# Exclusion and Verification of Remote Nuclear Reactors
with a 1-Kiloton Gd-Doped Water Detector

O. A. Akindele  Corresponding author; Email<EMAIL_ADDRESS>Lawrence
Livermore National Laboratory, Livermore, California 94550, USA  A. Bernstein
M. Bergevin  S. A. Dazeley  F. Sutanto  A. Mullen  J. Hecla  Lawrence
Livermore National Laboratory, Livermore, California 94550, USA

(August 27, 2024)

###### Abstract

To date, antineutrino experiments built for the purpose of demonstrating a
nonproliferation capability have typically employed organic scintillators,
were situated as close to the core as possible - typically a few meters to
tens of meters distant and have not exceeded a few tons in size. One problem
with this approach is that proximity to the reactor core require accommodation
by the host facility. Water Cherenkov detectors located offsite, at distances
of a few kilometers or greater, may facilitate non-intrusive monitoring and
verification of reactor activities over a large area. As the standoff distance
increases, the detector target mass must scale accordingly. This article
quantifies the degree to which a kiloton-scale gadolinium-doped water-
Cherenkov detector can exclude the existence of undeclared reactors within a
specified distance, and remotely detect the presence of a hidden reactor in
the presence of declared reactors, by verifying the operational power and
standoff distance using a Feldman-Cousins based likelihood analysis. A 1-kton
scale (fiducial) water Cherenkov detector can exclude gigawatt-scale nuclear
reactors up to tens of kilometers within a year. When attempting to identify
the specific range and power of a reactor, the detector energy resolution was
not sufficient to delineate between the two.

##  I Introduction

Antineutrino monitoring has been proposed for various nonproliferation
applications and reactor fuel compositions Bowden  _et al._ (2007);
Christensen  _et al._ (2015); Bernstein  _et al._ (2018); Akindele  _et al._
(2016); Bernstein  _et al._ (2020); Hayes  _et al._ (2012). All of these prior
studies used ton-scale scintillator detectors in close proximity (tens of
meters or less) to the reactor core. While short-distance monitoring with
scintillator detectors is less intrusive to reactor operations compared to
other verification methods, these detectors still require on-site
accommodation. For example, space and power must be provided for the
equipment, the materials used must be compliant with facility regulations, and
any maintenance on the detector will require access by a verification body.
Greater standoff distances could further reduce the intrusiveness of the
method by permitting deployment outside the reactor operator’s facility
grounds. However, to effectively probe a larger exclusion area requires a
larger target volume. Ton-scale near-field detectors still require on-site
compliance. Space and power must be provided for the equipment, the materials
used must be shown not to affect facility operations, and any maintenance on
the detector will require access by the verification body.

Antineutrinos are weakly interacting and can be detected at long distances
from their source of origin. This raises the question: can antineutrino
detection be used in the mid-field, which we define here to be approximately
10 to 100 km, to monitor the operation or presence of nuclear reactors? In
this article, we evaluate the ability to detect antineutrinos at a
hypothetical far-field deployment in the presence of other reactors producing
a high antineutrino background.

##  II The baseline detector design

Figure 1:  An illustration of the Gd-H2O baseline detector design, with a
vertical cutaway through the center. The width and height of the cylindrical
tank is 20-meters. In total, the detector will house 3,554 Photo-multiplier
Tubes (PMTs), 3,328 as part of the inner detector (20 $\%$ photocoverage)
facing the fiducial volume, and 226 veto PMTs facing the tank (2 $\%$
photocoverage)to reject cosmogenic events from within the veto volume. Other
components of the tank include: a top and bottom hatch, calibration ports, a
top deck for data acquisition (DAQ) electronics, and external access
locations.

.

In this study the hypothetical deployment is located in the Boulby Underground
Laboratory on the eastern side of the United Kingdom, an operating
potash/polyhalite mine Robinson  _et al._ (2003). The mine rock is low in
uranium, thorium, and radon compared to many other underground facilities. The
detector is modeled to be $1.1\ \mathrm{km}$ (2.86 km.w.e.) underground, and
approximately 26 km from the Hartlepool Reactor Complex. The Complex houses
two 1.5 GWth Advanced Gas Reactors (AGRs) yielding 3 GWth capacity. The
reactor antineutrino background at the Boulby mine is relatively high due to
the presence of a large number of other operating reactors in the UK and
Western Europe. For specific use cases, design variations may be employed to
maximize the sensitivity of the detector, such as increased photo-coverage,
large target volumes, or multiple detectors.

This article presents the sensitivity of a gadolinium-doped water (Gd-H2O)
detector, using the WATCHMAN collaboration’s 2019 baseline Gd-H2O detector
design Bernstein (2019). We refer to this design as ‘the Gd-H2O baseline
design’ or the ‘Gd-H2O detector’ throughout this article. Sensitivity
estimates are provided for exclusion of the existence of undeclared reactors
over a specified radial distance, and for determining the presence of a hidden
reactor near a declared reactor facility. The Boulby Underground Laboratory
site is used to provide a concrete example of sensitivity in a well-studied
background environment Robinson  _et al._ (2003).

The detection medium is contained in a cylindrical stainless-steel tank with a
20-meter height and diameter. The tank is filled with approximately 6 kilotons
of ultra-pure water mixed with gadolinium sulfate, for a total loading of
0.1$\%$ gadolinium by weight. The detector has two optically separated
regions, the muon veto region and the inner detector. Events occurring in the
3.3 m thick outer veto region are read out by 226 PMTs, while events in the
inner detector are read out by 3,328 PMTs. This equates to a 20$\%$ photo-
coverage for the inner detector and a 2$\%$ photo-coverage for the veto
detector. To reduce backgrounds caused by radiation from the PMTs, only events
which reconstruct within the central $\sim$1 kton fiducial volume will be
considered as candidate antineutrinos. An illustration of the detector is
shown in Figure 1.

Gadolinium-doped water is an ideal medium for far-field antineutrino
monitoring due to its chemical simplicity, low cost, and good optical
transparencyBeacom and Vagins (2004); Bernstein  _et al._ (2001). The long
attenuation length of the Gd-doped water allows the medium to be scaled to
larger volumes if required, based on the particular needs of real world
applications Marti  _et al._ (2020); Renshaw  _et al._ (2012). Water is a low
toxicity medium that has been deployed in many other neutrino detectors such
as Super KamiokandeFukuda  _et al._ (2001), and SNOAhmed  _et al._ (2004). The
addition of the capture agent gadolinium allows for an enhanced neutron
capture signal, favorable for experiments focused primarily on detecting
reactor antineutrinos through inverse beta decay (IBD).

In the IBD process, antineutrinos interact with quasi-free protons in the
water, producing a positron-neutron pair in the final state:

$\overline{\nu}_{e}+p\,\longrightarrow e^{+}+n.$ (1)

The positron is detected as a prompt signal through the Cherenkov light
emitted when its velocity exceeds the speed of light in the water. This is a
multiple threshold reaction in which the $\overline{\nu}_{e}$ energy must
exceed 1.8 MeV to generate an IBD reaction, and the resulting positron kinetic
energy must exceed $\sim$253 keV in water to generate Cherenkov light. The
neutron produced through IBD will elastically scatter off hydrogen in the
detector until thermalization, after which it can capture on either a
gadolinium or hydrogen nucleus. For gadolinium loading at 0.1%, the average
capture time is $\sim$30 $\mu$s after the prompt positron event Beacom and
Vagins (2004). Neutron capture on hydrogen account for 9$\%$ of captures and
will result in a single 2.2-MeV gamma ray, while captures on isotopes of
gadolinium accounts for 91$\%$ of captures and will result in a cascade of
gamma rays summing to $\sim$8 MeV. The gamma rays from neutron capture will
Compton scatter, and the Compton electrons may emit Cherenkov light. Due to
the threshold required for Cherenkov emission, not all of the scattered
electrons from gamma rays released from neutron capture on Gd will contribute
to the signal, but the neutron capture on Gd still produces a distinctly
bright signature.

Figure 2:  The PMT hit timing distribution from a set of 107 events [A], the
prompt PMT response to positrons as a function of energy [B], and the distance
between true and reconstructed vertex as a function of energy [C].

.

##  III Simulation and Reconstruction Framework

Various tools are used in the simulation, reconstruction, and event
categorization to predict detector response. The Reactor Analysis Tool-Plus
Additional Codes (RAT-PAC)Seibertet  _et al._ , employs Geant4 version 10.4
Agostinelli  _et al._ (2003), ROOT Brun and Rademakers (1997), and C++ to
perform high fidelity Monte-Carlo simulations of the events expected from
radiological processes, cosmogenically produced particles, and IBD. Following
event production in the detector, all the subsequent processes are modeled,
from optical photon production and transport through the water, to photon
collection in PMTs.

The accuracy of the complex decay scheme resulting from neutron capture on Gd,
as modeled in Geant4, has been an area of concern in recent years Yano  _et
al._ (2017); Hagiwara  _et al._ (2019). Neutron capture on 157Gd generates the
most prominent gamma ray cascade due to the larger cross-section relative to
the other isotopes. To remedy the modeling concerns of Geant4, the DANCE Chyzh
_et al._ (2011a)(Detector for Advanced Neutron Capture
Experiments)Collaboration’s gamma ray production results were incorporated
into RAT-PAC using DICEBOX Chyzh  _et al._ (2011b). The resulting simulation
was validated against the WATCHBOY detector’s neutron response and
demonstrated better agreement with experimental data than the previous 157Gd
gamma ray cascade model Sutanto  _et al._ (2020).

Following the simulation, the position and energy of each event are
reconstructed using Branching Optimization Navigating Successive Annealing
Iterations (BONSAI) Smy (2007). BONSAI uses the timing and the positions of
the PMT hits to reconstruct the vertex position of each event based on the
detected Cherenkov light and has been used by the Super Kamiokande
collaboration for low energy event reconstruction Carminati  _et al._ (2015).

Antineutrino interactions are characterized by simulating the response to
positron and neutron pairs. A flat positron energy spectrum was simulated to
understand the energy-dependent detector response. The emitted Cherenkov light
from positron interactions results in approximately 9 detected photo-electrons
(PE) per MeV. To inprove the energy resolution without increasing
contributions from backgrounds, the energy proxy is taken as the number of
PMTs that trigger from the prompt Cherenkov light in the first nine
nanoseconds.

The energy-dependent positron response is seen in Figure 2. Figure 2.A shows
that the PMT hit timing distribution from positrons primarily occurs within a
9 ns window following a start time defined by the event vertex. The negative
times observed and the full width of the peak are due to the 2 ns PMT timing
jitter, while the late light is caused by scattering in the detector. The
features around 40-70 ns are caused by after-pulsing in the PMTs. Figure 2.B
shows that positrons below 1 MeV do not produce events above the rate of
events seen from the dark rate in the PMTs. Lastly, once the prompt PMT hits
are registered, BONSAI is used to reconstruct the events. Below 2 MeV, the the
true vertex is reconstructed to 1 meter; above 3 MeV the vertex reconstruction
improves and rapidly converges at 50 cm, as shown in Figure 2.C.

##  IV Antineutrino Events of Interest

After event reconstruction the individual events were sampled based on the
reactor thermal power and standoff from the detector, $L$. The expected
detected number of antineutrinos $N(E_{\overline{\nu}_{e}})$ is given by:

$N(E_{\overline{\nu}_{e}},L)=\frac{n_{p}T}{4\pi
L^{2}}\sum_{l}N^{f}_{l}\phi_{l}(E_{\bar{\nu}_{e}})\sigma(E_{\overline{\nu}_{e}})P_{ee}(E_{\overline{\nu}_{e}},L).$
(2)

Here, $n_{p}$ refers to the number of quasi-free protons and $T$ is the
counting time of the experiment. The electron antineutrino survival
probability due to oscillations and the IBD cross section are given by
$P_{ee}$ and $\sigma$, respectively Vogel and Beacom (1999); Gonzalez-Garcia
_et al._ (2014). The individual contributions of fissile isotopes $l$ is
represented by the fissile fraction for the specific isotope $N^{f}_{l}$ and
the unique spectra for that isotope $\phi_{l}$, which is assumed to follow the
approximations taken from the Huber spectra determination Huber (2011).

In effect, neglecting contributions from the backgrounds, the measured
antineutrino signal will be governed by the standoff distance, burn-up, and
power of the facility being monitored. The power of the reactor can be
addressed through simple scaling as the thermal reactor power is directly
related to the sum of the energy of the individual isotopes undergoing
fission: 235U (201.912 MeV/fission), 238U (204.997 MeV/fission),239Pu (210.927
MeV/fission), and 241Pu (213.416 MeV/fission) Duderstadt (1976). The
Hartlepool reactors are AGRs, with more frequent refueling outages than
pressurized water reactors. Given that the time scale of the reactor cycles
for these reactors is on the order of weeks, and the dwell time for this
analysis is on the order of months, the fuel burn-up effect is neglected. The
analysis assumes static fissile contributions from 235U, 238U, 239Pu, and
241Pu based on the average fissile fraction of the Hartlepool Reactor Complex.

The systematic uncertainties for the antineutrino events were assumed to
persist from a combination of the oscillation parameters, the accuracy to
which the reactor power can be determined, uncertainties in the IBD cross-
section, and the reactor-antineutrino anomaly.

##  V Backgrounds

Figure 3: The antineutrino backgrounds are shown in [A]. Here, the total
expected number of antineutrino backgrounds (solid-black) from contributions
from the world reactor backgrounds (dashed-green), and uranium (dashed-dotted
yellow) and thorium (dotted blue) geoneutrinos. The reactor antineutrino flux
from the Hartlepool Reactor Complex is shown in [B] along with the
antineutrino background.

Near-field antineutrino detectors dedicated to either monitoring reactor
operation or neutrino oscillation physics have the benefit of using reactor
“off” data to characterize and subtract their backgrounds Ashenfelter  _et
al._ (2018). Given the reactor discovery and timeliness goals for a far-field
deployment, high-fidelity simulations are needed to understand when the
recorded number of events is in excess of the modeled number of background
events to a statistically significant degree. To do so, we divide our
backgrounds into two categories: accidentals and correlated events. For the
latter we consider contributions from other sources of antineutrinos, fast
neutrons, radionuclide events, and the spontaneous fission of trace amounts of
238U and 232Th in the water, while the muon interactions in the detector are
used to scale some of these correlated events and infer a deadtime. A detailed
simulation of the detector components and surrounding materials is used to
predict the rate of uncorrelated backgrounds.

###  V.1 World Reactor Antineutrinos and Geoneutrinos

Both geoneutrinos and the total world reactor antineutrino emission will
contribute to the detected antineutrino background. Geoneutrinos are mostly
emitted from the beta decay of uranium and thorium in the Earth’s crust and
mantle. Although emissions from 40K occur, their associated antineutrino
energies are below the IBD threshold and thus, not detected. Additionally, the
United Kingdom is bathed in a relatively high reactor antineutrino background
compared to the rest of the world, with 15 installed nuclear reactors
contributing to approximately 25 GWth of power. The total contribution of
antineutrinos from the Hartlepool Reactor Complex in the Boulby mine will be
85$\%$. The next nearest reactor is the Heysham Reactor Complex at 149 km and
will contribute 4.4$\%$ (a facility with approximately 6 GWth installed
capacity), approximately 2.14$\%$ will come from geoneutrinos, while most of
the remaining 8.5$\%$ of the antineutrino flux will come from other reactors
in the UK and the large installed nuclear capacity in France.

To quantify the antineutrino backgrounds, we take the non-Hartlepool
antineutrino spectrum from geoneutrinos.org, a web-based application that uses
the operating reactor capacity inputs from the Power Reactor Infotmation
System (PRIS) database and couples the output with the Huber antineutrino
spectrum, and a full treatment of oscillations Barna and Dye (2015); Calori
_et al._ (1984); Huber (2011). The plotted contributions of these backgrounds
are displayed in Figure 3.

To account for the refueling outages of the various reactors, a 10$\%$
systematic uncertainty was applied consistent with the typical time in which
reactors are not online. Additionally, the same considerations for the
antineutrino signal of interest is used for the systematic uncertainty in the
antineutrino background. Lastly, we incorporate the associated uncertainties
described in Ref Barna and Dye (2015).

###  V.2 Uncorrelated Backgrounds

Figure 4: [Color Online] Expected energy spectrum from the uncorrelated
backgrounds in the detector without the trigger requirement [A] and after the
PMT trigger requirement [B]. Contributions from the PMTs, water, PMT support
structure (PSUP), tank, concrete, and rock are included. Despite large
contributions of the concrete and rock layers around the cavern to the event
rate, these events can be removed with a threshold requirement of 9 inner PMT
hits within the trigger window of approximately 400 ns. After implementing PMT
hit threshold, the largest contribution to the accidental background is due to
the radiation from the PMTs. The accidental rate of the PMTs, PSUP, and the
veto PMTs are reduced by constraining the fiducial volume within the tank to
greater than 1.5-meter from the PMT wall.

.

Radiation from the decay of isotopes in the detector medium, PMTs, supporting
structures, and surrounding materials will be emitted at random in the
detector, providing a continuous uncorrelated background. The event rate due
to these backgrounds is expected to be high due to the large number of PMTs
and other detector structures. There is a finite probability that accidental
correlations will occur in close time and space coincidence, with similar
coincidence signatures as IBD candidates. To quantify these backgrounds,
contributions from radiological processes that can produce Cherenkov light
were included in the simulation. The main decays included were: 232Th chain,
238U chain, 222Rn chain as part of the 238U chain, 40K, 60Co, and 137Cs. The
2019 WATCHMAN conceptual design reports details the process for which the
radio-purity values of all components are determined and assumed Bernstein
(2019). From here we assign a conservative 10$\%$ systematic uncertainty to
our ability to precisely asses the radioactivity of all of the components. In
a real experiment we can significantly reduce these values by measuring the
singles rate and extrapolating to an assumed accidental background. For the
238U chain the following nuclides were simulated: 234Pa, 226Ra, 214Pb, and
214Bi. For the 232Th chain the following nuclides were simulated: 228Ac,
224Ra, 212Pb, 212Bi, and 208Tl. In all cases it is assumed that the daughters
in this chain are in secular equilibrium with their parent isotopes.

Radioactivity is simulated in both the inner and veto PMTs, the detection
medium water, the PMT support structure, the detector tank, the concrete
cavern, and the surrounding rock. Radiation production in the rock is only
simulated to a thickness of 14 m, as it is expected that self-shielding
dominates beyond that distance Paul and Lindstrom (2000). The rate of
accidental backgrounds in the detector, $R_{\mathrm{acc}}$, is expressed as:

$R_{\mathrm{acc}}=R_{\mathrm{p}}R_{\mathrm{d}}\Delta te^{-\Delta
t(R_{d}+R_{p})}\varepsilon_{d}.$ (3)

Here, $R_{p}$ is the expected prompt accidental signals and $R_{d}$ is the
expected delayed accidental signal. The time and spatial coincidence required
to satisfy an IBD-like event is set as $\Delta t$=100 $\mu s$ and
$\varepsilon_{d}$=0.05, respectively. The spatial coincidence,
$\varepsilon_{d}$, is the probability of 2 uncorrelated single events
reconstructing within the 2-meter distance cut. Simulations of the
uncorrelated backgrounds were performed to evaluate the spatial coincidence
probability which led to the assignment of a 20$\%$ systematic uncertainty.
Given that $\Delta t(R_{d}+R_{p})<<1$, the term in the exponential can be
ignored, and Equation (3) becomes:

$R_{\mathrm{acc}}=R_{p}R_{d}\Delta t\varepsilon_{d}.$ (4)

Additionally, the contribution from alpha decay is not included in the
simulation, as these particles are not expected to be relativistic in our
detector and don’t produce Cherenkov light. The simulated energy distribution
of detector components with and without the analysis selection threshold are
shown in Figure 4.

The largest impact to the uncorrelated rate is the radiation from the concrete
and rock. The contribution of the uncorrelated backgrounds to the veto
detector are discussed in the next section. Most of these events occur in the
outer veto region and produce very little light in the inner detector, hence
they can be removed with a threshold requirement of 9 prompt inner PMT hits.
After these analysis selction thresholds the strongest contributor to the
uncorrelated event rate is the radiation from the PMTs, with lower order
contributions from the veto PMTs, the water in the detector, and the PMT
support structure (PSUP). Prior knowledge of this contribution motivated the
use of low-radioactivity glass for the PMT selection. The contribution of PMT
dark noise is simulated assuming a conservative rate of 10 kHz following
Poisson statistics. The PMTs have a mean rate of 2 kHz; however, previous
experiments with submerged PMTs has shown that the singles rate can increase
when placed in water or scintillator HAMAMATSU .

###  V.3 Muons

Aside from the antineutrino background, the highest contribution to correlated
backgrounds originates from the progeny of cosmic-ray muons in the detector
and surrounding materials. The veto region is used to identify and reduce the
contribution of such backgrounds. The veto PMTs are facing outwards relative
to the inner detector, and have a photo-coverage of approximately 1.5$\%$. The
muogenic response of the detector is determined by simulating the energy and
directional distribution from a parameterization with a normalization to the
overall muon flux, $I_{\mu}$ in units of cm-2s-1 Mei and Hime (2006):

$\displaystyle I_{\mu}(h)=(67.97e^{-h/0.285}+2.071e^{-h/0.698})\times 10^{-6}$
(5)

The muon flux is determined by the depth in km.w.e., $h$, and shape of the
overburden. The overburden has a depth of 2.805$\pm$0.015 km.w.e. (kilometer
water equivalent). Using Equation (5), the expected muon flux is expected to
be (4.09$\pm$0.15)$\times 10^{-8}$ cm2 sec-1. The integrated muon flux was
simulated as 0.116$\pm$0.004 sec-1. In addition to the rate of muons, the
response in the detector is highly correlated to the muon energy and
direction. The energy distribution of the muon flux, $\dfrac{dN}{dE_{\mu}}$,
is assumed to be:

$\dfrac{dN}{dE_{\mu}}=Ae^{-bh(\gamma_{\mu}-1)}(E_{\mu}+\epsilon_{\mu}(1-e^{-bh}))^{-\gamma_{\mu}}.$
(6)

The angular distribution of the muons is taken from Ref Mei and Hime (2006),
and is described by the angular intensity, $I(\theta)$:

$I(\theta,h)=\sec\theta\times e^{-h/\gamma(sec\theta-1)}.$ (7)

Here, $\gamma_{\mu}$=3.77, $\epsilon_{\mu}$=693 GeV, and $b$=0.4/km.w.e., are
described in detail in Ref. Mei and Hime (2006). The values are the result of
fitting multiple experiments to a generalized form. Previous experiments have
demonstrated reasonable agreement between the simulated and observed muon
response Aharmim  _et al._ (2009). After the muons were simulated, we
determined the veto criteria by evaluating the response to muon events in the
detector as well as the response from uncorrelated backgrounds that may cause
the veto to trigger. For this study we want to maximize the veto trigger rate
from muons, while minimizing deadtime due to backgrounds. Figure 5 shows the
trigger rate in the veto detector as a function of the threshold PMT hits
required to define a muon event. Following a muon trigger, the experience
gained from the WATCHBOY detector suggests a 1 ms deadtime is needed to remove
the contributions from Michel electrons, after-pulsing, and muon induced
neutrons Dazeley  _et al._ (2016). If we assume an 8-veto-PMT-hit threshold,
and a 1 ms deadtime following a trigger the total deadtime of the detector is
expected to be $0.98\pm 0.04\%$. The detection efficiency for muons in the
veto detector is taken as 100$\%$. The contribution of undetected muons to the
background will be due to the induced rate of di-neutrons or the radionuclides
generated within 1 ms of their paramuon.

###  V.4  Muogenic Fast Neutrons

Although the veto region enables tagging of muon-induced fast neutron
contributions in the detector, its ability to reject fast neutrons produced in
the rock is limited. The veto region does act as a buffer region to protect
the inner detector from these neutrons. Although fast neutrons generated in
the rock can reach a multiplicity of up to 20, these events can mimic an IBD
event if two neutron captures are detected within the prescribed time and
spatial separation cuts. Higher order coincidences, or events with 3 or
greater coincidences, will be rejected; however, the di-neutron contribution
is an irreducible background and must be quantified to a high fidelity.

Fast neutrons’ inelastic collision with nuclei are poorly modeled by certain
simulation frameworks. A concern arose that the production of high neutron
multiplicity events in Geant4 may be inconsistent with measured data.
Indications that our Geant4-based simulation (version 4.9) may be inconsistent
with measured data were also found in comparisons with experimental data from
the WATCHBOY detector Sutanto  _et al._ (2020). The WATCHBOY detector was
deployed in KURF (Kimballton Underground Research Facility) for the purpose of
validating the muogenic response of fast neutrons and radionuclides. Although
the detector was not sensitive enough to measure the 8He and 9Li production, a
detailed measurement of the fast-neutron multiplicities in the rock was
generated and confirmed to be inconsistent with the Geant4 simulation’s
results. Alternative simulations of the WATCHBOY detector were also performed
using FLUKA (FLUktuierende KAskade). As outlined in Sutanto et al., the
results of the FLUKA simulation agreed with experimental results and validated
the use of this code making predictions for the Gd-H2O detector design Sutanto
_et al._ (2020).

The muon production described in the Mei and Hime study was simulated in FLUKA
for tracking the fast neutron production and multiplication in the rock and
detector Battistoni  _et al._ (2007). The detector design, cavern geometry,
and rock composition were imported into the FLUKA simulation to match the
geometry of the Geant4 simulation. To avoid the production of neutrons in
Geant4 from simulated fast neutrons in FLUKA while allowing for a consistent
detector response with the other simulated backgrounds, the histories of
muogenic neutrons were traced until their capture location in the detector.
Once the capture location was recorded from the FLUKA simulation, thermal
neutrons at the same location were simulated in Geant4 to produce a realistic
response to neutron capture and a consistent spatial reconstruction of events.
From Figure 6, the detected di-neutron rate in the fiducial volume is expected
to be 0.0356 events per day. A 40$\%$ systematic uncertainty on the di-neutron
rate was assigned due to the difference between the WATCHBOY measurement and
the FLUKA simulation Sutanto  _et al._ (2020).

Figure 5: Rate of triggers in the veto detector due to muon interactions
[green dots], radiation in the detector and surrounding material [blue
triangle], and the resulting dead-time [black star]. Up to a 10 veto PMT hit
threshold, the rate of triggers from muons is relatively constant, while the
rate of triggers from radiological backgrounds becomes negligible at a
threshold of 8-PMT hits. Figure 6: Cluster events as a function of
multiplicity from the fast muogenic neutrons [green dots] and the spontaneous
fission of 238U and 232Th in the detector [blue triangles]. The fast neutron
events was modeled using FLUKA, while the spontaneous fission of 238U and
232Th was modeled using FREYA Sutanto  _et al._ (2020); Randrup and Vogt
(2009).

###  V.5 Muogenic Radionuclides

Figure 7: [Color Online] Decay timing [A] and energy distribution [B] of the
radionuclides produced from muon events. The decay time distribution is
unitless and the height of the curves shows the relative distributions of
event. It can be seen that a majority of the radionuclides are generated past
the muon veto deadtime of 1 ms. The electron kinetic energy spectra was
generated from literature values of the beta endpoints following decay and are
shown in [B]. Given the 2 MeV energy threshold in this design, contributions
from 17N and 8He are minimized.

Radionuclides present an irreducible background that occurs in the detector
from muon spallation. The isotopes decay through the emission of a beta
particle to the excited state of the daughter nucleus. For the nuclei that are
excited beyond the neutron separation energy, the immediate evaporation of a
correlated neutron can mimic an IBD event. These so called $\beta$n reactions
can have lifetimes that exceed a reasonable veto-induced deadtime. The
production of radionuclides as a function of muon path length has been
calculated by Li and Beacom using FLUKA simulations Li and Beacom (2014). The
difference in the observed and predicted radionuclide production in Super
Kamiokande was used to identify the systematic uncertainty in using this
parameterization Fukuda  _et al._ (2001). For any water-based detectors,
$\beta$n reactions from the decay of 8He $(t_{1/2}=0.178\ \mathrm{sec})$, 9Li
$(t_{1/2}=0.119\ \mathrm{sec})$, 11Li $(t_{1/2}=0.0085\ \mathrm{sec})$, and
17N $(t_{1/2}=4.173\ \mathrm{sec})$ are of concern. Theoretically,
contributions from 16C are possible; however, due to their low production rate
they are assumed negligible for the present design.

The time dependence and beta-energy spectrum from these radionuclides are
shown in Figure 7. Despite being correlated with muon events in the inner
detector, these backgrounds persist past the 1-ms deadtime due to the the
lifetimes of these isotopes. A low-energy threshold would significantly reduce
the contributions from 17N given the endpoint energy of the largest $\beta$n
branches: 4.1 MeV (BR=37.5$\%$) and 3.3 MeV (BR=49.9$\%$). To understand the
detector response to these backgrounds, electrons sampled from the beta
spectra, and accompanying gamma rays were simulated to determine the prompt
response. The neutron produced from this process was assumed to be emitted
isotropically. The shape of the beta spectrum is described by:

$N(T)=C(T)F(Z,T)pE(Q-T)^{2},$ (8)

where $T$ is the kinetic energy, $C(T)$ is the shape function (in this study,
only the allowed decay is considered and hence this factor is a constant),
$F(Z,T)$ is the Fermi function used to correct for electron screening, $Z$ is
the charge of the final nucleus, $p=\sqrt{(E/c)^{2}-(mc)^{2}}$ is the
momentum, $E=T+mc^{2}$ is the total beta energy, and $Q$ is the energy
released for each decay.

In addition to the spallation rates, the lifetimes of the radionuclides were
used to determine the rate of interactions. Radionuclides that decay within 1
ms of the muon event will be rejected with close to 100$\%$ due to the imposed
deadtime of the detector. Additionally, it is assumed that radionuclides can
be tracked with a 90$\%$ efficiency, resulting in a 90$\%$ rejection for
radionuclides that decay within 1 ms to 1 sec after muon interactions. When
combining timing cuts with the detector response we expect to observe 0.225
IBD candidates per week from 17N, 0.098$\pm$0.025 per week from 9Li,
0.003$\pm$0.002 per week from 8He, and 0.001$\pm$0.001 per week from 11Li.

###  V.6 Spontaneous Fission

In addition to the contribution of accidental backgrounds in the detector,
trace amounts of 238U and 232Th in the water can create correlated events
through spontaneous fission. A spontaneous fission event will result in a
prompt gamma ray flash and the emission of multiple neutrons. Spontaneous
fission may mimic an IBD event if any one of the prompt gamma ray events, or a
neutron capture reconstructs as a positron candidate followed by the detection
of one fission neutron. As in the case of the fast neutron contamination of
the background, events with detected multiplicities greater than two are
neglected.

To effectively evaluate the contribution from spontaneous fission, the
momentum, energy, and multiplicities were calculated using Fission Reaction
Event Yield Algorithm (FREYA) Randrup and Vogt (2009), an useful tool for
calculating event-by-event correlations in fission observables. Figure 6 shows
the probability distribution of detected multiplicities for both 238U and
232Th for spontaneous fission in the detector. These values are plotted with
the detected fast neutron multiplicities because these backgrounds can be
rejected when additional events are recorded in that time window. In total,
the rate of IBD candidates from spontaneous fission of 232Th and 238U is
expected to be $2.60\pm 1.62$ events a year for an assumed uranium and thorium
concentration of 7.0 Bq and 0.9 Bq, respectively, in the 6.3 kiloton purified
Gd-doped water volume.

##  VI Event Summary

Table 1: Signal and background rates for the Gd-H2O baseline detector design, assuming deployment at the Boulby site. Rates include the signal from the Hartlepool Reactor Complex and all backgrounds evaluated in this study. The italicized values correspond to the statistical and systematic uncertainties.  Contribution | Events [year-1] |  $<\sigma>$/N
---|---|---
Reactor Signal | 354.32 $\pm$31.39 |
Statistical |  | 5.3$\%$
Thermal Power |  | 5$\%$
IBD Cross Section |  | 0.5$\%$
Neutrino Flux |  | 5$\%$
Antineutrino Background | 47.41 $\pm$9.01 |
Statistical |  | 14.5$\%$
Capacity Factor |  | 10$\%$
geoneutrinos.orgBarna and Dye (2015) |  | 5$\%$
Neutrino Flux |  | 5$\%$
Accidentals | 32.40 $\pm$9.21 |
Statistical |  | 17.6$\%$
Radioassay |  | 10$\%$
Voxelation |  | 20$\%$
Muogenic Radionuclides | 13.73 $\pm$7.80 |
Statistical |  | 26.9$\%$
Model ValidationLi and Beacom (2014); Zhang (2016) |  | 50$\%$
Muogenic Dineutrons | 13.00 $\pm$6.32 |
Statistical |  | 27.7$\%$
Model ValidationSutanto  _et al._ (2020) |  | 40$\%$
Spontaneous Fission | 2.60 $\pm$1.62 |
Statistical |  | 62$\%$
Model Validation |  | 3$\%$
Total | 463.46 $\pm$65.35 |

Figure 8: [Color Online] The energy and spatial distribution of the prompt
events [A and B ] and the delayed signal [C and D]. Here, the contributions
from the Hartlepool Reactor Complex (26 km standoff distance and 3 GWth
power), the world reactor background, the accidentals, muogenic dineutrons,
muogenic radionuclides, and spontaneous fission are shown. A 2 MeV threshold
is required for prompt events, while a 3 MeV threshold is required for delayed
events. All events must reconstruct 1.5-meters away from the PMT wall.

.

After setting a threshold of 2 MeV for the prompt positron, 3 MeV for the
delayed neutron, and a 1-kton fiducial volume. The greatest contributor to the
background is the world reactor antineutrino flux, followed by the coincident
rate of accidentals. The next largest backgrounds are muogenic radionuclides
and fast neutrons. A summary of the background rates is found in Table 1.
Although this study evaluates variable reactor power and standoff distances,
the signal rate shown is for the Hartlepool Reactor Complex at full reactor
power (i.e a nominal 26 km standoff distance and 3 GWth reactor power).

Two parameters in the detector response that have a distinct feature for both
the signal and background are the charge distribution profile, or in this case
the visible energy; and the location where the event is reconstructed. In the
reactor exclusion case discussed in Section VII, the main goal is to identify
when events can be seen above background. With this in mind, the two largest
contributors to the background are the accidentals and the reactor
antineutrino background. A large fraction of the accidentals is attenuated by
the buffer region, limiting their charge deposition to the lower portion of
the spectrum and constraining the event reconstruction to events closer to the
PMT wall. Although antineutrinos from the world reactor background will have
the same spatial response as the signal of interest, distortions in the
spectral response may occur due to the oscillation of the signal. The same
distortion from oscillations in the number of PMT hits is utilized to attempt
to determine the reactor power and standoff distance in the verification case
discussed in the next section. Figure 8 shows the spatial and energy
distributions of the signal and background events.

The values represented in Table 1 include both statistical and the systematic
uncertainties. In the absence of a physical detector, broad assumptions were
made when evaluating the systematic uncertainties based on model inputs,
previous measurements, and comparison studies Sutanto  _et al._ (2020);
Dazeley  _et al._ (2016); Roecker  _et al._ (2016); Li and Beacom (2014).
However, since the signal event rate in this design is high compared to most
backgrounds (apart from other reactors and accidentals) the systematic
uncertainties on those other backgrounds are negligible compared to the
statistical and systematic uncertainties for the two main backgrounds.

##  VII Sensitivity Methodology

This study evaluates the sensitivity of the Gd-H2O baseline detector design
for two specific cases:

  1. 1.

Excluding the presence of undeclared nuclear reactors from a given region.

  2. 2.

Confirming the reactor power and standoff of a declared nuclear facility.

In Case 1 the Hartlepool Reactor Complex is assumed to not exist, but
associated backgrounds calculated at the Boulby underground laboratory are
still used. For Case 2, the reactor search and ranging capability of the
detector is calculated for the Hartlepool complex. In both cases, the study
examines the detector’s ability to exclude various reactor powers and
standoffs based on a set of pre-determined conditions.

The sensitivity is evaluated by first determining the two-dimensional PDF for
the detector response as a function of energy deposition and spatial
reconstruction vertex for both the prompt and delayed signals. The spatial
reconstruction of the prompt positron and neutron are correlated and sampled
as such. From there, simplified Monte Carlos are used to identify the
confidence limits by fitting against the PDF scaled with the experiment time.
As different standoff distances and reactor powers are probed, simplified
Monte Carlos are fit against the hypothesis template. The results of which
determine the confidence level for Case 1 and 2.

Following closely the analysis procedure detailed in Albert et al., a
template, $T$, for the no-reactor case and the Hartlepool reactor experiment
is generated by sampling the two-dimensional PDF of the signal and background
event reconstruction for the energy response, $E$, and the reconstructed event
location, $\bar{r}$, for both the prompt signal, denoted by $p$, and delayed
signal, denoted by $d$, IBD candidate pair for the signal and background using
Equation (9) Albert  _et al._ (2018):

$T^{p,d}(\bar{r},E)=\sum_{i}N_{i}R^{p,d}_{i}(\bar{r},E)\times t.$ (9)

Here, $i$ refers to each process that can generate IBD candidates, $N$ refers
to the event rate of each process, $R$ refers to the reconstructed response to
each event, and $t$ is the experiment time. These templates are used to
understand sensitivity to deviations from the assumed reactor operations.

For each reactor power, detector standoff, and counting time; a simplified
data set was generated by randomly sampling the PDF of event reconstruction
for the charge distribution, reconstructed energy, and the reconstructed event
location for both the prompt and delayed IBD candidate pair for the signal and
background. These PDFs were generated using the RAT-PAC simulations by
evaluating the detector response as described in Sections IV and V.

The discussed sensitivity evaluations require that the confidence intervals
are known for the two cases. Simplified Monte Carlo experiments were generated
100,000 times from sampling the templates for Case 1 and 2 for each
investigated dwell time. Each Monte Carlo simplified experiment was then fit
using a negative log-likelihood approach to the corresponding template which
was scaled to the appropriate detector dwell time by minimizing
$\mathcal{L}_{IBD}$ determined from the prompt and delayed statistic,
$\mathcal{L}_{p}$ and $\mathcal{L}_{d}$. Here, $\mathcal{L}$ refers to the
log-likelihood fit performed using ROOFIT Verkerke and Kirkby (2003) and
MINUIT Lazzaro and Moneta (2010).

$\mathcal{L}_{IBD}=\mathcal{L}_{p}+\mathcal{L}_{d}.$ (10)

In this study bin-to-bin correlations have not yet been taken into account,
and the covariance matrix is assumed to be diagonal.

The sensitivity test statistic, $\lambda(\mu)$, is determined by comparing the
result of the fit for experiment $\mu$ to the best fit result for another
simplified Monte Carlo experiment $\mathcal{L}_{\mu_{best}}$:

$\lambda(\mu)=2(\mathcal{L}_{\mu}-\mathcal{L}_{\mu_{best}})$ (11)

Figure 9 demonstrates the test statistic, $\lambda$, for the Case 1 analysis.
A histogram of the resulting test statistics is generated, and the confidence
intervals (1-3$\sigma$) can be defined from the sample based on the spread
relative to the minimum value of $\lambda(\mu)$.

Figure 9:  Defined confidence interval based on the test statistic $\lambda$
for the sensitivity to exclude experiments from the hypothesis that there are
no nuclear reactors.

.

Similar to the process used to define the confidence intervals, a frequentest
approach was used to generate test statistics for each of the experiments to
compare the standard template of Case 1 $\&$ 2 Feldman and Cousins (1998).
Again, 100,000 simplified Monte Carlo experiments were run for each detector
standoff, dwell time, and reactor power. Following the results of the fits,
the distribution of the critical values were recorded. For each distribution a
delineation is made to determine where 90$\%$ of the experiments fit. This
value, $\lambda_{90}$, is used in combination with the previously determined
confidence intervals for Case 1 $\&$ 2 to determine the confidence level to
which an experiment agrees with a prior assumption.

##  VIII Results

Figure 10:  Sensitivity of the WATCHMAN detector to exclude or discover an
undeclared nuclear reactor as a function of thermal power and standoff
distance for a dwell time of one month [A], three months [B], and one year
[C]. Experiments inside of the contour bands indicate scenarios in which the
reactor power and standoff would disagree with the hypothesis that there are
no nuclear reactors present with a 90 $\%$ confidence level. The confidence
interval of 90$\%$ represents the percentage of simplified Monte Carlo for a
given reactor power and standoff fall within the 1, 2, and 3 $\sigma$
determined by statistical tests of the simplified Monte Carlos of the no
reactor hypothesis against the associated PDF template.

.

Figure 11:  Sensitivity of the WATCHMAN detector to confirm the operating
power of the Hartlepool Reactor complex for a dwell time of one month [A],
three months [B], and one year [C]. Experiments outside of the contour bands
indicate scenarios in which the reactor power and standoff would disagree with
the hypothesis that there is a 3GWth reactor at a 26 km standoff greater than
3$\sigma$ with a 90 $\%$ confidence level. The confidence interval of 90$\%$
represents the percentage of simplified Monte Carlo for a given reactor power
and standoff fall within the 1, 2, and 3 $\sigma$ determined by statistical
tests of the simplified Monte Carlos of a reactor complex with a 26 km
standoff with 3 GWth hypothesis against the associated PDF template.

.

Current safeguards documents used by the IAEA do not explicitly mention the
timeliness goals for an entire nuclear reactor facility, but rather for
significant quantities of material. A hidden nuclear reactor can contain or
produce direct use material, irradiated nuclear material, and uranium with
less than 20 $\%$ concentration of 235U Glossary (2002). In these three cases
the timeliness goal for the discovery of a significant quantity is one month,
three months, and one year, respectively; for which the significant quantities
are 8 kg of plutonium or 75 kg of low enriched uranium. The sensitivity of
Case 1 and Case 2 was simulated for these three dwell times to evaluate the
ability to exclude unknown nuclear reactors from that region.

Consistent with IAEA guidelines, the minimum reactor power capable of yielding
the diversion of a significant quantity of plutonium is approximately 50 MWth
Council  _et al._ (2005). The 50 MWth is based on the expectation that the
amount of plutonium, $M_{Pu}$ (in grams), that can be generated in a nuclear
reactor scales with the thermal power, $P_{th}$, by:

$M_{Pu}\approx 0.25\left[\dfrac{g}{MW_{d}}\right]\times P_{th}.$ (12)

Additionally, both typical commercial nuclear reactors and industrial
plutonium generation reactors operate with a thermal powers on the order of
GWth . As a result we evaluate the bounds of these thermal powers to better
generalize the use cases of far-field reactor monitoring with a kiloton scale
water Cherenkov detector.

###  VIII.1 Case 1: Exclusion and Discovery

In the application of a kiloton-scale water-Cherenkov antineutrino detector to
exclude the existence of nuclear reactors from a region, one must compare the
expected signal if no reactors are present to the detected antineutrino
signal. Figure 10 shows exclusion contours for the existence of a nuclear
reactor in a region around the Boulby mine location (assuming the Hartlepool
reactor complex does not exist) over dwell times of one month, three months,
and one year. The reactor standoff and power consistent with no reactors
present are shown as being in agreement to one, two, and three $\sigma$ to a
90$\%$ confidence limit.

Given the range of the reactor standoffs, the technology at this scale is
unlikely to be used to covertly monitor or discover nuclear reactors across
country borders. A sensitivity to discover nuclear reactors on the scale of
10s of km requires that there is a host country within that distance for the
suspected reactor location willing to deploy such a detector. However, the
results demonstrate the capability to confirm the absence of undeclared
nuclear reactors under a possible cooperative verification regime. For
example, we consider a possible scenario in which a host facility previously
had a nuclear reactor at a specific site. Despite the shutdown of nuclear
reactor operations, the facility is still used as a laboratory to support
other defense science or technologies that the host country intends to keep
covert, without violating the terms of the verification regime. The results
shown in this section highlight the level of non-intrusiveness (standoff) that
is available based on the nuclear reactor power. Additionally, this technology
can be used as a deterrent in a cooperative verification scenario. Locations
and regions where reactors would be difficult for surveillance and other
activities can adopt this technology to verify the absence of nuclear
reactors.

Nuclear reactors with power outputs of 10’s of MWth can be observed above
background to 3 $\sigma$ with 90$\%$ confidence at a range of no more than 10
km for a one year dwell time. Given this restricted range, the antineutrino
facility used to monitor nuclear reactors on the scale of research reactors
will likely need to be within or near the actual facility that a previously
existing nuclear reactor was located. Depending on the required limit set as
an anomaly trigger, events that indicate the presence of a nuclear reactor are
experiments that the Gd-H2O baseline design would be able to observe above
background. Specifically, a 50 MWth nuclear facility can be excluded or found
from a 5 km standoff within one year, while the Hartlepool nuclear reactor
complex is seen above background within the first month.

Similarly, nuclear reactors on order of 100 MWth can be excluded up to 30 km
distance within one year. This allows for less intrusive monitoring of an
entire geographical region. Nuclear reactors on order of GWth are
traditionally associated with commercial nuclear reactors; however, industrial
plutonium production reactors have historically had similar thermal powers
Diakov (2011).

The results presented here generalize the application of this detector design
to a range of standoff distances and reactor power levels. In the hypothetical
deployment configuration, the experiment will monitor two 1500 MWth nuclear
reactors at a 26 km standoff. Based on the results shown in Figure 10, the
baseline Gd-H2O detector design will be able to identify the presence of the
Hartlepool nuclear complex within a one month dwell time at greater than
3$\sigma$. Additionally, if one nuclear reactor were to shut down for
maintenance or refueling for one month, the detector would be able to identify
that there is a nuclear reactor above background with 3$\sigma$ confidence.
Given the range of this verification technology, three sigma at 90$\%$
confidence is considered conservative. In the case where there are other
verification and monitoring tools in place, a lower confidence may be used to
initiate a response.

###  VIII.2 Case 2: Verification of Reactor Powers

We perform the same analysis with the hypothesis of a 3-GWth reactor power at
a 26-km standoff to determine the sensitivity to both reactor ranging and
reactor power confirmation. The results of the capabilities to find a reactor
in this context are shown in Figure 11. It is expected that distinct
signatures in the oscillation pattern would allow the sensitivity to delineate
between large thermal capacity reactors at a far standoff, and low-powered
reactors at a close standoff. However, the combination of relatively low
statistics, the energy resolution of positrons from Cherenkov light, and the
energy threshold for the positron signal removes the signatures of the
oscillation patterns. To effectively determine the range of the reactor
complex requires a priori knowledge of the reactor power and vice versa.

Despite the inability to delineate between reactor power and standoff, there
are useful applications that can be identified from these capabilities. A
nuclear reactor facility may have commercial reactors that are used to produce
power. To share resources and personnel, another covert nuclear reactor
specifically for military applications may also be on the same site. If this
reactor is undeclared, it would not be included in a verification plan.
Additionally, this technology may be applied to a bilateral treaty with an
emphasis on reducing fissile material production. If the terms of such
agreements were to limit the production of plutonium, a Gd-H2O detector could
measure the produced amount of plutonium generated without the intrusive step
of being in close proximity to the reactor.

This hypothetical deployment was intended to monitor a facility with a total
capacity of 3 GWth. With a one year dwell time, if the Gd-H2O design were
used, the power of the Hartlepool reactors could be constrained to within 500
MWth at 3$\sigma$. Additionally, since the Hartlepool complex has two 1500
MWth nuclear reactors, an attempt will be made to detect one nuclear reactor
in the presence of the other.

Based on the results in Figure 11, the detector will be capable of observing
that both reactors are operating within four months at 3$\sigma$ with 90$\%$
confidence. One concern about this approach is that it is susceptible to
reactor operator malfeasance. In the case that the host facility were
attempting to mask a small reactor signal, they could simply report a higher
thermal output of the existing reactors.

##  IX Summary and Outlook

In this study we have used the WATCHMAN baseline Gd-H2O detector design to
determine the capability of such a detector to exclude the presence of an
undeclared nuclear reactor, and to verify the thermal power and standoff of
known reactor complexes. This provides context for the application for a
nominal 1-kton scale detector for reactor monitoring. To achieve these goals a
detailed understanding of the detector response to all of the expected
backgrounds, from accidentals stemming from radiation from internal detector
components, muon induced fast neutrons and radionuclides, and the world
antineutrino background was achieved through simulations.

The world antineutrino background will be the largest background in this
hypothetical deployment. Although sensitivity was identified for a range of
reactor powers and standoffs, the application of this technology in another
location on Earth would yield different results. The United Kingdom and
surrounding countries have a large installed nuclear capacity, making the
resulting antineutrino background a higher background relative to locations
with fewer reactors. Therefore, claims about the sensitivity of this design
are likely conservative compared to use of the same design in other
geographical locations with lower reactor backgrounds. Conversely, for
specific use cases and greater standoffs, larger fiducial volumes may be
necessary. Based on the recommendations from the NuTools study, it is unlikely
that a larger-scale detector will have utility based on cost and excavation
constraints Akindele  _et al._ (2021).

The WATCHMAN baseline Gd-H2O design highlights the application of known and
proven technology previously used to measure solar neutrinos, antineutrinos
from a supernova, and probe the possibility of proton decay, to aid in
nonproliferation efforts to discover nuclear reactors or verify their
operation Anderson  _et al._ (2019); Fukuda  _et al._ (2003). Further progress
in reactor discovery sensitivity can be explored through the use of photon
detection enhancements such as wavelength shifting plates and Winston cones,
through scalable media that produce more light from interactions such as
water-based liquid scintillator, and antineutrino directionality. All of such
measures are currently under investigation by the WATCHMAN collaborationFukuda
_et al._ (2003); Adams  _et al._ (2001); Yeh  _et al._ (2011); Land  _et al._
(2020); Ford  _et al._ (2022); Mullen  _et al._ (2022).

###### Acknowledgements.

We thank the WATCHMAN collaboration for the review of this article and helpful
comments. This material is based upon work supported by the Department of
Energy National Nuclear Security Administration under Award Number DE-
NA0000979 through the Nuclear Science and Security Consortium, and under Award
Number DE-NA0003920 through the Monitoring, Technology, and Verification
Consortium. This work was performed under the auspices of the U.S. Department
of Energy by Lawrence Livermore National Laboratory under Contract DE-
AC52-07NA27344 and released through LLNL-JRNL-814121. This work was also
sponsored through the Scientific and Technology Facilities Council. We thank
Jason Brodsky at LLNL for useful discussions and guidance when evaluating
sensitivity methodologies; and Michael Mendenhall and Ramona Vogt for guidance
navigating FREYA with our detector response.

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