mentioned above, an anomalous scenario can be detected within 114 days in the presence of a false power report. Additionally, the effects of misreported power shifts can give insight into the test's sensitivity to detector drifts. The detector used in this analysis has not been deployed long enough to study these effects, but the SONGS1 detector showed a less than 1% drift while taking data.21 

The antineutrino emission from a thorium MSR was analyzed to determine if the diversion of a significant quantity of 233U could be observed within the IAEA timeliness goal. In order to perform the analysis, we calculated the antineutrino emission spectrum of 233U, based on the fission product yields. Using a spectral and rate-time based analysis, the diversion 233U could be detected 61 and 53 days after the diversion of 8 kg of 233U, respectively; in a total counting period of 86 and 78 days. Usually a spectral analysis is more sensitive to diversion than the rate-time analysis because it provides more information about the antineutrino emission. In this analysis, the integral spectrum over the entire 55 day period is being binned into a single histogram so the day to day changes in the rate of each bin is averaged out.

Evaluating the antineutrino count rate gives insight into the power level of the reactor, where analyzing the detected antineutrino spectra is a reflection of its isotopic concentration. Although this method requires less time, relying solely on the count rate makes the analysis susceptible to operator malfeasance. When using the antineutrino count rate, there is a trade off between exceeding IAEA timeliness goals and being sensitive to false declarations of reactor power.

The test for material diversion was heavily dependent on counting statistics. Desirable test performances are attainable through feasible improvements to antineutrino detectors, such as better instrumentation for small scale antineutrino detectors or increasing the detector mass. Additionally, variations in thorium reactor designs may also effect the sensitivity to diversion. Some models incorporate scheduled refueling, reducing the counting time from 55 days to 30 days; or utilize epithermal and fast neutron energies, which would effect the antineutrino emission from fission. Other designs incorporating solid fuels do not separate the 233 Pa from the blanket. This changes the SNM from unirradiated direct use material to irradiated use material, allowing for longer diversion detection constraints.

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. LLNL-JRNL-646478, and supported by the Department of Energy National Nuclear Security Administration under Award Nos. DE-NA0000979 and LLNL-JRNL-703739.

1.
IAEA Safety Report Series,
2014
.
2.
N.
Bowden
,
A.
Bernstein
,
M.
Allen
,
J.
Brennan
,
M.
Cunningham
,
J.
Estrada
,
C.
Greaves
,
C.
Hagmann
,
J.
Lund
,
W.
Mengesha
 et al,
Nucl. Instrum. Methods Phys. Res., Sect. A
572
,
985
(
2007
).
3.
T.
Classen
,
A.
Bernstein
,
N.
Bowden
,
B.
Cabrera-Palmer
,
A.
Ho
,
G.
Jonkmans
,
L.
Kogler
,
D.
Reyna
, and
B.
Sur
,
Nucl. Instrum. Methods Phys. Res., Sect. A
771
,
139
(
2015
).
4.
V.
Bulaevskaya
and
A.
Bernstein
,
J. Appl. Phys.
109
,
114909
(
2011
).
5.
C.
Bemporad
,
G.
Gratta
, and
P.
Vogel
,
Rev. Mod. Phys.
74
,
297
(
2002
).
6.
T.
Mueller
,
D.
Lhuillier
,
M.
Fallot
,
A.
Letourneau
,
S.
Cormon
,
M.
Fechner
,
L.
Giot
,
T.
Lasserre
,
J.
Martino
,
G.
Mention
 et al,
Phys. Rev. C
83
,
054615
(
2011
).
7.
A.
Nuttin
,
D.
Heuer
,
A.
Billebaud
,
R.
Brissot
,
C.
Le Brun
,
E.
Liatard
,
J.
Loiseaux
,
L.
Mathieu
,
O.
Meplan
,
E.
Merle-Lucotte
 et al,
Prog. Nucl. Energy
46
,
77
(
2005
).
8.
R.
Wigeland
,
T.
Taiwo
,
H.
Ludewig
,
M.
Todosow
,
W.
Halsey
,
J.
Gehin
,
R.
Jubin
,
J.
Buelt
,
S.
Stockinger
,
K.
Jenni
,
B.
Oakley
 et al,
US DOE Fuel Cycle Technol.
8
(
2014
).
9.
I.
Gauld
,
O.
Hermann
, and
R.
Westfall
,
Report No. ORNL/TM-2005/39
, Version 6,
2009
.
10.
11.
N.
Haag
,
A.
Gütlein
,
M.
Hofmann
,
L.
Oberauer
,
W.
Potzel
,
K.
Schreckenbach
, and
F.
Wagner
,
Phys. Rev. Lett.
112
,
122501
(
2014
).
12.
T.
England
and
B.
Rider
,
Report No. ENDF-349, LA-UR-94-3106
, Los Alamos National Laboratory,
1994
.
13.
M.
Bhat
, in
Nuclear Data for Science and Technology
(
Springer
,
1992
), pp.
817
821
.
14.
P.
Vogel
,
G.
Schenter
,
F.
Mann
, and
R.
Schenter
,
Phys. Rev. C
24
,
1543
(
1981
).
15.
D.
Wilkinson
,
Nucl. Instrum. Methods Phys. Res., Sect. A
290
,
509
(
1990
).
16.
17.
A.
Hayes
,
J.
Friar
,
G.
Garvey
,
G.
Jungman
, and
G.
Jonkmans
,
Phys. Rev. Lett.
112
,
202501
(
2014
).
18.
I. S.
Glossary
,
International Nuclear Verification Series No. 3
(
IAEA
,
Austria
,
2001
).
19.
D.
Dwyer
and
T.
Langford
,
Phys. Rev. Lett.
114
,
012502
(
2015
).
20.
E.
Christensen
,
P.
Huber
,
P.
Jaffke
, and
T.
Shea
,
Phys. Rev. Lett.
113
,
042503
(
2014
).
21.
N.
Bowden
,
A.
Bernstein
,
S.
Dazeley
,
R.
Svoboda
,
A.
Misner
, and
T.
Palmer
,
J. Appl. Phys.
105
,
064902
(
2009
).