# Characterization of the Hamamatsu 8-inch R14688-100 PMT

Tanner Kaptanoglu  Ashley Rincon  Mackenzie Duce  Sawyer Kaplan  Joseph
Koplowitz  Skipper Lynch  Hong Joo Ryoo  Gabriel Orebi Gann

###### Abstract

Large-scale optical neutrino and dark-matter detectors rely on large-area
photomultiplier tubes (PMTs) for cost-effective light detection. The new
R14688-100 8-inch PMT developed by Hamamatsu provides state-of-the-art timing
resolution of around 1 ns (FWHM), which can help improve vertex reconstruction
and enable Cherenkov and scintillation light separation in scintillation-based
detectors. This PMT also provides excellent charge resolution, allowing for
precision photoelectron counting and improved energy reconstruction. The Eos
experiment is the first large-scale optical detector to utilize these PMTs. In
this manuscript we present a characterization of the R14688-100 single
photoelectron response, such as the transit-time spreads, the dark-rates, and
the afterpulsing. The single photoelectron response measurements are performed
for the 206 PMTs that will be used in Eos.

##  1 Introduction

Large-area photomultiplier tubes (PMTs) have been used in dozens of optical
neutrino and direct dark-matter experiments [1, 2, 3, 4, 5] as an effective
and cost efficient way of effectively covering large surface areas with photo-
sensitive detectors. An understanding of the availability and performance of
different large-area PMTs is crucial for future experiments, such as Theia
[6], in the selection of sensors [7], as well as for accurately simulating the
PMT response in existing detectors. The R14688-100 is one such large-area PMT,
that will be used for the first time in a large-scale experiment in the Eos
detector [8].

Eos is a 20-ton detector, designed to perform a demonstration of key
technology for future advanced neutrino detectors [8] that plan to distinguish
Cherenkov and scintillation light. This technology includes spectral sorting
of photons [9], novel types of liquid scintillators [10, 11], and fast timing
photodetectors [12]. The R14688-100 PMT from Hamamatsu was primarily selected
for use in the Eos experiment due to its excellent timing resolution of around
1 ns FWHM [13]. This can be compared to other PMTs of similar size that have
timing resolutions around 2 to 3 ns [13, 14, 15, 16]. This fast timing is an
important aspect in Cherenkov and scintillation separation, and it also helps
to improve vertex reconstruction in optical photon-based large-scale neutrino
detectors.

A total of 206 of these PMTs were purchased to be used in Eos. The experiment
requires precise characterization of each PMT to verify they each meet the
detector standard in a variety of metrics. In this manuscript, we characterize
the properties of these 206 PMTs. In detectors the size of Eos and larger, the
PMTs primarily detect single photons within a given event window, and thus the
single photoelectron (SPE) response is critical to determine. We also
investigate the dark-rate of several PMTs, the afterpulsing rate of a single
PMT, and present measurements of the PMT radio purity. These measured
characteristics are additionally used in precision modeling of Eos in the RAT-
PAC simulation software [17].

##  2 R14688-100 PMT

The R14688-100 Hamamatsu PMT is 202 mm in diameter with a high quantum
efficiency, super-bialkali photocathode and an expected transit time spread
(TTS) of around 1 ns full width at half maximum (FWHM) [13]. The neck and base
of the PMTs are by default water-proof potted and cabled by Hamamatsu (20
meter water proof cabling). The dynode is 10 stages and is box and linear-
focused. A picture of the PMT is shown in Figure 1.

Figure 1: The R14688-100 PMT with the black water-proof potting and the 20
meter SHV cable.

##  3 SPE Characterization

###  3.1 Experimental Setup

The experimental setup to measure the SPE response of the PMTs consists of a
central UV-transparent, cylindrical acrylic vessel (AV) which is 3 cm tall and
3 cm in diameter. A 90Sr $\beta$ source is placed above the acrylic vessel.
The $\beta$ particles enter the acrylic and produce Cherenkov light. A
Hamamatsu H11934-200 1-inch square PMT is optically coupled to the acrylic
vessel using Eljin Technology EJ-550 optical grease.

Two R14688-100 ‘measurement’ PMTs are placed 20 cm on either side of the AV.
The distance is selected to limit the coincidence rate between the trigger PMT
and the measurement PMTs to below 5%, which ensures we are primarily detecting
SPEs. The PMTs are wrapped in a one layer of magnetic shielding that spans
from the base of the PMT (where the cable exits) to the equator. The magnetic
shielding protects against the Earth’s magnetic field, which can deflect the
photoelectrons as they travel inside of the PMT, affecting the overall
collection efficiency. The strength of the magnetic field in the darkbox is
approximately 50 $\mu$T, but is reduced by about a factor of 5 inside of the
magnetic shielding. Further discussion of the magnetic shielding is provided
in A.

A picture of the SPE testing setup is shown in Figure 2. The space limitation
of the darkbox limits the testing to two PMTs at a time. The high voltage (HV)
for each PMT is selected such that the gain of the PMT is $1\times 10^{7}$.
All measurements are performed at room temperature.

Figure 2: The experimental setup to measure the SPE response of the R14688-100
PMTs.

The signal from the trigger PMT is used to start the data acquisition (DAQ).
Custom software reads out a V1742 CAEN waveform digitizer, which digitizes the
signals from each of the PMTs. The sampling rate of the digitizer is 5 GHz
over 1024 samples and it has 12-bit ADC over a 1 V dynamic range. The
waveforms for each channel are saved to an hdf5 files. A total of 500,000
total triggers are collected, which ensures that the statistical uncertainties
on the measured timing characteristics are less than 5%.

###  3.2 Analysis

The data analysis code processes the hdf5 files output by the DAQ. First, a
per-channel baseline is calculated by averaging over a 40 ns pre-trigger
window. Then, for each channel, the minimum voltage is identified (the PMT
pulses are downward going) and is referred to as the ‘peak’. The total charge
deposited, $Q$, is calculated by integrating the PMT pulse in a dynamic window
that ranges [-6, 12] ns around the peak of the pulse. This calculation is also
performed for the trigger PMT.

Prior to calculating the timing, events above a threshold of about 0.2 PE are
selected by enforcing $Q>0.3$. As discussed in Section 3, this removes less
than 5% of the SPE pulses.

The time of the measurement PMT pulse is calculated by applying a software-
based constant fraction discriminator, linearly interpolating between the
samples. The fractional threshold is set to 20%, but the precise value
selected does not impact the results. For the trigger PMT, which detects many
PEs per event, the time associated with a constant 2 mV threshold crossing
(again, applying inter-sample interpolation) is used. This method identifies
the time of the first PE detected by the trigger PMT and is more robust to the
shape fluctuations in the multi-PE (MPE) pulses.

The time-difference between the measurement PMT time and the trigger PMT time,
$\Delta\rm{t}$, is used to extract the timing characteristics of the
measurement PMT. The trigger PMT effectively acts to produce a time-zero that
has a very small jitter of about 270 ps (FWHM) [18], which add negligibly to
any jitter in the timing of the R14688-100 PMTs (which we expect to be around
1 ns FWHM).

###  3.3 Results

####  3.3.1 Charge

The charge distribution for the PMT with serial number VA1206 is shown in
Figure 3. The ‘pedestal’ peak centered around 0 pC (which extends outside of
the y-axis on the figure) corresponds to empty waveforms with no detected
photon. This comprises the vast majority of the coincidences, as the
coincidence rate is selected to be below 5%. The peak around 1.6 pC
corresponds to the detection of single photons with a gain of $1\times
10^{7}$. The value of the peak is determined by identifying the maximum bin
above 0.2 pC and fitting a Gaussian over the range that is 0.4 pC on either
side of the peak.

Figure 3: The charge distribution for PMT VA1206. The events around 0 pC
correspond to baseline events with no photon detected. The SPE events peak
around 1.6 pC and there is a small contribution for MPE events extending above
3 pC.

As identifiable in Figure 3 the one PE peak is well separated from the zero PE
peak. This is often quantified using a peak-to-valley (P/V) ratio. The P/V is
calculating by identifying the total counts in the peak bin and dividing by
the total counts in bin at 0.5 pC. The selection of this value is arbitrary,
but it allows for a stable definition that is not impact by small changes in
the width of the baseline peak around 0 pC. The P/V for VA1206 is 4.58, and
the PMTs typically have values above 4. This can be compared directly to other
types of large-area PMTs, which have values around 2 to 3 [14, 19].

Because the P/V is so large for these PMTs, relatively few PMT pulses fall
below the 0.3 pC threshold applied for the timing measurement, described
below. If the charge distribution extrapolates linearly down to 0 pC under the
pedestal, less than 5% of the SPE pulses are lost from the roughly 0.2 PE
threshold. This highlights the advantage of the large P/V ratio for these
PMTs, indicating that any threshold applied below the peak will have a
relatively small efficiency sacrifice.

####  3.3.2 Timing

The $\Delta\rm{t}$ distribution for the PMT with serial number VA1206, running
at a gain of $1\times 10^{7}$, is shown in Figure 4. The overall offset of
$\Delta\rm{t}$ from zero is set by cable delays and is arbitrary. As
discussed, because the trigger PMT has an extremely fast response, the
$\Delta\rm{t}$ distribution is primarily showing the transit-time (TT)
distribution for single photoelectrons detected by the measurement PMT. The
width of the prompt light, peaking around 70 ns in the $\Delta\rm{t}$
distribution, can be fit with a Gaussian function to extract the transit-time
spread (TTS).

Figure 4: The $\Delta\rm{t}$ distribution for PMT VA1206. Note the offset in
$\Delta\rm{t}$ from zero is set by cable delays and is arbitrary.

Because the prompt TT distribution is not perfectly Gaussian (rather, it is
slightly skewed right), the fit-range selected impacts the measured TTS
distribution. After binning the $\Delta\rm{t}$ distribution in 0.2 ns bins,
the peak is identified and a Gaussian is fit using a range that is $\pm 0.6$
ns around the peak. The FWHM of the fitted Gaussian is taken to be the TTS of
the PMT. By adjusting the fit range between $0.2$ to $1.0$ ns in steps of
$0.2$ ns, the fitted value of the TTS varies at most by 5%, which is the
largest source of systematic uncertainty.

The values of the TTS are reported using the $\pm 0.6$ ns range. The average
TTS across the PMTs is 1.00 ns and the standard deviation is 0.08 ns. This
indicates that these PMTs achieve a state-of-the-art timing resolution and
that the behavior is very consistent from PMT to PMT.

In addition to the prompt light, there is a clear contribution of light that
comes between 5 to 40 ns late, as identified in Fig. 4. This effect is due to
elastic scatters of the PE off of the first dynode, before being accelerated
back some time later. The fraction of detected photons that are late is
quantified by identifying the prompt peak and integrating a window that is
between 5 and 40 ns after the prompt peak and comparing that value to the
integral of the full timing window. Averaging over all of the tested PMTs, the
fraction of late-light is 9.39 $\pm$ 0.58%.

####  3.3.3 High Voltage Scan

In order to determine the high voltage that yields a gain of $1\times 10^{7}$
the high voltage is scanned across a range of values, and the gain is
determined by measuring the mean of the charge distribution. For two PMTS,
VA1293 and VA1300, we investigated the TTS and gain as a function of high
voltage from 1650 V to 2500 V. The results are shown in Figure 5. Notably, at
large gains of around 5$\times 10^{7}$, reached with supply voltages around
2400 to 2500 V, the TTS is improved from around 1 ns to about 0.8 ns.

Figure 5: The gain (left) and TTS (right) as a function of the supply voltage
for two PMTs. The uncertainties on the TTS include the statistical and
systematic errors summed in quadrature.

####  3.3.4 Dark-Rate

The constrained timeline for the Eos construction and the installation of the
PMTs restrained the total number of PMTs that could be dark-rate tested, but
14 PMTs were successfully tested. The dark-rate of the PMTs is measured at
least twenty hours after the dark-box has been closed, allowing the PMT dark-
rate to settle to baseline.

The rate is extracted by fitting a 50 ns pre-trigger window, prior to the
Cherenkov light emission, with a flat polynomial. The total counts in that
window is converted to a rate and is well-described by the uniform model. Over
the 14 PMTs measured we find an average dark-rate of 2175 $\pm$ 1400 Hz, with
a minimum rate of 590 Hz and a maximum rate of 5024 Hz. This level of
variation is typical for large-area PMTs [14, 19].

The measurements are performed at room temperature around 22∘ C. The expected
temperature of the water in Eos is 15∘ C, which would lead to an approximate
decrease by a factor of 2-3 for the dark-rates [20, 19]. The measured dark-
rates for these PMTs are similar to those reported for other large-area PMTs
[13, 14, 15, 16, 12].

####  3.3.5 SPE summary

A summary of the SPE testing results is provided in Table 1. The SPE results
for every PMT is provided in B.

Parameter | Mean | Maximum | Minimum
---|---|---|---
HV (V) | 1989 $\pm$ 143 | 2500 | 1700
Charge P/V | 5.69 $\pm$ 0.92 | 7.36 | 3.97
TTS (ns) | 1.00 $\pm$ 0.08 | 1.23 | 0.83
Late-Fraction (%) | 9.39 $\pm$ 0.58 | 11.2 | 7.46
Table 1: The mean, standard deviation, maximum, and minimum values of the
measured SPE parameters for a gain of $1\times 10^{7}$.

##  4 Afterpulsing

Signal generated by residual ions inside of the PMT can cause delayed signals
that occur hundreds of ns or several $\mu$s after an initial PE. Specifically,
a generated PE can ionize residual gases inside of the PMT, such as helium.
The ions then slowly drift back to the photocathode, where they are absorbed,
creating a single PE or multiple PEs that are delayed relative to the initial
signal. The time-difference between the initial signal and the delayed signal
is determined by the type of gas in the PMT, the electric field strength, and
the size of the PMT. Notably, these afterpulses are produced via a different
mechanism then what we call late-pulses in Section 3.3.2. For reference, the
formation of afterpulses in large-area PMTs has been studied in Refs. [12, 21,
22].

###  4.1 Experimental Setup

A blue LED is directed at an R14688-100 PMT, operating at a gain of $10^{7}$,
and pulsed at 100 Hz with a 30 ns pulse width. The amplitude of the pulse is
adjusted to change the total amount of prompt PE detected. Data is collected
across a variety of different intensities to study the afterpulsing rate as a
function of the number of PE in the prompt pulse.

The CAEN V1742 digitizer has a maximum window width of about 2 $\mu$s, which
was insufficient for measuring the afterpulses. Therefore, the afterpulsing
setup digitized the PMT waveforms on a Lecroy Waverunner 9054 at 1 GS/s over a
50 $\mu$s window. The data is collected using custom software called lecrunch
which outputs the waveforms to hdf5 files.

###  4.2 Analysis

In order to identify the prompt pulse, generated by the LED light, and the
subsequent afterpulses, the waveform is split into distinct windows. First, a
0.2 $\mu$s window at the beginning of the waveform is used to calculate the
baseline. Then a 19.6 $\mu$s pre-trigger window is used to identify dark-
pulses, in order to correct for their contribution in the afterpulsing window.
A 0.4 $\mu$s window is used to identify the location of the prompt pulse and
the following 29.8 $\mu$s is used to look for afterpulsing.

In the primary peak, where we expect the data to be MPE, the pulse is easily
identified and integrated over a 60 ns window (centered around the peak). To
roughly calculate the number of PE (NPE) detected in this window, the
integrated charge is divided by the value of mean of the SPE charge
distribution. The afterpulsing rate is then measured as a function of the NPE
in the primary pulse.

The pulses in the dark-window and the afterpulsing window are identified by
applying a 3 mV threshold and identifying threshold crossings. A threshold
counting is only counted if the waveforms is below threshold on the previous
sample. This threshold corresponds to roughly 0.2 PE.

###  4.3 Results

Five datasets are collected, varying the intensity of the LED. In the first
dataset, the LED is dimly lit, with an average occupancy of around 2 PE. In
the final dataset, the LED is pulsed such that the PMT has an average
occupancy of almost 30 PE per pulse.

The time distribution of the afterpulses for one of the datasets, with an
average occupancy of 5 PE, is shown in Figure 6. The afterpulsing distribution
shows two clear peaks around 500 ns and 5.0 $\mu$s after the initial prompt
light from the LED, which occurs at 0 ns in Figure 6. The locations and
heights of each of these peaks reflects different gases at different amounts
present in the PMT. By around 16.0$\mu$s we no longer identify any
afterpulsing above the dark noise background. The sharp cut-off at shorter
times is due to the 400 ns window used to identify the hit-time of the prompt
light, and it is possible some of the afterpulses with shorter times are not
identified.

Figure 6: The timing distribution of the afterpulses for a dataset with an
average occupancy of 5 PE. The events from the dark-rate, taken from a pre-
trigger window, are shown as a direct comparison. The prompt light arrives at
0 ns for this figure.

Most importantly, we study the afterpulsing rate as a function of the number
of detected PE from the prompt LED light. These results are given in Figure 7.
The figure shows the average number of afterpulses as a function of NPE, where
a value of 0.5 indicates that in half of the events there was an afterpulse
identified. A value larger than one would indicate more than one afterpulse
per prompt LED pulse.

Figure 7: The average number of afterpulses detected for a given number of
prompt NPE. A linear fit indicates that the average number of afterpulses
produced for a 1 PE signal is 0.016.

For the dimmest LED setting, with an integrated charge that indicates that we
are primarily measuring one or two PE per LED pulse, the afterpulsing rate was
about 2.5%. The linear fit indicates an average rate of 1.6% for an occupancy
of 1PE; however, the fit clearly breaks down at very low occupancy, indicated
by the negative value for the y-intercept. The linear fit is useful for
interpolating and extrapolating to higher occupancy.

It should be noted that the calculation of the average number of afterpulses
does not include several factors. First, no correction is made for an
efficiency loss from the SPE selection, and a rough efficiency loss of 5% was
estimated in Section 3.3.1. Second, any afterpulses with timing less than 400
ns are not included in this calculation, as discussed in relation to Figure 6.
Again, we expect this to have a relatively small effect, as the 400 ns time-
window is short relative to the 20 $\mu$s window to identify afterpulses.
Finally, we do not account for MPE afterpulses, and assume the pulses are SPE.
To check this assumption, we look at the charge distribution of the
afterpulses, and even at the highest LED intensity, we find only about 5% of
the afterpulses are MPE.

##  5 Radiopurity Assay

PMTs are often a source of significant radioactive backgrounds in neutrino and
dark-matter experiments [23]. This comes primarily from uranium and thorium
intrinsic to the PMT glass and dynode that produces $\gamma$-rays that can
travel through buffer material into the sensitive detector volume.

Samples taken from an intentionally broken R14688-100 PMT, provided by
Hamamatsu, were sent to the low background counting facilities at the Black
Hills Underground Campus. Measurements were performed on the 4850’ level of
the Sanford Underground Research Facility (SURF) [24, 25, 26] to measure the
radioactivity of the PMT. The samples were broadly grouped in two categories:
(1) the crushed glass from the PMT bulb and (2) the metallic and ceramic parts
the make-up the dynode structure and the rest of the PMT. These two groups are
measured separately in the SURF facilities using the Morgan detector station
(see Ref. [24] for details). The results are provided in Table 2. The total
weight of the glass and dynode parts is 0.51 kg and 0.39 kg respectively.
Notably, Hamamatsu communicated that the glass for these PMTs is possible to
construct with lower radioactivity [27].

Sample | U (mBq/kg) | Th (mBq/kg) | K (mBq/kg)
---|---|---|---
PMT glass | 3144 $\pm$ 158 | 4486 $\pm$ 257 | 7874 $\pm$ 398
PMT dynode | 421.2 $\pm$ 28.2 | 55.8 $\pm$ 5.0 | 219 $\pm$ 24
Table 2: The results of the radiological assay of the PMT parts, performed at
SURF.

##  6 Discussion

Based on the results shown in this manuscript, the R14688-100 is a promising
candidate for future large-scale neutrino experiments, such as Theia, that
hope to utilize fast timing to improve background rejection [6]. Additionally,
existing detectors with planned upgrades that already utilize 8-inch PMTs,
such as SNO+ [28], could directly replaced old PMTs with these modern PMTs.
This improvement would more than double the detection efficiency and improve
the TTS by more than a factor of three [29].

Additionally, the ability to identify the number of photons detected by a PMT
will be important for future scintillation based neutrino detectors [30]. This
would help improve energy resolution by providing a more precise measure of
the total light detected. Thus, the ability to distinguish one PE from zero,
two PE from one PE, etc. will be an important aspect of future photosensors.
Given the large P/V ratio measured in this manuscript, the R14688-100 PMT
provides excellent discrimination capability for PE counting.

The timing of the R14688-100 PMT, measured to be on average around 1 ns (FWHM)
across 206 PMTs, is the primary motivation for using this large-area PMT. This
state-of-the-art timing is at least twice as good as other large-area PMTs,
and could significantly improve reconstruction performance and background
rejection in future scintillation-based neutrino experiments [31]. About 10%
of the light is detected late relative to the prompt peak, which is typical
for large-area PMTs. The dark-rate of the PMTs has not been robustly
characterized at the temperatures standard for large detectors; however,
initial measurements of several PMTs at room temperature indicate dark-rates
consistent with other PMTs of similar sizes. Lastly, we performed an
afterpulsing measurement of a single PMT, which indicated afterpulsing rates
around 2% per PE, with peaks in the timing distribution around 500 ns and 5
us.

##  7 Conclusion

In this manuscript the SPE detection performance is characterized for 206
large-area Hamamatsu R14688-100 PMTs. The fast timing and excellent P/V makes
it an ideal PMT for use in Eos, where these features will be used to perform
Cherenkov and scintillation separation and precision photon counting.
Ultimately, this will help improve reconstruction and reduce backgrounds.
These measurements can also be directly input into simulation software in
order to better simulate the detector response. Finally, measurements made of
afterpulsing rate, dark-rate, and radioactivity of the PMT provide important
details for Eos and for future experiments deciding on the type of PMT to use.

## Data Availability Statement

The data used in this manuscript is available in an accessible postgres
database hosted at Lawrence Berkeley National Lab. If interested, please
contact the author for database connection information. The results for the
full list of all tests performed on the Eos PMT is available at
https://nino.lbl.gov/pmts/.

##  8 Acknowledgements

Thank you kindly to Brianna Mount and Douglas Tiedt for performing the
background counting measurements and analysis at the Black Hills State
University Underground Campus and the Berkeley Low Background Facility. The
work conducted at Lawrence Berkeley National Laboratory was performed under
the auspices of the U.S. Department of Energy under Contract DE-
AC02-05CH11231. This project was funded by the U.S. Department of Energy,
National Nuclear Security Administration, Office of Defense Nuclear
Nonproliferation Research and Development (DNN R&D). Author M. Duce was
supported by the Department of Energy and National Nuclear Security
Administration, United States through the Enabling Technology and Innovation
Consortium under Award Number DE-NA0003921.

##  Appendix A Magnetic Shielding Tests

The performance of PMTs is known to be affected by even weak ambient magnetic
fields, such as that of the Earth’s. These magnetic fields deflect the
electron trajectories via the Lorentz force, and tend to decrease the overall
PE collection efficiency of the PMT. Thus, flexible magnetic shielding, such
as FINEMET${}^{\text{\textregistered}}$, that extends around the PMT can be
used to improve the overall detection efficiency [32].

In this section, we investigate two different designs for a flexible magnetic
shielding and test the impact on the PMT collection efficiency. Figure 8 shows
one of the magnetic shielding designs, and the second design is very similar
with the slant height reduced to 14 cm. These designs are based on the those
presented in Ref. [32], which studied the impact of FINEMET magnetic shielding
on the 8-inch PMTs used in the Daya Bay experiment.

Figure 8: Two dimensional pattern of one of the conical magnetic shielding
designs that was tested, based on the designs used for the Daya Bay experiment
[32].

The focus of the magnetic shielding testing is for applications in Eos and
therefore only a handful of configurations are run. More complete magnetic
shielding tests on similar PMTs, such as those conducted in Refs. [32], [16],
and [14], use externally applied magnetic fields to look at the changing
efficiency as a function of magnetic field strength. Here we primarily focus
on the impact of the magnetic shielding when shielding only against the
Earth’s magnetic field. Therefore, these tests are not general performance
characterization as a function of magnetic field strength, but rather a
handful of configurations relevant for Eos, that provide some useful context
for future detectors as well.

In the SPE experimental setup (shown in Figure 2) the photomultiplier tubes
are wrapped in the FINEMET magnetic shielding. However, the gain and TTS of
the PMT are measured both with and without magnetic shielding and no
significant change is identified in our setup. Tests performed to understand
changes to the PMT detection efficiency are described in the following
sections.

###  A.1 Experimental Setup

The setup designed to test changes in the PMT efficiency consists of a blue
LED pointed at a dichroic filter, which splits the light towards two different
PMTs. Directly behind the dichroic filter is an R14688-100 ‘measurement’ PMT.
At 90 degrees from the filter is a H11934-200 1-inch ‘monitoring’ PMT (the
same PMT used as the trigger PMT in the SPE setup). The monitoring PMT is used
to measure the relative intensity of the light to normalize across different
trials. This is necessary as the intensity of the LED drifts slightly, as it’s
temperature changes.

The LED is pulsed with 25 ns pulse width at 100 Hz, using a function generator
with an intensity such that the measurement PMT detects around 50 PEs per
pulse. The high intensity is useful to measure small relative changes in
efficiency, which would effectively shift the total number of PEs detected in
each pulse from the LED. A total of 100,000 events are collected in each
trial. The pulse from the function generator is split and also used to trigger
the DAQ. The DAQ system is identical to that described in Section 3.1.

Measurements are performed with the two different magnetic shielding designs
and with no magnetic shielding around the measurement PMT. Due to the
orientation of the darkbox, the PMTs are placed pointing 10 degrees off of
north-south. With respect to this positioning, the magnetic field is measured
at the front-face of the PMT (no magnetic shielding) to be 32 $\mu$T up-down,
34 $\mu$T left-right, and 12 $\mu$T in-out. With the magnetic shielding, each
component is reduced by more than a factor of five.

###  A.2 Analysis

The PMT pulses from both the measurement and monitoring PMT are integrated
using 60 ns windows, with baselines estimated in a 40 ns pre-trigger window.
The width of the integration window is set to capture the full width of the
PMT pulse for both PMTs. The metric used to measure the efficiency change
across configurations is the total integrated charge at the measurement PMT,
$Q$, normalized by the integrated charge at the monitoring PMT, $Q_{m}$,
$\epsilon=Q/Q_{m}$.

###  A.3 Results

Measurements of $\epsilon$ are collected across several trials for each of the
three configurations, as detailed in Table 3. The different trials are run
under identical conditions, but after removing and replacing the magnetic
shielding (if applicable) and ramping the high voltage down and then back up,
in order to understand the measurement systematics. Six of the trials are
performed with one of the 14 cm slant height magnetic shielding design, where
the systematics are most robustly tested. Across the runs in the same
configuration, there is at most a 3% variation in the value of $\epsilon$, as
identified in Table 3 in the trials with the 14 cm slant height design.

$Q$ (pC) |  $Q_{m}$ (pC) | $\epsilon$ | Slant Height (cm) | Trial
---|---|---|---|---
75.91 | 12.26 | 6.19 | 0 | 1
76.74 | 12.36 | 6.20 | 0 | 2
76.80 | 12.45 | 6.17 | 0 | 3
76.48 | 12.39 | 6.17 | 14 | 1
76.89 | 12.60 | 6.10 | 14 | 2
78.24 | 12.69 | 6.17 | 14 | 3
78.88 | 12.64 | 6.24 | 14 | 4
79.68 | 12.86 | 6.20 | 14 | 5
79.98 | 12.75 | 6.27 | 14 | 6
81.80 | 13.19 | 6.20 | 17 | 1
82.88 | 13.32 | 6.22 | 17 | 2
Table 3: The results of the magnetic shielding tests with varying magnetic
shield designs, using PMT VA1166. $\epsilon$ is constant within the expected
3% systematic uncertainty.

Notably, the value of $\epsilon$ does not change between the different
configurations, indicating no increase or decrease in the overall collection
efficiency from using the magnetic shielding. This indicates shielding of the
ambient magnetic fields generated by the Earth is not effective for increasing
the collection efficiency of this particular PMT. However, these results are
specific to the magnetic field strength at the particular location the tests
were run. Because the primary goal was to determine if individual PMT magnetic
shielding was necessary for Eos, the lack of any clear significant impact in
these tests led to the decision to remove individual shielding components
around each PMT.

##  Appendix B List of Results for All PMTs

Table LABEL:tab:all_spe_results provides a list of the high voltage, charge
peak, charge peak-to-valley, TTS, and late-pulsing percentage for all PMTs
tested in the SPE setup.

Table 4: All of the SPE characterization results at a gain of $1\times 10^{7}$. The TTS is the FWHM. PMT ID | High Voltage |  $Q$ Peak [pC] |  $Q$ P/V | TTS [ns] | Late-light Pct. (%)
---|---|---|---|---|---
VA1059 | 1960 | 1.54 | 5.62 | 1.035 | 8.81
VA1060 | 2395 | 1.62 | 5.29 | 0.835 | 8.83
VA1062 | 1980 | 1.54 | 5.53 | 0.915 | 8.98
VA1064 | 1865 | 1.58 | 5.75 | 0.985 | 8.96
VA1065 | 1950 | 1.62 | 4.87 | 1.008 | 9.27
VA1066 | 1875 | 1.57 | 5.36 | 1.053 | 9.82
VA1067 | 1935 | 1.57 | 4.76 | 1.038 | 9.64
VA1068 | 1720 | 1.58 | 4.32 | 1.115 | 9.18
VA1070 | 1900 | 1.52 | 4.59 | 1.226 | 8.18
VA1071 | 1900 | 1.59 | 3.97 | 1.113 | 9.03
VA1072 | 1830 | 1.61 | 5.24 | 0.975 | 9.17
VA1073 | 1950 | 1.59 | 4.68 | 1.014 | 9.18
VA1074 | 1900 | 1.56 | 5.85 | 1.056 | 9.79
VA1075 | 1920 | 1.49 | 6.84 | 1.020 | 8.89
VA1076 | 1900 | 1.62 | 5.89 | 1.091 | 9.45
VA1077 | 1850 | 1.54 | 4.73 | 1.137 | 8.51
VA1078 | 1800 | 1.57 | 5.71 | 1.137 | 8.76
VA1080 | 1845 | 1.56 | 5.11 | 1.044 | 8.58
VA1081 | 1700 | 1.58 | 5.80 | 1.108 | 8.12
VA1082 | 1705 | 1.58 | 5.24 | 1.107 | 8.43
VA1084 | 1940 | 1.56 | 6.73 | 1.041 | 8.93
VA1086 | 1955 | 1.56 | 6.08 | 1.017 | 8.84
VA1088 | 2040 | 1.63 | 6.48 | 0.932 | 9.88
VA1089 | 1790 | 1.58 | 5.64 | 1.101 | 9.51
VA1090 | 1840 | 1.56 | 6.05 | 1.165 | 8.73
VA1091 | 1820 | 1.57 | 7.15 | 1.113 | 8.73
VA1092 | 1810 | 1.59 | 6.33 | 1.045 | 8.16
VA1093 | 1745 | 1.57 | 6.09 | 1.188 | 9.20
VA1094 | 1725 | 1.62 | 6.09 | 1.149 | 9.44
VA1095 | 1720 | 1.61 | 4.96 | 1.011 | 8.86
VA1097 | 2020 | 1.68 | 6.98 | 0.976 | 9.17
VA1098 | 2105 | 1.57 | 5.68 | 0.987 | 9.10
VA1099 | 1980 | 1.58 | 6.58 | 0.928 | 9.82
VA1100 | 2100 | 1.55 | 4.94 | 0.958 | 9.19
VA1101 | 1860 | 1.62 | 5.42 | 1.134 | 9.42
VA1102 | 1925 | 1.60 | 6.07 | 1.087 | 10.14
VA1103 | 1950 | 1.58 | 6.39 | 1.030 | 9.35
VA1104 | 2080 | 1.61 | 5.56 | 0.946 | 9.94
VA1105 | 2050 | 1.56 | 5.77 | 0.942 | 9.62
VA1106 | 1955 | 1.59 | 5.70 | 0.975 | 10.05
VA1107 | 1895 | 1.52 | 5.98 | 1.011 | 9.86
VA1108 | 2020 | 1.59 | 5.64 | 1.004 | 9.97
VA1110 | 1980 | 1.55 | 6.26 | 0.988 | 10.38
VA1111 | 2150 | 1.56 | 6.95 | 1.019 | 9.55
VA1113 | 1840 | 1.60 | 6.82 | 1.043 | 9.98
VA1114 | 1880 | 1.58 | 6.36 | 1.041 | 9.86
VA1115 | 1870 | 1.58 | 6.47 | 1.030 | 9.91
VA1116 | 2070 | 1.59 | 5.62 | 0.970 | 10.01
VA1117 | 2085 | 1.63 | 5.76 | 0.992 | 9.87
VA1119 | 1825 | 1.63 | 5.48 | 1.114 | 9.60
VA1120 | 2110 | 1.55 | 5.71 | 0.885 | 9.65
VA1121 | 1915 | 1.61 | 5.81 | 1.057 | 9.67
VA1123 | 1845 | 1.62 | 7.16 | 1.020 | 9.86
VA1124 | 1790 | 1.61 | 6.90 | 1.106 | 9.64
VA1125 | 1900 | 1.66 | 6.09 | 0.974 | 10.34
VA1126 | 1935 | 1.56 | 5.80 | 1.109 | 9.53
VA1127 | 1870 | 1.56 | 6.62 | 1.039 | 9.64
VA1128 | 1955 | 1.62 | 5.53 | 1.001 | 9.65
VA1129 | 1915 | 1.55 | 6.76 | 1.118 | 9.94
VA1130 | 1865 | 1.56 | 7.14 | 1.060 | 9.82
VA1131 | 1945 | 1.60 | 6.31 | 0.975 | 10.10
VA1132 | 1825 | 1.56 | 6.13 | 1.087 | 9.16
VA1134 | 2030 | 1.56 | 5.74 | 0.970 | 10.38
VA1135 | 1860 | 1.63 | 6.95 | 1.008 | 9.77
VA1136 | 2010 | 1.62 | 5.79 | 1.095 | 10.93
VA1137 | 2025 | 1.73 | 6.59 | 1.072 | 11.17
VA1138 | 2100 | 1.69 | 6.18 | 1.005 | 10.15
VA1139 | 1955 | 1.69 | 6.18 | 1.005 | 10.15
VA1140 | 2100 | 1.60 | 5.76 | 0.977 | 9.83
VA1141 | 1945 | 1.63 | 6.48 | 1.002 | 9.99
VA1142 | 2160 | 1.54 | 5.78 | 0.864 | 9.46
VA1143 | 2220 | 1.80 | 5.40 | 1.011 | 10.29
VA1144 | 1930 | 1.55 | 5.09 | 1.105 | 9.40
VA1145 | 2065 | 1.62 | 5.74 | 1.000 | 10.66
VA1146 | 1995 | 1.55 | 5.80 | 1.018 | 9.79
VA1148 | 1980 | 1.56 | 5.53 | 0.997 | 10.08
VA1149 | 2045 | 1.52 | 6.03 | 1.010 | 10.24
VA1150 | 1870 | 1.60 | 5.91 | 1.033 | 9.64
VA1151 | 1930 | 1.51 | 5.67 | 1.164 | 9.61
VA1252 | 2095 | 1.53 | 6.12 | 0.908 | 9.77
VA1154 | 1990 | 1.59 | 6.31 | 0.983 | 9.37
VA1155 | 2050 | 1.53 | 6.14 | 1.101 | 9.40
VA1156 | 2015 | 1.59 | 6.23 | 0.947 | 9.95
VA1157 | 2170 | 1.55 | 5.03 | 0.897 | 9.43
VA1158 | 2150 | 1.55 | 5.96 | 0.946 | 9.71
VA1159 | 1920 | 1.58 | 6.29 | 1.072 | 9.06
VA1160 | 1900 | 1.56 | 5.73 | 1.059 | 9.26
VA1161 | 1905 | 1.54 | 5.37 | 0.961 | 9.42
VA1162 | 2150 | 1.66 | 5.26 | 0.834 | 10.27
VA1164 | 2130 | 1.64 | 5.70 | 0.938 | 9.54
VA1165 | 2035 | 1.61 | 6.22 | 0.978 | 8.60
VA1166 | 2190 | 1.54 | 6.02 | 0.841 | 9.65
VA1168 | 1900 | 1.59 | 7.26 | 1.035 | 9.18
VA1170 | 2265 | 1.65 | 6.57 | 0.921 | 9.74
VA1172 | 2280 | 1.52 | 4.24 | 0.911 | 8.56
VA1173 | 2200 | 1.52 | 5.51 | 0.953 | 9.29
VA1174 | 2060 | 1.60 | 6.52 | 0.921 | 8.91
VA1175 | 2060 | 1.63 | 4.43 | 1.026 | 7.46
VA1176 | 2150 | 1.63 | 6.20 | 0.853 | 9.77
VA1177 | 2040 | 1.61 | 7.27 | 0.919 | 9.61
VA1178 | 2040 | 1.48 | 5.37 | 0.922 | 9.40
VA1179 | 2040 | 1.68 | 5.42 | 0.987 | 9.72
VA1180 | 2255 | 1.62 | 5.30 | 0.939 | 9.60
VA1181 | 2180 | 1.60 | 6.01 | 0.878 | 9.35
VA1182 | 2350 | 1.31 | 4.60 | 0.924 | 8.78
VA1183 | 2010 | 1.45 | 6.42 | 0.912 | 9.24
VA1184 | 1980 | 1.52 | 5.83 | 0.980 | 9.02
VA1185 | 1955 | 1.64 | 6.25 | 0.959 | 9.75
VA1186 | 1995 | 1.59 | 5.88 | 0.974 | 9.27
VA1187 | 1925 | 1.55 | 5.37 | 0.918 | 9.60
VA1188 | 2165 | 1.50 | 5.40 | 0.929 | 9.37
VA1189 | 2100 | 1.57 | 4.99 | 0.933 | 9.85
VA1190 | 2050 | 1.60 | 5.75 | 1.016 | 9.40
VA1191 | 2180 | 1.56 | 5.43 | 0.969 | 9.22
VA1192 | 1955 | 1.53 | 6.47 | 0.927 | 9.00
VA1193 | 2080 | 1.56 | 5.76 | 1.075 | 9.44
VA1195 | 1720 | 1.60 | 6.46 | 1.123 | 9.14
VA1196 | 2500 | 1.50 | 4.75 | 0.920 | 9.57
VA1197 | 2220 | 1.52 | 5.17 | 0.968 | 8.59
VA1202 | 2310 | 1.46 | 4.43 | 0.846 | 8.99
VA1205 | 2260 | 1.59 | 4.44 | 0.939 | 9.11
VA1206 | 2110 | 1.60 | 4.58 | 0.914 | 9.25
VA1207 | 2110 | 1.78 | 5.20 | 0.895 | 9.82
VA1208 | 2290 | 1.62 | 5.18 | 0.874 | 10.02
VA1213 | 2205 | 1.54 | 4.54 | 0.880 | 9.41
VA1215 | 1935 | 1.54 | 4.05 | 0.934 | 9.17
VA1216 | 2020 | 1.67 | 4.94 | 0.945 | 9.17
VA1217 | 2125 | 1.53 | 5.10 | 0.989 | 8.60
VA1218 | 2015 | 1.51 | 5.16 | 1.025 | 9.60
VA1220 | 2040 | 1.51 | 5.15 | 1.062 | 9.32
VA1223 | 2025 | 1.65 | 4.51 | 1.023 | 9.66
VA1224 | 1950 | 1.55 | 5.69 | 0.974 | 9.30
VA1225 | 1800 | 1.62 | 5.50 | 1.093 | 9.55
VA1226 | 2015 | 1.54 | 6.02 | 1.017 | 9.11
VA1227 | 1860 | 1.51 | 6.85 | 1.028 | 9.36
VA1228 | 1850 | 1.56 | 5.46 | 1.120 | 8.85
VA1229 | 1865 | 1.50 | 5.01 | 1.101 | 8.97
VA1230 | 2050 | 1.73 | 7.36 | 0.911 | 9.17
VA1231 | 1980 | 1.66 | 5.11 | 0.917 | 9.30
VA1232 | 2425 | 1.70 | 4.76 | 0.845 | 9.05
VA1233 | 2170 | 1.51 | 6.61 | 0.935 | 9.67
VA1235 | 2105 | 1.48 | 4.67 | 0.892 | 7.27
VA1237 | 1910 | 1.61 | 5.53 | 1.037 | 9.47
VA1238 | 1790 | 1.52 | 4.52 | 0.979 | 8.75
VA1239 | 2050 | 1.57 | 4.72 | 1.022 | 9.38
VA1240 | 1810 | 1.54 | 5.45 | 1.063 | 8.86
VA1241 | 1980 | 1.67 | 5.26 | 0.926 | 9.19
VA1242 | 2045 | 1.60 | 5.86 | 0.946 | 9.94
VA1243 | 2045 | 1.61 | 6.30 | 1.012 | 9.35
VA1244 | 2100 | 1.49 | 4.81 | 0.866 | 8.91
VA1245 | 1945 | 1.64 | 5.23 | 1.063 | 8.80
VA1246 | 1900 | 1.52 | 5.03 | 0.978 | 8.43
VA1247 | 2075 | 1.52 | 4.85 | 0.934 | 8.05
VA1248 | 1920 | 1.57 | 5.52 | 1.049 | 10.04
VA1249 | 1860 | 1.49 | 5.58 | 0.951 | 8.68
VA1251 | 2095 | 1.49 | 4.85 | 0.988 | 9.11
VA1252 | 2095 | 1.53 | 6.12 | 0.908 | 9.77
VA1253 | 1930 | 1.50 | 5.40 | 1.024 | 9.08
VA1254 | 2005 | 2.00 | 6.65 | 0.986 | 10.06
VA1255 | 2020 | 1.58 | 5.92 | 0.969 | 10.21
VA1256 | 2075 | 1.59 | 5.65 | 0.852 | 9.05
VA1257 | 2170 | 1.49 | 6.09 | 1.012 | 10.36
VA1258 | 1910 | 1.55 | 5.04 | 0.968 | 10.02
VA1259 | 1810 | 1.66 | 6.17 | 1.064 | 10.28
VA1260 | 2230 | 1.61 | 6.17 | 0.953 | 10.51
VA1263 | 1925 | 1.59 | 5.17 | 0.976 | 8.66
VA1264 | 1880 | 1.54 | 6.33 | 1.010 | 10.21
VA1265 | 2350 | 1.66 | 7.38 | 0.791 | 7.53
VA1266 | 1980 | 1.58 | 5.46 | 1.050 | 9.60
VA1267 | 1990 | 1.58 | 5.27 | 0.882 | 9.24
VA1268 | 1850 | 1.49 | 5.08 | 0.972 | 8.55
VA1269 | 2180 | 1.59 | 6.19 | 0.949 | 10.29
VA1270 | 1970 | 1.54 | 4.76 | 0.895 | 9.30
VA1271 | 1820 | 1.51 | 4.96 | 1.006 | 8.79
VA1272 | 2000 | 1.59 | 5.95 | 0.962 | 10.61
VA1273 | 2110 | 1.61 | 6.32 | 0.902 | 11.64
VA1274 | 1955 | 1.59 | 4.99 | 0.946 | 9.33
VA1276 | 2230 | 1.56 | 4.62 | 0.873 | 8.96
VA1277 | 2095 | 1.53 | 5.15 | 0.867 | 9.36
VA1278 | 2155 | 1.59 | 5.46 | 0.890 | 9.40
VA1279 | 2085 | 1.65 | 5.83 | 0.934 | 9.01
VA1280 | 1810 | 1.62 | 6.05 | 1.192 | 8.66
VA1281 | 1905 | 1.58 | 5.54 | 1.082 | 8.72
VA1283 | 2040 | 1.52 | 4.74 | 0.919 | 9.54
VA1284 | 1880 | 1.59 | 5.72 | 0.970 | 8.56
VA1285 | 2190 | 1.55 | 5.38 | 0.936 | 9.62
VA1286 | 1890 | 1.61 | 4.77 | 0.991 | 9.30
VA1287 | 1975 | 1.56 | 4.36 | 0.928 | 9.17
VA1288 | 2065 | 1.58 | 5.65 | 0.878 | 9.23
VA1289 | 2030 | 1.49 | 4.88 | 0.911 | 9.55
VA1290 | 2070 | 1.53 | 5.62 | 0.950 | 8.94
VA1291 | 1865 | 1.57 | 5.67 | 1.030 | 8.80
VA1293 | 1845 | 1.58 | 5.37 | 0.952 | 8.22
VA1295 | 1880 | 1.60 | 5.59 | 0.999 | 9.26
VA1298 | 1855 | 1.64 | 5.64 | 1.000 | 9.90
VA1299 | 2035 | 1.60 | 5.30 | 0.939 | 9.96
VA1300 | 1900 | 1.57 | 5.00 | 1.026 | 8.92
VA1301 | 1790 | 1.62 | 5.68 | 1.126 | 8.63
VA1302 | 1975 | 1.58 | 5.67 | 1.008 | 8.72
VA1303 | 1805 | 1.57 | 5.92 | 1.074 | 8.37
VA1305 | 1855 | 1.64 | 4.83 | 1.118 | 8.48
VA1307 | 1745 | 1.54 | 5.33 | 1.171 | 8.64
VA1309 | 1840 | 1.65 | 5.28 | 1.083 | 9.52
VA1312 | 1905 | 1.60 | 5.30 | 1.117 | 8.23
VA1313 | 1805 | 1.58 | 5.16 | 1.134 | 8.25
VA1314 | 1770 | 1.56 | 5.23 | 1.145 | 8.07

## References

  * [1] Q.. Ahmad  “Direct evidence for neutrino flavor transformation from neutral current interactions in the Sudbury Neutrino Observatory”  In _Phys. Rev. Lett._ 89, 2002, pp. 011301  DOI: 10.1103/PhysRevLett.89.011301
  * [2] Y. Fukuda  “Evidence for oscillation of atmospheric neutrinos”  In _Phys. Rev. Lett._ 81, 1998, pp. 1562–1567  DOI: 10.1103/PhysRevLett.81.1562
  * [3] C. Arpesella  “Direct Measurement of the Be-7 Solar Neutrino Flux with 192 Days of Borexino Data”  In _Phys. Rev. Lett._ 101, 2008, pp. 091302  DOI: 10.1103/PhysRevLett.101.091302
  * [4] R. Ajaj  “Search for dark matter with a 231-day exposure of liquid argon using DEAP-3600 at SNOLAB”  In _Phys. Rev. D_ 100.2, 2019, pp. 022004  DOI: 10.1103/PhysRevD.100.022004
  * [5] F.. An  “Observation of electron-antineutrino disappearance at Daya Bay”  In _Phys. Rev. Lett._ 108, 2012, pp. 171803  DOI: 10.1103/PhysRevLett.108.171803
  * [6] M. Askins  “THEIA: an advanced optical neutrino detector”  In _Eur. Phys. J. C_ 80.5, 2020, pp. 416  DOI: 10.1140/epjc/s10052-020-7977-8
  * [7] Liang-Jian Wen et al.  “A quantitative approach to select PMTs for large detectors”  In _Nucl. Instrum. Meth. A_ 947, 2019, pp. 162766  DOI: 10.1016/j.nima.2019.162766
  * [8] T. Anderson  “Eos: conceptual design for a demonstrator of hybrid optical detector technology”  In _JINST_ 18.02, 2023, pp. P02009  DOI: 10.1088/1748-0221/18/02/P02009
  * [9] Tanner Kaptanoglu et al.  “Spectral Photon Sorting For Large-Scale Cherenkov and Scintillation Detectors”  In _Phys. Rev. D_ 101.7, 2020, pp. 072002  DOI: 10.1103/PhysRevD.101.072002
  * [10] Minfang Yeh  “A new water-based liquid scintillator and potential applications”  In _Nucl. Instrum. Meth. A_ 660, 2011, pp. 51–56  DOI: 10.1016/j.nima.2011.08.040
  * [11] Steven D. Biller, Edward J. Leming and Josephine L. Paton  “Slow fluors for effective separation of Cherenkov light in liquid scintillators”  In _Nucl. Instrum. Meth. A_ 972, 2020, pp. 164106  DOI: 10.1016/j.nima.2020.164106
  * [12] Tanner Kaptanoglu  “Characterization of the Hamamatsu 8” R5912-MOD Photomultiplier Tube”  In _Nucl. Instrum. Meth. A_ 889, 2018, pp. 69–77  DOI: 10.1016/j.nima.2018.01.086
  * [13] Hamamatsu  “Photomultiplier tube R14688-100: Hamamatsu Photonics” [Accessed June 15, 2023], https://www.hamamatsu.com/us/en/product/optical-sensors/pmt/pmt_tube-alone/head-on-type/R14688-100.html, 2023
  * [14] J. Brack  “Characterization of the Hamamatsu R11780 12 inch Photomultiplier Tube”  In _Nucl. Instrum. Meth. A_ 712, 2013, pp. 162–173  DOI: 10.1016/j.nima.2013.02.022
  * [15] Xiang-Cui Lei  “Evaluation of new large area PMT with high quantum efficiency”  In _Chin. Phys. C_ 40.2, 2016, pp. 026002  DOI: 10.1088/1674-1137/40/2/026002
  * [16] N. Barros et al.  “Characterization of the ETEL D784UKFLB 11 in. photomultiplier tube”  In _Nucl. Instrum. Meth. A_ 852, 2017, pp. 15–19  DOI: 10.1016/j.nima.2017.01.067
  * [17] Morgan Askins  “ratpac-two”  Github, https://github.com/rat-pac/ratpac-two, 2023
  * [18] Hamamatsu  “Datasheet for R11265U SERIES / H11934 SERIES” [Accessed June 16, 2022], 2019
  * [19] O.. Akindele  “Acceptance tests of Hamamatsu R7081 photomultiplier tubes”, 2023  arXiv:2306.09926 [physics.ins-det]
  * [20] Hamamatsu  “Photomultiplier Tubes, Basics and Application, Fourth Addition” [Accessed Aug. 10, 2023], https://www.hamamatsu.com/content/dam/hamamatsu-photonics/sites/documents/99_SALES_LIBRARY/etd/PMT_handbook_v4E.pdf, 2023
  * [21] Nural Akchurin and Heejong Kim  “A study on ion initiated photomultiplier afterpulses”  In _Nucl. Instrum. Meth. A_ 574.1, 2007, pp. 121–126  DOI: https://doi.org/10.1016/j.nima.2007.01.093
  * [22] K.J. Ma  “Time and amplitude of afterpulse measured with a large size photomultiplier tube”  In _Nucl. Instrum. Meth. A_ 629.1 Elsevier BV, 2011, pp. 93–100  DOI: 10.1016/j.nima.2010.11.095
  * [23] D.. Akerib  “An Ultra-Low Background PMT for Liquid Xenon Detectors”  In _Nucl. Instrum. Meth. A_ 703, 2013, pp. 1–6  DOI: 10.1016/j.nima.2012.11.020
  * [24] Douglas Tiedt, Brianna Mount and Ayla Rodriguez  “Counting facilities at the Black Hills Underground Campus”  In _AIP Conference Proceedings_ 2908.1, 2023, pp. 020003  DOI: 10.1063/5.0161194
  * [25] D.. Akerib  “The LUX-ZEPLIN (LZ) radioactivity and cleanliness control programs” [Erratum: Eur.Phys.J.C 82, 221 (2022)]  In _Eur. Phys. J. C_ 80.11, 2020, pp. 1044  DOI: 10.1140/epjc/s10052-020-8420-x
  * [26] J. Aalbers  “Background determination for the LUX-ZEPLIN dark matter experiment”  In _Phys. Rev. D_ 108.1, 2023, pp. 012010  DOI: 10.1103/PhysRevD.108.012010
  * [27] Hamamatsu, private communication
  * [28] V. Albanese  “The SNO+ experiment”  In _JINST_ 16.08, 2021, pp. P08059  DOI: 10.1088/1748-0221/16/08/P08059
  * [29] S.D Biller et al.  “Measurements of photomultiplier single photon counting efficiency for the Sudbury Neutrino Observatory”  In _Nucl. Instrum. Meth. A_ 432.2, 1999, pp. 364–373  DOI: https://doi.org/10.1016/S0168-9002(99)00500-8
  * [30] M. Akashi-Ronquest  “Improving Photoelectron Counting and Particle Identification in Scintillation Detectors with Bayesian Techniques”  In _Astropart. Phys._ 65, 2015, pp. 40–54  DOI: 10.1016/j.astropartphys.2014.12.006
  * [31] B.. Land et al.  “MeV-scale performance of water-based and pure liquid scintillator detectors”  In _Phys. Rev. D_ 103.5, 2021, pp. 052004  DOI: 10.1103/PhysRevD.103.052004
  * [32] Mingjun Chen  “Development of a magnetic shield for 20-inch microchannel plate photomultiplier tubes”  In _Nucl. Instrum. Meth. A_ 1039, 2022, pp. 167128  DOI: 10.1016/j.nima.2022.167128