# The MIGDAL experiment:
Measuring a rare atomic process to aid the search for dark matter

H. M. Araújo  Department of Physics, Imperial College London, UK  S. N.
Balashov  Particle Physics Department, STFC Rutherford Appleton Laboratory, UK
J. E. Borg  F. M. Brunbauer  CERN – European Organization for Nuclear
Research, Geneva, Switzerland  C. Cazzaniga  ISIS Neutron and Muon Beams, STFC
Rutherford Appleton Laboratory, UK  C. D. Frost  F. Garcia  Helsinki Institute
of Physics, University of Helsinki, Finland  A. C. Kaboth  Department of
Physics, Royal Holloway University of London, UK  M. Kastriotou  I. Katsioulas
School of Physics and Astronomy, University of Birmingham, UK  A. Khazov  H.
Kraus  Department of Physics, University of Oxford, UK  V. A. Kudryavtsev
Department of Physics & Astronomy, University of Sheffield, UK  S. Lilley  A.
Lindote  LIP–Coimbra & Department of Physics, University of Coimbra, Portugal
D. Loomba  Department of Physics & Astronomy, University of New Mexico, USA
M. I. Lopes  E. Lopez Asamar  Department of Physics, Universidad Autónoma de
Madrid, Spain  P. Luna Dapica  P. A. Majewski  T. Marley  C. McCabe
Department of Physics, King’s College London, UK  A. F. Mills  M. Nakhostin
T. Neep  F. Neves  K. Nikolopoulos  E. Oliveri  L. Ropelewski  E. Tilly  V. N.
Solovov  T. J. Sumner  J. Tarrant  Technology Department, STFC Rutherford
Appleton Laboratory, UK  R. Turnley  M. G. D. van der Grinten  R. Veenhof

###### Abstract

We present the Migdal In Galactic Dark mAtter expLoration (MIGDAL) experiment
aiming at the unambiguous observation and study of the so-called Migdal effect
induced by fast-neutron scattering. It is hoped that this elusive atomic
process can be exploited to enhance the reach of direct dark matter search
experiments to lower masses, but it is still lacking experimental
confirmation. Our goal is to detect the predicted atomic electron emission
which is thought to accompany nuclear scattering with low, but calculable,
probability, by deploying an Optical Time Projection Chamber filled with a
low-pressure gas based on CF4. Initially, pure CF4 will be used, and then in
mixtures containing other elements employed by leading dark matter search
technologies – including noble species, plus Si and Ge. High resolution track
images generated by a Gas Electron Multiplier stack, together with timing
information from scintillation and ionisation readout, will be used for 3D
reconstruction of the characteristic event topology expected for this process
– an arrangement of two tracks sharing a common vertex, with one belonging to
a Migdal electron and the other to a nuclear recoil. Different energy-loss
rate distributions along both tracks will be used as a powerful discrimination
tool against background events. In this article we present the design of the
experiment, informed by extensive particle and track simulations and detailed
estimations of signal and background rates. In pure CF4 we expect to observe
8.9 (29.3) Migdal events per calendar day of exposure to an intense D-D (D-T)
neutron generator beam at the NILE facility located at the Rutherford Appleton
Laboratory (UK). With our nominal assumptions, 5$\sigma$ median discovery
significance can be achieved in under one day with either generator.

###### Contents

  1. 1 Introduction
  2. 2 Signal and backgrounds
    1. 2.1 Tracks in low pressure gas
    2. 2.2 Signal rates
    3. 2.3 Angular distribution of nuclear recoils
    4. 2.4 Background mitigation strategy
  3. 3 The MIGDAL detector
    1. 3.1 The Optical Time Projection Chamber
    2. 3.2 Optical readout
    3. 3.3 Charge readout
    4. 3.4 Data acquisition
    5. 3.5 Calibration
  4. 4 Neutron beam
    1. 4.1 Facility and generators
    2. 4.2 Shield and collimator design
  5. 5 Track simulations
    1. 5.1 Primary tracks
    2. 5.2 Electron transport in gas
    3. 5.3 The Gas Electron Multipliers
    4. 5.4 ITO strips
    5. 5.5 Electronics response
    6. 5.6 The camera image
    7. 5.7 Track reconstruction
  6. 6 Sensitivity
    1. 6.1 Signal acceptance
    2. 6.2 Backgrounds
    3. 6.3 Sensitivity
  7. 7 Migdal in other elements
    1. 7.1 Binary mixtures with noble elements
    2. 7.2 Group-IV compounds
  8. 8 Conclusion
  9. A Nuclear recoils in neutron scattering

##  1 Introduction

Most dark matter (DM) direct detection experiments search for rare nuclear
recoils from the elastic scattering of DM particles off nuclei in ordinary
matter. Below some small nuclear recoil (NR) threshold – typically
$\mathcal{O}$(keV) – this signature is not detectable, defining a DM mass
threshold which depends on the mass of the target nucleus. This simple model
assumes a recoiling nucleus moving together with its electrons, inducing
ionisation and excitation of the neighbouring atoms. However, it has long been
recognised that the sudden acceleration of the nucleus can lead to direct
ionisation of the atomic electrons – both in nuclear scattering [1, 2] as well
as in $\alpha$ and $\beta$ radioactive decay [3, 4, 5]. This phenomenon, the
so-called ‘Migdal effect’, predicts a small but non-zero probability for
atomic ionisation if the timescale for the nuclear ‘jolt’ is much shorter than
the electronic orbital periods. In these cases the nucleus initially moves
relative to its electrons without ‘carrying’ them, which may lead to the
ionisation of the recoiling atom – producing an electronic recoil (ER) signal
in the detector.

Several early studies recognised that this effect may provide an alternative
signature for the direct detection of DM [6, 7, 8, 9], but it was only
recently that Migdal’s approach has been reformulated to yield a relation
between NR and ER energies and ionisation probabilities as a function of ER
energy [10], highlighting this as an attractive process to search for sub-GeV
mass DM particles: for a given mass, the maximum available ER energy exceeds
that in the NR channel – and ER signals are easier to detect as their
responses are ‘unquenched’ – effectively making sub-threshold NR interactions
detectable indirectly, albeit with low probability.

The Migdal effect has been observed in nuclear decay processes in decades
past. In the 1950s, a measurement was performed of K- and L-shell ionisation
accompanying $\beta$ decay from [147]Pm and [210]Bi [11]. Later, the effect
was measured from K-, L- and M-shell electron shake-off accompanying the
$\alpha$ decay in [238]Pu and [210]Po [12, 13, 14], and in mono-cetylphosphate
with a large content of [32]P [15]. More recently, electron ionisation has
been observed following the $\beta$ decay of trapped [6]He+ ions and
$\beta^{+}$ decay in heavier [19]Ne+ and [35]Ar+ ions [16, 17].

Apart from the observation of the effect in both light and heavy elements,
these measurements confirm that the phenomenon is not restricted to isolated
atoms, appearing also in molecular compounds and in solids. Additionally,
although we will refer to this process exclusively as the ‘Migdal effect’,
these and other references show that this phenomenon has been described by
various names through the decades, including, but not limited to, ‘electron
shake-off’111Following the ionisation of an atom or molecule (e.g., through
photoionisation), it is possible for additional electron ionisation to occur,
a phenomenon also known as shake-off (e.g., [18, 19, 20]). This should not be
confused with the effect that we consider here, where ionisation follows from
a sudden perturbation to the nucleus of the atom or molecule. ‘neutron-impact
ionisation’ [21, 22], ‘electron excitation by neutron-nucleus scattering’
[23], or ‘atom excitation by jolting’ [24, p. 149].

Despite the lack of experimental confirmation in nuclear scattering – where
the change in the motion of the nucleus is brought about by scattering with an
electrically neutral projectile – this process has been invoked to extend the
science reach of several DM search technologies to sub-GeV particles [25, 26,
27] – with those with very low energy thresholds and ER backgrounds benefiting
the most. Several collaborations have now published DM results exploiting the
reformulation of the Migdal effect in Ref. [10]: LUX applied it first,
decreasing the DM mass threshold from 4 GeV to 400 MeV [28], followed by
searches from several other experiments [29, 30, 31, 32, 33, 34, 35]. However,
to our knowledge no measurement has confirmed the theory to date, even for
isolated atoms – and there could be important departures for molecular
species, liquids and solids (see, e.g., [36, 37, 38]).

The MIGDAL (Migdal In Galactic Dark mAtter expLoration) collaboration aims to
achieve the unambiguous detection of the Migdal effect under the most
favourable conditions. We will use energetic neutrons as projectiles and a
low-pressure gas detector so that ionisation tracks from NR and ER can be
imaged and traced to a common vertex, which is the tell-tale signature of the
Migdal effect. Although our measurements will probe an energy regime well
above that being exploited by DM experiments, the systematic study of Migdal
probabilities in various atomic and molecular species will allow us to
establish if the theoretical predictions are sound over a wide energy regime.
Work to develop the theoretical calculations at relevant energies has
progressed in parallel [39].

Mature technology to achieve an unambiguous observation already exists,
developed partly by the collaborating groups [40, 41, 42], among others –
especially in the directional DM detection community [43, 44].

The measurement is illustrated schematically in Fig. 1. Our choice of base gas
is CF4 – for its high scintillation yield and emission spectrum compatible
with complementary metal oxide semiconductor (CMOS) camera readout – as the
active (working) medium in an Optical Time Projection Chamber (OTPC). The
detector allows three-dimensional (3D) track reconstruction through the
following detector sub-systems: $i)$ track ionisation is drifted to a double
glass Gas Electron Multiplier (GEM) system and converted to an optical signal
which is imaged by a CMOS camera; $ii)$ the amplified charge is collected at
an Indium Tin Oxide (ITO) anode plane segmented into readout strips to obtain
the perpendicular coordinate; $iii)$ a photomultiplier tube (PMT) detects both
the primary and secondary scintillation light to provide the absolute ‘depth’
coordinate. The detector is exposed to high-flux D-D (2.47 MeV) and D-T (14.7
MeV) neutron generators, with significant shielding and collimation providing
background mitigation and a controlled scattering environment.

Our initial goal is to observe clearly the Migdal effect in pure CF4;
subsequently, this will be mixed with other gases, including the noble
elements and other gases based on Si and Ge. This article focuses on the
initial pure-CF4 deployment, but some discussion is offered on future
measurements with other gas mixtures. There have been other proposals to
achieve a measurement in argon and xenon gas at higher pressures [45] and in
the condensed phase [46, 47].

Figure 1: Schematic representation of the MIGDAL experiment showing the OTPC
exposed to neutrons, with interactions in the low-pressure CF4 gas amplified
by a double glass-GEM system; the active volume of the OTPC is approximately
10$\times$10 cm2 by 3 cm in the drift direction; neutron interactions take
place in a volume $\approx 9\\!\times\\!9$ cm2 by 1.3 cm. Optical signals are
recorded by an external camera and a photomultiplier tube, while amplified
track ionisation is detected by an ITO-strip anode. An example 2D-projected
Migdal event (scaled 10$\times$) is shown, featuring a 5-keV electron and a
150-keV fluorine nuclear recoil originating from the same vertex – simulated
using Degrad [48] and SRIM [49] plus Garfield++[50], respectively.
Illustrative signals in the various detector systems are also shown.

In this article we describe the design of the experiment, informed by
simulations and preliminary test data from ancillary systems. The paper is
organised as follows. In Section 2 we describe the behaviour of NR and ER
tracks in low-pressure gas, and introduce the neutron-induced processes
responsible for signal and background interactions; we summarise calculated
Migdal rates, giving context to the experimental challenge. An appendix
reviews pertinent aspects of neutron scattering kinematics and neutron cross
sections. In Section 3 an overview of the experiment is given, including the
main design drivers for each detector subsystem and key design choices. In
Section 4 we describe the neutron beam and host facility, the design of the
collimator and shield elements, and mention key beam-induced backgrounds. In
Section 5 we detail the modelling of particle tracks in the gas and their
detection by the optical and charge readout systems. Section 6 discusses the
expected sensitivity of the experiment to Migdal events. Section 7 addresses
the extension of the measurement to other gas mixtures. We conclude by
discussing the outlook for our programme in Section 8.

##  2 Signal and backgrounds

Detection of the rare Migdal event topology, consisting of two short tracks
with a common vertex, using a low-pressure OTPC detector requires optimisation
based mostly around the gas composition and density (pressure). The latter
operational parameter governs almost the whole experimental approach by
impacting two key physical parameters which are in tension with each other:
the neutron scattering rate in the active volume increases with pressure, but
the length of the resulting ER and NR tracks decreases. The electron track
length is particularly important as this determines the ability to
discriminate between ER and NR tracks, as well as the detection threshold for
Migdal events. In this section we discuss the behaviour of NR and ER tracks in
the low-pressure gas, as well as the signal and background rates after a
simple threshold based on track length has been defined. Other experimental
parameters that depend on the gas composition and density will be discussed in
Section 3, where a more detailed account of the experiment is given.

###  2.1 Tracks in low pressure gas

Figure 2: Left – Track length in CF4 at 50 Torr for electrons (mean projected
range calculated with Degrad [48], CSDA range with ESTAR [51], and the
practical range formula from Ref. [52]), and mean projected range for carbon
and fluorine ions from SRIM [49]). Right – Electronic and nuclear energy loss
rates (CSDA) along carbon and fluorine ion tracks in CF4 at 50 Torr,
calculated with SRIM and electronic energy loss for 20 keV electrons obtained
with ESTAR; called out values are interim particle energies (in keV) remaining
at that point in the track.

Low-energy electrons have convoluted tracks, and their spatial extent can be
characterised by various metrics of ‘range’ – with some of the most common
depicted in Fig. 2 (left). For the purpose of design optimisation we adopted
the ‘practical range’ for electrons [52]. This is longer than the ‘mean
projected range’ along the direction of incidence (which is the mean of a wide
distribution), but not quite as long as the ‘Continuous-Slowing-Down
Approximation (CSDA) range’, which corresponds to the full track length in 3D.
Simulations show that the practical range corresponds approximately to the
99th percentile of the projected range distribution in our conditions. We
adopt a 4-mm practical range to motivate an energy threshold of 5 keV for
electrons as a nominal design value, which is conveniently calibrated in CF4
by 5.9 keV X-rays from 55Fe. Other estimators for electron range will be used
when analysing data, both real and simulated, but for the design process we
opted for this simple metric; the sensitivity of the experiment does not
change dramatically for electron threshold ranges $\pm$1 mm around this value.

At our energies of interest NR tracks are straighter than those from low-
energy electrons and hence their mean projected range is closer to the CSDA
range. The mean projected range for 12C and 19F recoils is also shown in Fig.
2 (left), obtained from SRIM [49]. In this case, the 4-mm threshold translates
to 130 keV and 170 keV for the two recoil species, respectively.

This point is illustrated in Fig. 2 (right), which shows the energy loss rates
as a function of distance along the track for 20 keV electrons and for 19F and
12C ions with end-point energies resulting from D-T neutrons (2.8 MeV and 4.2
MeV). Electronic and nuclear stopping powers are shown for the ions, which are
due to inelastic collisions with bound electrons and with nuclei,
respectively. The numerical values indicated at various points along the
electronic energy loss curves are the interim particle energies in keV during
the slowing down process. For example, it can be inferred that the CSDA range
for 170 keV 19F ions is 4–5 mm, which is close to the value seen on the left
panel of the same figure.

Significantly, a distinctive ‘head-tail’ difference can be observed in the
energy loss rate along the tracks between electrons and the heavier ion
recoils. The former lose more energy at the end of the track, while for the
latter the opposite is true. This feature gives unique power to identify
Migdal events against some backgrounds.

We note that the ratio between electronic and nuclear losses decreases towards
low recoil energies; the fraction of the energy available in the electronic
channel (the so-called ‘quenching factor’) has been derived for binary gases
including CF4 [53]. A measurement of this parameter is one of the goals of the
experiment, exploiting the directional capability of the OTPC. As discussed
later, the NR spectrum leading to a Migdal detection is not critically
dependent on this parameter.222Hereafter, we use ‘keVee’ units to denote the
electron-equivalent energy of nuclear recoil interactions which can be
measured via scintillation or ionisation post-quenching, and reserve ‘keV’ to
denote particle energy.

The opposing trend in energy loss rate along ER and NR tracks also poses a
technical challenge for track reconstruction in the immediate vicinity of the
Migdal vertex. As Fig. 2 (right) confirms, the two recoil types have very
different magnitudes in ‘dE/dx’ at production: a 5 keV electron loses energy
at its minimum rate of 0.74 keV/mm, while a 2.7 MeV fluorine recoil does so at
its maximum rate of 186 keV/mm. An accurate measurement of both recoils
requires some 3 orders of magnitude in GEM dynamic range (specifically, in
ionisation density in the GEM holes between the maximum signal and the noise
floor for optical detection), which brings the OPTC close to the Raether limit
[54] – a challenging regime for achieving stable operation.

###  2.2 Signal rates

For the purpose of signal estimation we define an observable Migdal event as
an interaction containing an ER track protruding out of the penumbra of an NR
track in the 2D image, such that the Migdal topology can be unambiguously
detected. The extent of the NR penumbra is determined by the large energy
deposition near the vertex and diffusion of its ionisation cloud. We adopt the
nominal 5 keV electron threshold, noting that lower energies will nonetheless
be recorded in our data and available for analysis, depending on whether these
can be detected past the NR penumbra. Here we caution that Migdal emission
necessarily leads to atomic deexcitation [10], and for light atoms this is
dominated by Auger (or Coster-Kronig) emission rather than X-ray fluorescence.
However, in most of this article we assume that, for nominal operating
conditions, the sub-mm Auger electron tracks ($\lesssim$0.65 keV [55]) will
not be resolvable near the vertex. We return to this topic in Section 7, since
some interesting conclusions can be drawn for heavier elements.

The Migdal signal rate induced by D-D or D-T neutrons depends on the
properties of the neutron beam, the volume and pressure of the OTPC, the
neutron interaction cross section with atomic nuclei, and on the Migdal
electron emission probability – how likely it is for an electron to be ionised
during the sudden-collision process between the neutron and an atomic nucleus.
The total neutron flux and that entering the active region of the OTPC are
given in Table 1. The two generator yields differ by an order of magnitude,
but the D-D collimator is shorter giving a comparable flux through the
detector, as described in Section 4 where the neutron systems are detailed.

Table 1: Nominal neutron beam parameters and estimated event rates from the
D-D and D-T generators in CF4 gas at 50 Torr. Beam widths are indicated at
FWHM and for 99% of flux (‘halo’). Interaction rates are given for all NR
tracks originating in the active region and also for those fully contained
within an 8$\times$8 cm2 fiducial region and track length greater than 4 mm.
Migdal interaction rates (no efficiencies considered) are given for tracks
contained in the fiducial region, at track thresholds of 3 mm, 4 mm and 5 mm.
The baseline scenario (4 mm, in bold) integrates the NR spectrum from 130 keV
for carbon and 170 keV for fluorine, and electron energies in the range 5–15
keV; rates are indicated also for a low electron energy threshold (0.5 keV).

Generator | D-D | D-T
---|---|---
Nominal neutron energy (MeV) | 2.47 | 14.7
Neutron intensity (n/s) |  |
Emitted ($4\pi$) | $1\\!\times\\!10^{9}$ | $1\\!\times\\!10^{10}$
Active region | $2.6\\!\times\\!10^{5}$ | $4.7\\!\times\\!10^{5}$
Beam width/halo (cm) |  |
Vertical | 9.0/9.0 | 9.2/9.2
Horizontal | 1.4/1.8 | 1.3/1.5
Recoil spectrum (MeV) |  |
12C mean/end-point | 0.37/0.71 | 0.97/4.2
19F mean/end-point | 0.17/0.47 | 0.52/2.8
Interaction rates (evt/s) |  |
Total | 53 | 68
Signal-inducing | 53 | 48
Elastic | 40 | 37
Contained tracks† (evt/s) |  |
Total | 15 | 22
Signal-inducing | 15 | 18
Elastic | 11 | 14
Migdal rates† (interactions/day) |  |
NR track$\,\geq\,$4 mm, ER$>$0.5 keV | 7,250 | 26,430
Tracks$\,\geq\,$3 mm (ER $\in$ 4–15 keV) | 89 | 255
Tracks$\,\geq\,$4 mm (ER $\in$ 5–15 keV) | 43 | 131
Tracks$\,\geq\,$5 mm (ER $\in$ 6–15 keV) | 22 | 74

† In 8$\times$8 cm2 fiducial region, NR track $\geq\,$4 mm unless indicated.

The experiment is designed such that neutrons interact minimally with the
detector structure around the low-pressure CF4 gas in the active region, where
they scatter off 12C or 19F nuclei. The mean and end-point of the respective
recoil spectra are given in Table 1. The neutron scattering rates on CF4 gas
at 50 Torr in the active region of the OTPC are also listed, calculated with
GEANT4 [56] v10.5.1 (G4NDL 4.5); event rates of 50–70 per second are expected.
Although we will analyse all tracks starting inside the TPC, only a fraction
of those will be above the NR threshold, and only a fraction of those are
fully contained (head and tail) within a more restricted fiducial region
(8$\times$8 cm2), and the rates for these tracks are also listed in the table.

Neutron scattering cross sections at D-D and D-T energies are listed in Table
2, taken from the ENDF/B-VIII.0 [57] database which was used to validate our
Monte Carlo simulations. This table lists processes that produce events
featuring ‘bare’ nuclear recoils, i.e. those with no accompanying charged
tracks. In addition to elastic scattering, these include inelastic scattering
and neutron capture (where the $\gamma$-rays can easily escape the detector)
as well as $(n,2n)$ reactions: these can all contribute to the Migdal signal
rate (we label this sum $\sigma_{s}$). In general, the dominant interaction in
CF4 is with 19F mostly due to molecular composition. In particular, elastic
scattering on 19F dominates the interaction rate in CF4 for D-D neutrons, and
yields 62% of all signal-inducing NR events; 12C provides a further 12%.
Inelastic scattering on 19F contributes the remaining 26%, with around half
coming from scattering via the $n=2$ level at 197 keV. With D-T neutrons,
elastic scattering on 19F contributes to $\sigma_{s}$ in similar proportions
to the D-D case – but more inelastic levels from both isotopes are accessible
in this case (adding up to 21% of the signal-inducing recoil events). This
discussion highlights another advantage of CF4 as the target gas: the natural
abundance of carbon and fluorine is dominated by a single isotope of each
species, so the neutron inelastic interactions are relatively simple.

Table 2: Neutron cross sections at 2.47 MeV and 14.7 MeV from ENDF/B-VIII.0 [57] (all values in mb); $\sigma_{0}$ denotes the total cross section, and the four signal-inducing processes ($\sigma_{s}$) include partial cross sections for elastic scattering $(n,n)$, inelastic scattering $(n,n^{\prime})$, the $(n,2n)$ threshold reaction, and radiative capture $(n,\gamma)$. | 2.47 MeV (D-D) | 14.7 MeV (D-T)
---|---|---
nucleus |  12C |  19F |  12C |  19F
$\sigma_{0}$ | 1,613 | 3,038 | 1,379 | 1,786
$(n,n)$ | 1,613 | 2,131 | 895 | 985
$(n,n^{\prime})$ | – | 907 | 426 | 235
$(n,2n)$ | – | – | – | 52
$(n,\gamma)$ | 0.05 | 0.09 | 0.15 | 0.03
$\sigma_{s}/\sigma_{0}$ | 100% | 100% | 96% | 71%

Each signal-inducing NR has a small probability of emitting a detectable
electron via the Migdal effect. In calculating the Migdal event rates, we use
the ‘semi-inclusive’ probabilities as a function of the electron kinetic
energy from Ref. [39]. This improves on the calculations by Ibe and co-workers
[10] in two key ways. Firstly, it does not employ the dipole approximation,
which breaks down in our NR energy regime. Secondly, the semi-inclusive rate
accounts for the possibility of ionisation together with excitation of other
electrons in the atom, as well as multiple-ionisation in the Migdal process in
which one electron is above the ER threshold while additional electrons are
below threshold. The semi-inclusive process therefore leads to the same
characteristic Migdal event topology of an ER and NR track with a common
vertex since any additional electrons will not be observable with our
detector. When we refer to electron energy in the ensuing discussion, we
exclusively refer to the kinetic energy of the above-threshold Migdal
electron.

We note that the calculations in both Ref. [39] and Ref. [10] are for isolated
atoms rather than for the nuclei in a CF4 molecule. Corrections to these
probabilities, and hence to the Migdal event rates that we present here, are
therefore expected, although we anticipate that these will be relatively
small. This is because, over most of our ROI, electrons emitted with D-D and
D-T neutrons are the inner-most ones, where the deviation from atomic wave-
functions are small. A more extensive discussion of the theoretical rates is
given in Ref. [39].

Figure 3: Double-differential Migdal rates for tracks contained in the OTPC
from D-D (left) and D-T (right) generators. The contours are based on the NR
thresholds of 130 keV and 170 keV for C and F, respectively. The area bound by
the contours encompasses 68%, 90% and 95% of the signal; we note that the
$y$-axis refers to the energy carried by the most energetic electron in the
semi-inclusive calculation [39].

Double-differential Migdal event rates with respect to NR and ER energies are
shown in Fig. 3 for D-D (left) and D-T (right) neutrons. The plots consider
only tracks contained in the 8$\times$8 cm2 fiducial region; this selection
softens the NR spectrum in the search sample, especially removing carbon
recoils from D-T neutrons. The sharp discontinuities at 470 keV (left) and
2,815 keV (right) NR energy occur at the 19F end-point energies and highlight
that the Migdal rates in CF4 are dominated by fluorine. The log-scale colour
maps illustrate that, in general, the rate drops off exponentially with
increasing electron energy; therefore, a low ER threshold is essential for
this experiment. The differential rate depends on the product of the electron
emission probability with the differential neutron cross section. The
interplay between these leads to features in the Migdal rate, e.g. the rise at
$E_{r}\sim 400$ keV (left) and the broad peak at $E_{r}\sim 1000$ keV (right).

As described previously, we define our nominal region of interest (ROI) to
include NR and ER tracks each longer than 4 mm sharing a common vertex. This
corresponds to NR energies greater than 130 keV and 170 keV for C and F ions,
and ER tracks with energy greater than 5 keV. At the upper end of the ROI we
extend to the NR end-point energies, while for ER tracks we accept up to 15
keV. As the Migdal rate drops off steeply with ER energy, this upper value has
little effect on the signal rate – but it will play a role in limiting
background rates (cf. Section 6.2).

Migdal rates per live day are given in the last few rows of Table 1 for the
nominal ROI plus additional threshold scenarios. These are obtained by
integrating the differential rates exemplified in Fig. 3 as indicated in the
table. With both neutron sources the Migdal yield originates mostly in
fluorine, with the carbon contribution being modest: 10% for D-D and 14% for
D-T. The first entry utilises a very low ER threshold (0.5 keV) to highlight
the large number of events with small track lengths hidden below the detection
threshold. Other scenarios correspond to a smaller ($\pm 1$ mm) deviation from
the nominal value of 4 mm. We conclude that the number of potentially
detectable Migdal events per live day is always significant, especially for
the D-T generator, and that small departures from the nominal electron
threshold are reasonably inconsequential: a decrease to 3 mm approximately
doubles the event rate, while an increase to 5 mm threshold halves the rate.

###  2.3 Angular distribution of nuclear recoils

In addition to event rates, we may also consider the angular distributions of
the recoiling nuclei in the laboratory frame, as this will impact the design
of the OTPC and inform how data are analysed. Figure 4 illustrates the neutron
angular cross sections for CF4, as well as energy spectra for the two atomic
species recoiling elastically. In the elastic case the recoil energy can be
uniquely determined from the scattering angle, while in inelastic scattering
the energy (not shown) is double-valued for a given recoil angle, up to a
maximum angle which is lower than 90∘ in the laboratory frame. Inelastic
scattering does contribute to some features observed in the figure. An
extensive discussion of the nuclear recoil distributions induced by the
scattering of fast neutrons is given in A.

Figure 4: Polar representations of nuclear recoil angle distributions from D-D
(left) and D-T (right) neutrons. The black arrows indicate the direction of
the neutron beam. The colour maps represent the neutron cross section as a
function of NR angle in the laboratory frame, with darker red corresponding to
increasing cross section on a linear scale; these include the signal-
generating processes listed in Table 2 for CF4. A small contribution from
19F($n$,$2n$) in the backward direction is omitted in the D-T plot. The solid
lines show calculated recoil energies for elastic scattering only, with 12C in
blue and 19F in green. The energy scale refers to this energy plot only, which
is independent of the colour map.

As expected, most elastic recoils are emitted with low energies at large
angles with respect to the beam and, conversely, the most energetic recoils
are emitted in the forward ($+x$) direction, and the same is true for the
inelastic case; this determines the optimal orientation between the beam and
the OTPC, including the optimisation of its geometry, accounting for the
maximum NR range as a function of angle and the orientation of the charge
readout strips as discussed later.

For D-D neutrons, both elastic and inelastic scattering contribute to the
broad peak observed near 72∘ in the overall angular cross section, with a
smaller enhancement around 34∘ which is mostly due to inelastic scattering off
the $n=3,4,5$ levels in 19F. At this neutron energy, fluorine recoils are more
numerous at all angles: from a factor of approximately four in the forward
direction, to greater than 10 above 70∘.

The polar distribution for recoils from D-T neutrons is strongly peaked around
80∘, with a modest enhancement near 52∘. Around 3% of the signal-inducing
events come from 19F($n$,$2n$) reactions, with half of those emitted in the
backward direction (these are not represented in the figure). In the D-T
experiment, 12C recoils dominate below 15∘, while the fluorine-to-carbon ratio
peaks sharply (13$\times$) at around 57∘: this is due both to an enhancement
of the fluorine cross sections and to a significant dip in the carbon cross
sections near those angles.

A good understanding of these distributions will aid with data analysis: $i$)
to make robust ‘head-tail’ determinations for NR interactions, since the only
processes that can yield ‘backward’ tracks have low probability; $ii$) by
enabling NR energy reconstruction from scattering kinematics: for quenching
factor measurements, for analysis of tracks which are not fully contained in
the OTPC, and possibly to circumvent NR response saturation near the start of
the NR track; and $iii$) by allowing us to focus on angular regions with
higher signal yields and, possibly, to help distinguish between the
contribution of each atomic species – see example in Section 7.

###  2.4 Background mitigation strategy

The exposure of a sensitive detector to a very high flux of energetic neutrons
will inevitably lead to the production of background topologies which can bear
close resemblance to the signature presented by the Migdal signal. These
backgrounds include various atomic processes leading to particle emission
directly from the neutron-induced NR track, as well as random associations
between an NR track and unrelated low-energy electrons – either beam-
coincident or purely accidental.

A quantitative discussion of background processes is postponed until Section
6.2, as this must follow a full description of the experiment. Here we
introduce the main strategy for background mitigation, which is central to the
experimental design: the operation of the detector using a low pressure gas.
This enables two powerful avenues for background discrimination: $i)$ the
reconstruction of extended tracks allows selection of the distinct Migdal
event topology; and $ii)$ by reducing the interaction probability for
energetic photons (of both internal and external origin) near the NR track, an
important class of potential backgrounds is mitigated effectively. We do not
anticipate this measurement to be background limited.

Photon interaction probabilities for 50 Torr of CF4 are shown in Fig. 5. The
thicker lines highlight the probability that 5–15 keV photoelectrons or
Compton electrons are produced up to a distance of 3 mm from the photon
origin, which we consider here to coincide with the NR track vertex. A low-
energy electron track in this (generously sized) region may give rise to a
background topology (note that the spatial resolution of the OTPC is a
fraction of this value in all three dimensions). Photoelectric absorption
causing ROI electrons within 3 mm occurs with $\mathcal{O}(10^{-3})$
probability; this is applicable to X-ray emission from various atomic
processes. In turn, Compton scattering of $\gamma$-rays is down at
$\mathcal{O}(10^{-6})$ probability; this applies, for example, to nuclear
radiation from inelastic neutron scattering. Both types of photon-emitting
process would otherwise be important sources of background.

Figure 5: Photon interaction probabilities within a 3 mm distance for CF4 at
50 Torr, using data from Refs. [58, 59]. Photoelectric data are shown in
green, with the 5–15 keV photoelectron energy range highlighted by the thicker
green line. Compton interaction probabilities are shown in blue, with the 5–15
keV Compton electron region of interest shown by the thicker blue line; the
latter was obtained by integrating the Klein-Nishina cross section formula
between the appropriate angles.

The use of a light-element gas in the first stage of the experiment is also
important for the success of the initial measurement. Electron and X-ray
emission from atomic deexcitation anywhere along the NR track are in principle
problematic, and as long as atomic shell energies lie below the electron ROI
these will not produce a background. K-shell binding energies for carbon and
fluorine are 284 eV and 697 eV, respectively. One notable example already
highlighted above is the Auger emission accompanying the Migdal effect –
although we expect some Auger electrons to be resolvable in 55Fe calibration,
they should not be visible past the NR track penumbra for light-element
recoils.

##  3 The MIGDAL detector

###  3.1 The Optical Time Projection Chamber

Figure 6: Schematic representation of the MIGDAL detector, showing a side view
(upper panel) and the top view of the setup (lower panel). The inset details
the main chamber volume, with the OTPC viewed by a CMOS camera and a
photomultiplier tube, both located behind reentrant viewport flanges outside
of the gas space. The collimator shown is for the D-T experiment; the D-D
collimator is just under half the length.

TPCs are excellent radiation detectors, providing a complete, three-
dimensional (3D) image of the ionisation released in an active volume filled
with a gas or a liquid. A key technical advance was the introduction of gas
scintillation with optical readout for 2D imaging [60], later in combination
with the Gas Electron Multiplier (GEM) [61, 62]. The OTPC technology has been
successfully used, for example, in imaging of exotic nuclear decays [63].
Modern detection techniques deploying TPCs with imaging capability are
reviewed in Ref. [64].

The MIGDAL experiment will benefit from these advances to deploy a combination
of 2D-projection imaging using a CMOS camera, signal amplification with the
cascade of two thick glass-GEMs [65], and electronic readout in the drift
direction providing timing information for depth-coordinate reconstruction.
Operation with a low pressure scintillating gas (50 Torr of CF4, 0.24 mg/cm3)
will allow the reconstruction of low-energy tracks in 3D.

The setup is illustrated in Fig. 6 – with the longer collimator designed for
the D-T generator. The TPC structure will be installed vertically in a 10-inch
cubic vacuum chamber made from aluminium alloy, sealed by 6 aluminium Conflat
flanges (DN200CF). Flanges at the front and rear incorporate 150 $\mu$m and
250 $\mu$m-thick aluminium windows to minimise neutron interactions near the
active volume; the rear window is located at the end of a 19.5 cm long exit
flange. These windows are epoxy-sealed and must be able to endure stresses
from vacuum/pressure cycling. Flanges at either side of the cube support
reentrant optical viewports to allow prompt and secondary scintillation light
to be detected by a photomultiplier and a camera, which view the TPC from
opposite sides. The two remaining flanges provide electrical connections (bias
and readout), gas inlet/outlet ports, and two small 50-$\mu$m-thick aluminium
windows for calibration with external sources.

The D-T neutron beam is coupled to the active region of the TPC using a 1-m
long air-filled collimator made from pure copper, installed between the
neutron generator head and the front of the cube. Together with a front shield
composed of various materials, the collimator creates a well-defined neutron
beam with minimum halo passing through the detector. These elements – and the
shorter D-D collimator – are detailed in Section 4.333In an earlier design
this was a vacuum collimator with entrance window near the neutron generator,
to mitigate secondary particle production in the window material near the
OTPC. After careful evaluation of these backgrounds we have opted for a less
challenging design using an air-filled collimator, moving the detector window
nearer the chamber. The exit window arrangement was similarly retracted (as
shown in Fig. 6), although the actual window flange can also be attached
directly to the chamber.

####  3.1.1 Active region

Particle tracks will be created in the 3.0-cm drift region defined between a
cathode mesh and the first GEM, as exemplified in Fig. 1; the active area
defined by the GEMs measures 10$\times$10 cm2. The short drift gap will allow
full development of most tracks while minimising diffusion of the primary
ionisation. The cathode mesh (15.0$\times$12.6 cm2) is woven from 280
$\mathrm{\mu}$m aluminium wire and has 66% optical transparency, transmitting
the CF4 luminescence through to the photomultiplier. Its support ring
(18.6$\times$17.4 cm2) is made from two aluminium alloy halves, with the mesh
clamped in between.

Three field-shaping rings, made of 2-mm diameter pure copper wire and spaced
by 10 mm, will maintain a uniform electric field in the active volume. The two
upper field-shaping electrodes are interrupted at the entrance and exit of the
neutron beam to prevent spurious interactions that could generate background.
The third is located at the level of the top electrode of the first GEM, and
is wider to match the cathode ring dimensions.

The discontinuity of the field-shaping rings for the neutron beam means that
the field is distorted in the drift region, which will require the
fiducialisation of the active volume during analysis. To optimise the field in
the active volume, electrostatic finite-element analyses have been developed
using the COMSOL Multiphysics software with the AC/DC module. A full model of
the detector including all TPC elements is shown in Fig. 7 (left). The field
has been studied in two volumes with transverse dimensions of 10.0$\times$10.0
cm2 and 8.0$\times$8.0 cm2. The electric fields in the three key regions of
the detector – the drift, transfer and induction regions – are 200, 600 and
400 V/cm, respectively. In the drift region the field is constant along the
TPC axis – direction ‘A’ in Fig. 7 (right) – while there is a strong non-
uniformity of $\approx$40% in field strength at the corners of the larger area
(along C); this decreases to $\approx$10% at the corners of our more
restricted 8.0$\times$8.0 cm2 signal-search area (along B).

Figure 7: Electrostatic design of the TPC. Left – Detector model used in
COMSOL; the active volume between the cathode and the first GEM lies between
the two sets of field-shaping electrodes. Right – Distribution of electric
field lines between the cathode and the first GEM in the direction
perpendicular (upper map) and parallel to the beam (lower map).

The drift field in the restricted 8$\times$8 cm2 region will be 200 V/cm, at
which the transverse electron diffusion in pure CF4 at 50 Torr has a minimum
value of 260 $\mathrm{\mu}$m/$\smash{\sqrt{\mathrm{cm}}}$; in these conditions
the drift velocity is $\approx$13 cm/$\mu$s. The electric field non-uniformity
due to discontinuity of the field-shaping rings will create a variation of the
electron diffusion and drift velocity at the level of 5%, which is acceptable
for our experiment.

The two glass-GEMs with 14.5$\times$14.5 cm2 overall dimension and
10.0$\times$10.0 cm2 active area will be cascaded for signal amplification,
with a combined gain of $\sim$105; these are manufactured by Radiment Lab
Inc., Japan. The charge-transfer region between them is only 2 mm long in
order to minimise transverse diffusion. The glass-GEMs are 570 $\mathrm{\mu}$m
thick, with 2-$\mathrm{\mu}$m copper cladding on both sides, and a dense
pattern of holes with $\approx$170 $\mathrm{\mu}$m diameter and a pitch of 280
$\mathrm{\mu}$m. Beyond the second GEM electrons will drift until they are
collected by a segmented anode made from a transparent ITO layer patterned
into readout strips; the length of this so-called induction region is also 2
mm to ensure the short duration of the induced pulses.

####  3.1.2 Gas system

The gas system consists of a vacuum pumping station and a gas filling station,
as illustrated in Fig. 8. It is located inside the neutron ‘bunker’ (described
in Section 4), and supplied by gas cylinders (CF4 plus noble gases) located
outside of this area. The performance of the detector is influenced by gas
purity, especially the presence of electronegative contaminants, and the goal
is to be able to take high-quality data for over one day on a single gas load.
Therefore, the design involves only metal-gasket seals and other low-
outgassing materials. To achieve high purity initially, the chamber will be
pumped to $\sim$10-5 Torr, with the quality of the vacuum monitored by a
Pfeiffer QMC-200 residual gas analyser (RGA); this is followed by purging the
system with pure argon. Entegris GateKeeper GPU-80 gas purifiers are used to
purify both types of gas. The mixing chamber will be filled to prepare the
required gas mixture prior to insertion into the detector, with the
composition measured precisely with a Lambda BGA244 Binary Gas Analyser (BGA).
When the required ratio is achieved, the mixing vessel is isolated and the gas
is introduced to the detector through a needle valve to the desired pressure.
The gas flow rate is monitored with a Teledyne Hastings HFM300 flowmeter. The
pressure in the chamber is measured by a Keller LEO5 digital manometer to a
precision of $<$1 Torr at 50 Torr.

Figure 8: The gas system design, including pumping station and gas
mixing/assaying and delivery hardware.

###  3.2 Optical readout

The optical readout of the detector involves two sensors: a photomultiplier
tube (PMT) to detect the prompt and secondary scintillation signals from the
CF4 gas; and a camera system to image the particle tracks in the $x,y$ plane
after amplification by the GEMs. We describe these in turn.

####  3.2.1 Camera system

A scientific CMOS camera (Hamamatsu ORCA-Fusion, C14440) will be used to image
the secondary scintillation light produced by particle tracks as their
ionisation is amplified by the GEMs. The camera is mounted inside a light-
tight enclosure on the side of the chamber, viewing the second GEM through a
Kodial glass viewport and the ITO anode plate – as shown previously in Fig. 6.
The optical system is focused on the GEM surface using a fast lens
(EHD‐25085‐C F0.85) with focal length of 25.6 mm. The optical system can image
the 10$\times$10 cm2 active area at distances of $\sim$12 cm. Precise
alignment of the optical axis is achieved using a 2D linear stage.

The 15$\times$15 mm2 CMOS sensor has 2,304$\times$2,304 pixels, with a
spectral sensitivity extending from $\sim$320 nm to $\sim$1,000 nm. This is
well-matched to the secondary scintillation spectrum of CF4, with the camera
reaching a quantum efficiency (QE) of $\approx$75% at the $\sim$620 nm peak
wavelength [66]. The Peltier-cooled CMOS sensor operates at $-15^{\circ}$C in
combination with liquid cooling, offering a read-out noise of $\sim$1.4
electrons (rms) and dark current of $\sim$0.2 electrons/pixel/second. The
camera reads the contents of the pixels with 16-bit analog-to-digital
converters. A 2$\times$2 digital binning will be utilised for reduced data
volume and improved signal-to-noise ratio at the expense of lower image
resolution.

The camera will be operated in a free-running (internal) trigger mode: it will
continuously image the GEM system at the maximum rate of 89.1 frames/s,
corresponding to an exposure of 11.2 ms per frame. The camera readout uses a
rolling shutter which allows for zero dead-time at the expense of an 11.2 ms
time separation between the top and bottom rows of each image. This time
separation is challenging when trying to maintain synchronicity with the
photomultiplier tube. If a scintillation event occurs when the readout is
located at the middle row of the image, there is an equal probability of the
event appearing on the current frame or the following frame, and some
probability that the event is split across two frames. In the latter case the
images can be combined, at the expense of signal-to-noise ratio.

The maximum f/0.85 aperture setting allows for maximal optical sensitivity, at
the expense of a shallow depth of field and greater vignetting. The shallow
depth of field is expected to introduce a slight blur at the edges of the
image, but as the resolution is limited by the GEM pitch this should be a sub-
dominant effect. Vignetting can be accounted for via a flat-fielding
correction based on images of uniformly distributed tracks from an 55Fe
calibration source, although signal-to-noise may be reduced towards the edges
of the image where the intensity is compromised.

We estimate a detection efficiency for GEM photons integrated across the
secondary scintillation emission spectrum of $\sim$0.1%, including geometrical
light collection, optical transmission coefficients and camera QE. Combined
with a nominal charge gain of 105 and a photon-to-electron ratio of 0.34 [67]
(all angles), this yields just over 30 detected photons per electron at the
output of the GEMs.

####  3.2.2 Photomultiplier readout

A VUV-sensitive, 3-inch Hamamatsu R11410 PMT is a distinct part of the optical
readout system: it views the active region of the OTPC through its cathode
mesh, from a reentrant enclosure attached to the main chamber and located
opposite to the camera position – as shown in Fig. 6. Within this hermetic
enclosure, the PMT is secured against a MgF2 viewport, 50 mm away from the
cathode. The external location avoids operation at low pressure and proximity
to the neutron beam, but adequate optical coupling to the active region is
still achieved with the reentrant design. The PMT is negatively biased to
deliver a gain of $5\\!\times\\!10^{6}$, and the near-ground signal is
digitised by the DAQ system along with the ITO-strip signals.

The main function of the PMT readout is to detect both the primary and the
secondary scintillation signals from the active volume, which we denote by
‘S1’ and ‘S2’, respectively. The S2 pulse provides a convenient trigger for
the acquisition, while the S1 signal (recorded in the pre-trigger region of
the waveforms) determines the interaction time, and hence the absolute depth
coordinate ($z$). In addition, for tracks oriented towards the cathode or the
first GEM, the time difference between these two pulses also will help
identify tracks only partially contained in the drift region.

The primary scintillation of CF4 has two main continua, one centred at 160 nm
in the VUV region and a UV/visible component extending between 200 nm and
$\sim$400 nm [68, 69, 70]; a further continuum exists above 550 nm which is
particularly strong in the case of secondary scintillation from electron
avalanching [66]. The PMT quantum efficiency is significant down to its 160 nm
cutoff (e.g. 23% at 165 nm), and the viewport transmission is 85% at those
wavelengths; the PMT enclosure is purged with argon gas to prevent significant
VUV absorption. In summary, the PMT system has reasonable sensitivity to the
VUV scintillation, it is fully sensitive to the UV/visible component, and is
partially sensitive to the red/infrared emission.

The prompt CF4 scintillation yield is affected noticeably by pressure, with
the shorter wavelength components increasing and the longer wavelength ones
progressively disappearing as the pressure decreases. Below 1 bar the emission
from $\alpha$-particles in the range 220–500 nm increases to $>$2 photons/keV
[71]; we use this value to estimate the yield for NR tracks. Light collection
simulations using the ANTS2 package [72] provide an estimate of light
collection efficiency averaged over the active volume of $\sim$1%, peaking at
2% at the centre of the OTPC.

An S1 analysis threshold of a single photoelectron (phe) is likely possible,
enabled by the short drift length of the OTPC and high drift speed of the gas,
combined with the low dark count rate of the PMT ($\sim$500 c/s). This
threshold translates to an average NR energy of around 50 keV for interactions
near the optical axis of the OTPC, rising to 100 keV for those near the edge
of the active region. Clearly, such a low S1 threshold brings significant
stochastic fluctuations from counting statistics to the NR threshold, but this
detection efficiency curve is easily calculable.

Secondary light generated in the GEMs will also be detected by the PMT. The
smaller response generated within the first GEM should be detectable, as the
direct light collection efficiency is significant; however, photons from the
second GEM – mostly reflected inside the chamber – still dominate the overall
response due to the additional gain. The transit time between GEMs is too
small for the two optical pulses to be fully resolved over the longitudinal
diffusion of the electron cloud even for parallel tracks, and so the signals
from the two GEMs combine into a single S2 pulse containing a few hundred phe
for NR signals at threshold.

The absolute $z$ coordinate can be determined from the time delay between the
S1 and S2 pulses. A timing resolution of 10 ns or better is achieved by the
fast scintillation decay time of CF4 (6.2 ns [73], see also [70]), the 9 ns
(FWHM) transit time spread for this PMT model, and a 2-ns sampling time at the
DAQ digitisers. A spatial resolution of $\sim$1 mm or better should therefore
be within reach for the smallest NR signals.

###  3.3 Charge readout

The OTPC bias and ionisation readout circuits are depicted in Fig. 9; the five
bias voltages (HV1…5) set up the three electric fields and deliver 530 V
across each GEM; the values are indicative only, they will be adjusted for the
GEM resistance (100–300 M$\Omega$ expected).

Figure 9: Electrical circuit showing the OTPC bias and readout.

Depth resolution will be achieved by reading out the charge deposited on the
transparent anode-strip plate at the end of the induction gap, as proposed in
Ref. [42], using transimpedance amplifiers. The anode strips are made from a
low-resistivity film (4 $\Omega$/square) of indium tin oxide (ITO) deposited
on a 1.1-mm thick glass plate, with the ITO patterned into 120 strips on a
pitch of 833 $\mu$m. This enables not only some lateral resolution, which
helps reduce ambiguity and thus simplifies event reconstruction, but also
reduces the capacitance seen by each amplifier, thus lowering the equivalent
input charge noise. The camera readout drives the transparency requirement for
this plate. The ends of the ITO strips are covered with an Al-on-Cr coating to
enable wire-bonding to a Kapton flexible PCB/cable for connection to the
vacuum feedthrough.

It is advantageous to orient the ITO strips perpendicularly to the beam axis
for D-D neutron-induced recoil energies above $\sim$230 keV and D-T neutron-
induced recoil energies above $\sim$750 keV, so this orientation was selected.
Figure 3 does not suggest that most Migdal events will involve nuclear recoils
above these energies, but that figure refers only to contained tracks, which
tend to have lower energies. Eventually, we aim to analyse all tracks with
origin within the fiducial region.

Pairs of strips (60 strips apart) are connected to each DAQ readout channel to
reduce channel count. To minimise capacitance and the risk of interference
from external signal sources, the amplifiers will be located on two PCBs
connected directly to the external connector of the vacuum feedthrough. These
circuits, shown in Fig. 10, are built from commercial parts, and include arc
protection and amplifiers/buffers for driving the (10 m) cables to the DAQ in
the control room outside of the neutron bunker.

Figure 10: Circuit representing each of the 60 electronic channels. It
utilises fast and low-noise commercial amplifiers (LMH6629), configured for
high speed and low gain. The inputs are protected using D5V0F4U6SO low-
capacitance ESD diodes. Various extra resistors have been added to ensure
stability when operated with low gain and a capacitive source impedance.

Charge-sensitive preamplifiers (Ortec 142IH) equipped with spark protection
circuits will be used to read out the charge signals induced on the GEMs.
Those induced on the second GEM would allow us to measure the overall gas gain
of the system for 5.9 keV X-rays, which is important for monitoring the
detector gain stability during the experiment. Despite the large dynamic range
of the preamplifier (100 MeV energy deposition in Si), it is expected that the
preamplifier attached to the second GEM will saturate for energetic NRs
($\gtrsim$100 keV) and, therefore, the output of the preamplifier attached to
the first GEM would be used for the energy measurement from $\sim$100 keV to 4
MeV.

Charge induced on the cathode is due to the motion of all charge carriers –
i.e. electrons and positive ions – in the drift region. A cathode pulse is
composed of a fast electron component from electron drift towards the first
GEM, and a slow ion component due to the drift of positive ions toward the
cathode. The amplitude of the fast electron component carries very useful
information on the depth of interaction along the $z$-axis and on the
orientation of the NR track, as demonstrated in Ref. [74]; eventually, we aim
to make use of this information.

###  3.4 Data acquisition

At the heart of the data acquisition (DAQ) system is an Acqiris CC121 crate
with 17 DC265 modules, for a total of 66 digitiser channels with 8-bit
vertical resolution and maximum sampling frequency of 500 MS/s. This setup is
used to record waveforms from the PMT anode (in dual-range mode), the higher-
potential GEM electrodes, the cathode, and the 60 anode strip pairs. The
trigger signal is derived from the PMT and fed to the external trigger input
of the digitisers to start the acquisition of a new event, and is also
recorded in the data stream as a separate channel. The camera images are
stored using a separate data stream. Figure 11 shows the DAQ block diagram.

Figure 11: Box diagram highlighting the three main data acquisition elements:
digitisers, camera and FPGA – controlled and read out by a common PC.

A purpose-developed, Linux-based DAQ software (MiDAQ) controls the overall
data acquisition workflow and is responsible for the interface with the
Acqiris crate and the Hamamatsu camera. It allows configuration of the
sampling rate, waveform and pre-trigger duration, and the full-scale of each
channel, as well as to set the camera’s exposure time, image binning and scan
mode.

All signals of interest lie in a short time window of $\lesssim$0.5 $\mu$s, to
which we add at least 0.5 $\mu$s of pre-trigger waveform for baseline
parameter estimation. We plan to digitise at 500 MS/s (2 ns sampling) but may
reduce this to 250 MS/s in some datasets to minimise deadtime and data volume.
The camera is operated independently in free-running mode, and images can be
directly synchronised with the recorded waveforms during offline analysis via
microsecond-precision timestamps which are generated by the software for each
DAQ event and each image, and recorded in both data streams.

The timing diagram in Fig. 12 shows example timelines for three events
recorded by the three main DAQ elements. When an interaction takes place in
the active volume of the detector it produces a primary scintillation signal
(S1) which is typically below our trigger threshold. The ensuing large
secondary scintillation (S2) pulse produced by the GEMs triggers the Acqiris
digitiser, which records also pulses induced on the ITO strips as well as on
the cathode and the two GEMs.

Figure 12: Timing diagram of the DAQ output electronic signals. A secondary
scintillation pulse from the GEMs triggers the Acqiris digitisers to record
waveforms of the induced charge pulses. The camera runs in a free continuous
mode with a rolling shutter and a minimum exposure time of 11.2 ms. All the
triggers are recorded by the FPGA pulse register.

Although the length of the recorded waveforms is only a few $\mu$s, the
deadtime caused by the data-transfer bottleneck is around 3 ms. Due to this,
the following event (depicted by a dotted line), will not be recorded by the
digitiser, and signals from the PMT and the electrodes will be missing.
However, it will still be captured by the camera, and hence it delivers only
partial information about this event – causing a potential background from
random coincidences. To record this kind of occurrence and avoid event
confusion in the image analysis an FPGA pulse counter with 1 ns timing
resolution was developed; this will help MiDAQ record the timing of all
triggers (DT) as well as the camera’s output pulses indicating the start time
(FT) of each frame. The timing information of the recorded waveforms (DTj) and
individual exposures (FTi) will be embedded into the digitiser’s data stream
and in the frame’s metadata, respectively, and used later to synchronise
between the j-th waveform and i-th frame. A future development will include
the full digitisation of all PMT waveforms by the FPGA.

Ancillary sensors and other equipment required for operation of the experiment
are queried each minute and their information is recorded by MiDAQ with each
event, allowing its use during offline analysis. This includes the pressure
and composition of the gas in the chamber, the ambient temperature, the bias
voltages on the TPC electrodes and the position of the 55Fe calibration
source.

Data from the Acqiris digitisers will be stored in binary format. Each event
includes the 66 Acqiris waveforms, the unique trigger timestamp plus the
ancillary sensors – taking up around 12 kB per event after compression. In
addition, each binary file includes a global header with the relevant
information on the channel and trigger settings used in the run. The images
from the CMOS camera are stored in MTIFF files, with each 16-bit TIFF image in
$2\times 2$ binning mode, occupying 1.2 MB after compression. The image
timestamp and the FPGA trigger timing information are recorded as metadata.
Significant local storage ensures continuous operation while saved data are
transferred to a computing cluster for offline analysis.

A new software framework – MiDAS – was developed for data reduction and
extraction of the information of interest from each triggered event. This will
be carried out offline using dedicated C++ algorithms. Besides pulse
identification and parameterisation functions, MiDAS provides also event
display.

###  3.5 Calibration

The planned calibration measurements will deliver the necessary information to
optimise the operation of the detector for each gas composition and pressure,
and the 3D reconstruction of the ionisation track images. The various OTPC
electrodes will be biased to provide high gas gain, good energy resolution,
large dynamic range, minimum electron diffusion, and stable operation free
from destructive sparks. Optimisation of these parameters will be carried out
using low energy X-rays from 55Fe (5.9 keV) and 241Am (13.8 keV),
$\alpha$-particles from 241Am, and highly-ionising fission fragments from
252Cf.

Two dedicated X-ray calibration windows are provided on one of the flanges,
sealed with 50 $\mathrm{\mu}$m Al foil; these have around 5 mm wide entrance
aperture and a pyramidal shape that allows exposure of the drift and transfer
regions separately. The 55Fe source is permanently attached to the chamber on
a movable shaft for remote deployment on demand. The 5.9 keV 55Fe X-rays are a
key calibration tool, producing photoelectrons just above our 5 keV ER
threshold uniformly across the active volume; sub-keV Auger electrons should
be visible in some cases too. A 80 MBq source will be used for this purpose.
Each X-ray interaction creates an average of 172 electron-ion pairs for a
W-value of 34.2 eV for CF4 [75]. From the number of primary pairs the gas gain
of the GEM system will be determined from a charge-to-voltage calibration of
the charge-sensitive preamplifier connected to the second GEM (cf. Fig. 9). A
second calibration point is provided by the 13.8 keV X-rays from a 7.7 MBq
241Am source.

The response of the camera to low-energy electrons (range, energy and
uniformity) will be calibrated with the same X-ray sources. After subtracting
the mean noise using dark frames, the electron energy is extracted by
integrating the pixel values after applying a noise smoothing image filter. A
previous energy measurement of 55Fe interactions with our CMOS camera yielded
a good energy resolution of 28% (FWHM). The electron range will also be
studied carefully at these energies. These datasets will be essential for
flat-fielding the camera image and the PMT response.

The transverse diffusion of electrons during their drift towards the anode is
another critical parameter affecting the amount of detail that can be
extracted from the particle tracks, i.e. the spatial resolution in the camera
images. This will be quantified by measuring the width of $\alpha$-particle
tracks fired at known locations parallel to the anode plane. The 241Am
$\alpha$-source can be deployed inside the chamber, behind a 1-cm long PEEK
collimator with 1-mm aperture, which is attached to the cathode frame and
pointing from the side of the active region. These tracks will also help
develop the 3D reconstruction algorithms.

A 252Cf fission source will be used to evaluate the detector response to
highly-ionising particles that can potentially limit the dynamic range of the
detector by causing destructive sparks. Fission fragments can have ionisation
densities much larger than those of C and F recoils from D-T neutrons, and
hence the dynamic range of the detector can be probed and safe operating
voltages determined before the actual neutron beam experiment. A 37 Bq 252Cf
fission source has been acquired for this purpose. The average energies of the
fission fragments are 103 MeV and 78 MeV for the average light and heavy
fragments, respectively, leading to primary ionisation densities approximately
ten times larger than the maximum expected from the C and F recoils.The source
will be mounted in two locations inside the chamber: behind the cathode mesh
and on the side of the TPC, with the particle beam oriented perpendicularly to
the ITO strips.

The uniformity and cross-talk of the anode-strip response will be measured
using a precision pulse generator with a fast rise time (2 ns) using test
inputs in the preamplifiers. A charge-injection probe was used prior to
assembly to study the ionisation response at various points along a strip, to
inform the electronics response model.

Blue LED pulses will be used periodically to monitor the single photoelectron
response of the PMT and the timing synchronisation between the PMT and the
camera. One LED is fibre-coupled into the space in front of the camera (also
visible to the PMT) and another is installed in the PMT enclosure.

Calibration of the camera response to NR interactions is needed to evaluate
their energy and hence enable the nuclear scattering kinematics: this requires
first the discrimination between C and F recoils, which we aim to achieve by
comparing their stopping power against total energy. We intend to measure the
quenching factor (QF) of CF4 and other gases in the $\sim$0.1–1 MeV energy
range. In addition to supporting the Migdal analysis, these measurements are
of interest to the dark matter community as such data are scarce. The well-
defined neutron direction in concert with a measurement of the recoil angle –
within some angular resolution – can potentially provide a precise estimate of
the recoil energy – cf. A. The recoiling species and recoil angle can be
determined from the 3D reconstructed tracks. The estimated recoil kinetic
energy can then be compared to the energy deposited in the drift region by the
energetic ions to provide the electron-equivalent deposited energy and hence a
QF measurement. We plan to conduct such measurements also at lower GEM gain
(to avoid saturation) and at several drift electric fields to check for charge
recombination effects.

Figure 13: Quenching factor of C and F ions in CF4 estimated using TRIM and
the methods found in Ref. [53] (labelled ‘TRIM-C/F’ and ‘Hitachi-C/F’).
Experimental QF values reported in Ref. [76] for C and F ions in CF4 are also
shown (‘Comimac-C/F’).

Prior to such QF measurements, we will use the quenching factors estimated
from TRIM to reconstruct NR energies in the Migdal search. This is a
reasonably well established technique where such measurements are unavailable,
with TRIM providing reasonable values – particularly for ion energies in the
tens of keV. Other QF estimates for CF4 can be found in [53], which combines
methods from Ref. [77] and energy loss calculations from SRIM to calculate the
quenching factor in molecular gases. Ref. [76] also includes a QF measurement
for C and F ions in 50 Torr CF4 gas. Figure 13 depicts all of these data.

##  4 Neutron beam

###  4.1 Facility and generators

The MIGDAL experiment will be hosted at the ISIS Neutron and Muon Source
facility of the Rutherford Appleton Laboratory (UK). The choice of the
specific neutron sources is driven by two factors. Firstly, the suppressed
cross section of the Migdal effect requires the use of intense neutron beams.
Secondly, monoenergetic sources are preferred for an initial measurement in
order to control systematic uncertainties from the neutron energy spectrum.
For these reasons MIGDAL will use commercial deuterium-deuterium (D-D) and
deuterium-tritium (D-T) fusion generators at the Neutron Irradiation
Laboratory for Electronics (NILE) at ISIS, as depicted in Fig. 14.

Figure 14: Rendered view of the experimental set up at the NILE facility with
the MIGDAL detector deployed in front of the D-T generator within the neutron
bunker (some of the upper shielding removed for the purpose of display). The
long copper-made D-T collimator can be seen encased in the multi-layer shield.
The control room is located outside of the concrete wall.

Initially, the experiment will use a D-D generator from Adelphi Technology
Inc. Nominally, this source produces monoenergetic neutrons at around 2.45
MeV, emitted isotropically at a rate of 109 n/s. However, it should be noted
that 2.45 MeV is the kinetic energy of neutrons emitted in the fusion reaction
for the hypothetical case when the reactants are at rest: the precise neutron
energy is given by the kinematics of the reactants and, for the real case of a
D beam accelerated onto a D target, it is a function of the emission angle and
of the energy of the incoming ion – i.e., of the applied high voltage [78]. At
100 kV operating voltage, appropriate for the Adelphi device, we expect the
neutron energy to vary from around 2.15 MeV at 180∘ (backward direction) to
2.8 MeV at 0∘ (forward direction). The energy is $\approx$2.47 MeV at 90∘,
where the MIGDAL experiment is placed. The flux per unit solid angle has also
a marked dependence on the emission angle [79]. Considering this angular
distribution together with the slowing down of the deuterium ions in the
target, the result is a broadening of the neutron energy spectrum with respect
to the ideal (monoenergetic) case, as described in Ref. [80]. In that
reference the broadening is shown to reach a minimum of around 2% (FWHM) at
90∘ and a maximum at 0∘. While the flux per unit angle is lowest in the
perpendicular direction (by a factor of $\sim$2) due to the geometry of this
generator, the experiment can be placed closer in this orientation, partially
compensating for the lower flux. These reasons motivate the decision to place
the MIGDAL experiment at 90∘ for the D-D generator setup.

In a second stage of the experiment we will employ a D-T generator (also from
Adelphi) that emits $\sim$14 MeV neutrons with a yield of 1010 n/s. This
device also uses a microwave plasma ion source and a high voltage to induce
the fusion reaction on a target, and can produce neutrons either continuously
or in pulses with a minimum length of 100 $\mu$s. The D-T generator energy and
flux also have an angular dependence [78, 81], although the flux anisotropy is
much less severe with respect to the D-D case: there is only a 3% difference
in angular flux and the source can be well approximated as isotropic. For 100
kV operation, the neutron energy varies from around 13.5 MeV at 180∘ to 14.7
MeV at 0∘, and is $\approx$14.1 MeV in the perpendicular direction.
Considering the geometry of the D-T generator, it was decided that the
experiment would be placed at 0∘ in the D-T configuration, corresponding to
14.7 MeV neutron energy. This is the deployment shown in Fig. 14. An
experimental study of the flux and energy broadening similar to that presented
in Ref. [82] is under way.

While the D-D generator has a lower yield than the D-T source, the lower
neutron energy in the former case implies suppressed levels of secondary
radiation from inelastic scattering, which is expected to lead to lower
backgrounds in the search for the Migdal effect. In addition, D-D neutrons
will allow the Migdal effect to be studied at lower NR energies, approaching
the regime of interest for direct dark matter detection. On the other hand,
the D-T device will allow the verification of new predictions in a different
kinematic regime which indicate that multiple Migdal ionisation becomes
significant [39].

In addition to neutrons from nuclear fusion, the D-D and D-T sources will also
emit an intense flux of secondary radiation due to inelastic interactions and
radiative capture in the generator material, plus an X-ray component caused by
bremsstrahlung of electrons from the generator plasma. Due to the small mean
free path of charged particles in this energy regime, this secondary radiation
will consist mostly of $\gamma$-rays. The photon flux will be measured in-situ
after commissioning of the devices. The background from the secondary
radiation produced by the generators is assessed in Section 6.2.

The NILE facility, shown in Fig. 14, consists of a concrete bunker situated at
ISIS and will accommodate both generators; it features interlocked access. An
external control room hosts the DAQ and control electronics for the
experiment. The thickness of the bunker walls and the distribution of
additional concrete blocks around the D-T generator has been determined by
radio-protection considerations. Besides this shielding intended for
biological safety, experiments at NILE such as MIGDAL must include additional
shielding and collimation in order to ensure that the background from
secondary radiation is suppressed to acceptable levels. The specific shielding
developed for MIGDAL is discussed below.

In a future phase, the experiment may be deployed at the ChipIr instrument at
the Second Target Station of ISIS. The ChipIr instrument [83] provides an
intense and collimated beam of neutrons with spectrum similar to that produced
in the atmosphere by cosmic radiation (5.6$\times$106 n/cm2/s above 10 MeV)
[84]. One of the main applications of this facility is to test the effect of
fast neutrons on electronic devices. The ChipIr neutrons are produced by
spallation of 800 MeV protons of the ISIS accelerator onto a tantalum-coated
tungsten target. The ChipIR spectrum is continuous and extends to much higher
energies, and hence it offers the possibility of testing the Migdal effect in
another kinematic regime; this setup would bring a new class of backgrounds
that have not been studied.

###  4.2 Shield and collimator design

The experiment requires a well-defined beam of primary neutrons that passes
through the active volume while avoiding any other primary or secondary
radiation that would otherwise interact in the OTPC. For this purpose the
detector chamber is surrounded by dedicated shielding, with a frontal
penetration to accept primary neutrons (termed the ‘collimator’ in this
paper), plus another opening downstream to allow the beam to exit the chamber
with minimal interactions.

As mentioned in Section 3.1, an air-filled collimator design has been adopted,
followed by a 150-$\mu$m thick Al entrance window: Monte Carlo simulations
indicate that the secondary radiation produced by neutron interactions in the
air outside of the chamber or in the window are not a dominant source of
background. Most secondary radiation detected in the OTPC is typically
produced in two steps. Inelastic neutron interactions produce $\gamma$-rays in
the surrounding materials (mainly shielding and the collimator itself). These
photons then interact in the collimator and detector elements (mainly cathode
and first GEM) to produce electrons that easily reach the active volume. Other
contributions to the total non-NR event rate are subdominant. In particular,
events where a photon interacts directly in the active volume are suppressed
owing to the low gas pressure.

The shielding and collimator designs are driven by two needs. Firstly, NR
vertices in the active volume should lie between 6 mm and 24 mm from the first
GEM, in order to $i$) ensure that the Migdal event is largely contained in the
active region, and $ii$) minimise diffusion of the drifting electrons. This
requirement constrains the beam width in the direction perpendicular to the
GEM surface, and implies the suppression of the beam halo in order to avoid
neutron interactions in the GEMs and the cathode. Secondly, the total
interaction rate in the active volume must approach the camera frame rate
($\sim$90 Hz) to maximise the number of single-interaction frames. Based on
these requirements, the design of the shielding and collimator proceeded by
minimising the fraction $f_{other}$ of non-NR events in the total interaction
rate. At the end of this optimisation procedure it was verified that the
resulting designs do not contribute significantly to the background for the
Migdal search (cf. Section 6.2).

This optimisation procedure was organised in three stages. First, only the
front part of the shielding design was refined, in the absence of any other
material surrounding the experiment, and assuming a simple collimator design
by default. Second, the collimator design was iterated using the front
shielding configuration resulting from the previous step. Finally, the lateral
and posterior parts of the shielding were included and optimised, accounting
for the effect of the bunker and the concrete material within.

The above procedure relies extensively on Monte Carlo simulations using two
frameworks. Initially, the BDSim software [85] was used for an initial
assessment of the thickness of each shielding layer, based on the predicted
radiation fluxes entering the detector chamber. BDSim is built on top of
GEANT4, customised to study radiation fluxes caused by the interaction of
particle beams with surrounding materials. A dedicated GEANT4 simulation of
the experiment and its environment was then developed to complete the
remaining stages of the optimisation.

The layout of the front part of the shielding depends on the neutron source
considered. For the D-D generator, it consists of a layer of borated high-
density polyethylene (BHDPE) to efficiently moderate and subsequently capture
neutrons, followed by a layer of lead to attenuate $\gamma$-rays from
inelastic scattering and radiative capture. The optimal thickness of each
layer was found to be 30 cm and 10 cm, respectively. The shielding for the D-T
generator (Fig. 14) will also use BHDPE and lead, but is preceded by a layer
of iron to efficiently moderate primary neutrons down to $\sim$5 MeV via
inelastic scattering. In this case, the optimal thickness of the iron, BHDPE
and lead layers was found to be 70 cm, 20 cm and 10 cm, respectively.

The collimator consists of a penetration (hereafter the beam ‘tunnel’) in the
front shield, surrounded by walls which fulfill the following purposes: they
moderate primary neutrons that lie outside the acceptance of the active volume
whilst avoiding part of the shielding as they propagate through the beam
tunnel; and they attenuate $\gamma$-rays from the shielding that might enter
the beam tunnel and reach the detector chamber. The entire collimator setup
will be embedded in a rectangular passage through the shielding with
3$\times$9 cm2 cross section.

The D-D collimator walls consist of an inner layer of BHDPE for neutron
moderation, surrounded by a thin layer of lead for $\gamma$-ray attenuation.
This arrangement is convenient because primary neutrons that reach the
collimator lead through the beam tunnel can be moderated by the innermost
BHDPE layer, and therefore the probability of producing inelastic scattering
in that metal is suppressed. In turn, the D-T collimator walls are made from a
single layer of copper only, which provides both efficient fast-neutron
moderation via inelastic scattering and $\gamma$-ray attenuation (while iron
could also be considered for this purpose, copper was preferred for
engineering reasons). Note that since neutrons enter the collimator walls at
grazing incidence, even thin BHDPE or Cu layers (for the D-D and D-T
generators, respectively) are able to provide sufficient moderation.

The longitudinal section of the beam tunnel in the camera ($x,y$) plane is
shown in Fig. 15. In this plane, the first part of the tunnel has constant
width, changing to a linear taper after 35 cm. This design, hereafter referred
to as the double-trapezoid configuration, has been devised to account for the
fact that primary neutrons are emitted by a small but extended source. For the
D-D generator, Monte Carlo simulations show that the double-trapezoid
configuration improves $f_{other}$ by $\sim$25% compared to the simpler fully-
tapered design which is optimal for a point source. Similar results were
obtained for the D-T generator.

Figure 15: Longitudinal section of the front shield and collimator designed
for the D-D source, illustrating the double-trapezoid collimator concept. The
materials are borated polyethylene (light grey) and lead (blue grey). The
approximate size of the D-D generator target is also shown, along with the
lines that define the envelope of the beam passing through the collimator
(red).

The width of the beam tunnel entrance is determined by the size of the region
where neutrons are emitted inside the generator, while the exit aperture is
set by the required size of the beam in the active volume. The remaining
dimensions of the tunnel (the intersection between the two parts of the
tunnel, and the slope of the divergent walls) are adjusted in order to ensure
that the walls of the last part of the collimator lie outside the line-of-
sight of the primary neutrons (see Fig. 15), thereby suppressing the
production of secondary radiation from inelastic scattering near the active
volume.

The section of the beam entering the active volume has diffuse edges, and its
size is given as the full width at half maximum of the neutron distribution in
the transverse plane. For the D-D and D-T generators, the size of the beam
section is predicted to be 1.4$\times$9.0 cm2 and 1.3$\times$9.2 cm2,
respectively. The size of the beam halo is defined, for each axis, as the
width of the region that contains 99% of the total neutron flux entering the
active volume. The corresponding predictions are 1.8$\times$9.0 cm2 and
1.5$\times$9.2 cm2 for the D-D and D-T generators, respectively. While
neutrons entering the active volume are mostly monoenergetic, the spectrum
features a low-energy tail due to elastic and inelastic interactions in the
front shielding and the collimator. This population of degraded energy
represents only $\sim$3% and $\sim$1% of the total neutron flux for the D-D
and D-T generators. We have also confirmed that the fraction of ‘backward
neutrons’ entering the OTPC after scattering in the shielding is small: only
$\sim$1% of the flux above 100 keV neutron energy with the D-D generator, and
lower still for D-T neutrons.

Despite this being a leading consideration for our material selection, neutron
capture in the front shield and collimator will activate materials and produce
$\gamma$-rays that may enter the active volume. For the main elements present
in these structures (H, C, Fe, Cu and Pb), neutron capture produces either
stable nuclides or radioisotopes where $\gamma$-ray emission either does not
occur (e.g. 209Pb) or is not important (e.g. 54Fe and 63Cu). For 65Cu (30.8%
of natural abundance), the probability of $\gamma$-ray emission from radiative
capture is non-negligible, but still modest (9.2%).

Gamma-rays produced by inelastic neutron interaction in the generator head
will also reach the active volume through the beam tunnel. This is the main
contribution to the total $\gamma$-ray flux entering the active volume for the
D-T source, while this flux is subdominant for the D-D source due to the lower
energy and different configuration of the generator head. The photon rate
entering the active volume for the D-T generator is predicted to be
approximately 600 Hz, corresponding to $\sim$70% of the total $\gamma$-ray
flux. This rate is $\sim$0.1% of that of primary D-T neutrons entering the
detector. The low-energy component of this photon flux (below 200 keV) is
expected to be the dominant source of background for the D-T experiment, as
detailed in Section 6.2. A thin (2 mm) layer of lead placed between the
generator head and the collimator is predicted to attenuate these low-energy
photons by 58% while allowing 82% of primary neutrons to pass through without
scattering. A combination of 1.3 mm of lead followed by 1 mm of tin to absorb
the K-shell X-rays from the first layer is able to increase the photon
attenuation to 69% while keeping the same fraction of unscattered primary
neutrons.

##  5 Track simulations

A dedicated ‘end-to-end’ simulation of the detector has been created to study
tracks produced in the OTPC. This comprises three main parts, which model the
journey of ionisation electrons from production in the active region to
collection by the ITO strips. These simulation elements cover: the active
volume, where primary tracks are created and the ionisation drifts towards the
entrance to the first GEM; the GEM system, including the two GEMs and the
transfer region between them; and the induction gap, where a current is
induced on the ITO strips. These three components are detailed below.

###  5.1 Primary tracks

The first stage of the simulation is the production of nuclear and electron
recoil tracks in the active volume with appropriate ionisation. Two pieces of
software are used to generate the tracks: Degrad [48], a Fortran program which
produces sites of ionisation for electron tracks with energies above the
detection threshold; and TRIM [49], a Visual Basic program which is used to
simulate the path of nuclear recoils through a medium. TRIM not only details
the energy loss due to electronic processes but, crucially, it includes
information about the generated secondaries in its detailed collision
output.444TRIM is operated in the fast ‘Ion Distribution and Quick Calculation
of Damage’ mode. We utilise the EXYZ.TXT output file, which gives details of
all collisions of the primary ion even without the ‘Full Cascade’ mode; where
the species of the secondary nuclear recoil is ambiguous, the COLLISION.TXT
file can be used to determine it. Once the species and energies of the
secondary nuclear recoils have been ascertained, other primary tracks of
appropriate energy can be rotated into place and used as secondaries. Since
each primary track has details of its own secondary collisions, the process
can be repeated recursively until all recoils have been accounted for
throughout the whole chain. This is more efficient than using the full cascade
mode. By locating the secondary NR sites and ascertaining the target atom
species, subsequent secondary tracks can be ‘stitched’ into place at the
appropriate angles by considering the kinematics of elastic scattering.
Ignoring inelastic scattering in these determinations is expected to produce
angular deviations of $<$5∘, which is not resolvable by our detector after
diffusion.

TRIM does not provide the ionisation deposits along NR tracks, but the
tabulated electronic energy loss can be used to approximate this. The energy
lost due to electronic processes along each step in a track is divided by the
W-value of the gas to give the mean number of ionisation electrons expected
per step. The number actually generated is re-sampled from a Poisson
distribution with a Fano factor of 0.2 appropriate for CF4 [86] and released
uniformly along each (small) step. We confirmed that the QF calculated for
these tracks agrees with that returned by TRIM.

In order to produce Migdal-like events, an electron track is overlaid on a
nuclear recoil track with a common vertex. The initial NR track direction is
obtained either from Monte Carlo or from our analytical calculations (cf. A),
while the electron is emitted isotropically. Although calculations in helium
show that the emission is preferentially in the direction opposite to the
nuclear recoil [22], we conservatively assume that the Migdal electron is
emitted isotropically, which implies some fraction of electrons will be
aligned with, and therefore hidden by, the NR track. These ‘Migdal electrons’
are generated with Degrad, specifically from X-ray interactions yielding the
appropriate (photo-)electron energy plus the accompanying atomic deexcitation
which is also released at the vertex. Figure 16 shows two examples of ‘Migdal-
like’ events. In each event, ionisation electrons are represented by black
points in the 3D image and by blue points in the projections onto 2D planes.

Figure 16: Two 3D representations of ‘Migdal-like’ events after 15 mm of drift
in the $z$-direction. The $x\\!-\\!y$ and $x\\!-\\!z$ projections are labelled
according to their mode of acquisition ($y\\!-\\!z$ is not recorded). The left
event contains a 7.5 keV electron, with a 5 keV electron on the right panel.
Both are paired with a 150 keV fluorine recoil (denser track). The right image
shows a clear fork-like topology towards the beginning of the NR track due to
the production of a 14 keV secondary (carbon) recoil (see Section 6.2.1). The
position of the Migdal vertex is (0,0,0).

###  5.2 Electron transport in gas

The ionisation electrons produced in the active volume drift under the
influence of an electric field towards the anode; avalanche multiplication
takes place upon entering the GEM stack. The transport of electrons in the gas
is modelled using the Garfield++ [87, 88, 50] framework, which relies on
Magboltz [89, 90] for the estimation of the transport properties in the gas
mixture. The electron drift velocity, longitudinal and transverse diffusion in
CF4 at 50 Torr provided by Magboltz are given in Fig. 17 (left) as a function
of electric field. Figure 17 (right) shows the corresponding Townsend and
attachment coefficients.

In an effort to optimise the simulation speed while retaining the highest
possible precision, different approaches are used for the different regions.
In the drift region diffusion is modelled through a Gaussian smearing. Within
the GEMs, where the avalanche amplification takes place, and in the transfer
region between the two GEMs, the highest level of detail is obtained by
exploiting the microscopic tracking capability of Garfield++. In this, each
electron is followed between individual collisions with the atoms of the gas.
Finally, in the induction region, where a large number of electrons is
present, the Garfield Monte-Carlo integration technique is applied. In this
technique, the transport parameters are integrated over 100 collisions, and
subsequently the longitudinal and transverse diffusion is sampled from the
expected distribution.

Figure 17: Electron transport properties of CF4 at 50 Torr. Left – Drift
velocity and diffusion. Right – Attachment and Townsend coefficients. Nominal
fields in the drift (D), transfer (T) and induction (I) regions are indicated.

###  5.3 The Gas Electron Multipliers

Electron multiplication in the detector is realised as a two-stage process,
whereby the electrons produced in the avalanche in the first GEM subsequently
initiate new avalanches in the second GEM. Thus, the operating voltages of the
two GEMs need to be tuned both for overall gain and for gain balance between
the two GEMs. The electric field strength in the transfer region between the
two GEMs also needs to be chosen to improve the transparency of the system, in
terms of the fraction of electrons produced in the first GEM that enter the
holes of the second GEM. At the same time, any attachment of electrons in the
CF4 needs to be minimised.

As mentioned above, within the two GEMs and in the transfer region between
them the electron transport is modelled using the microscopic tracking
capabilities of Garfield++. These provide the highest level of detail but
result in substantial computational cost, given the large number of electrons
being microscopically tracked, which prohibits the production of the number of
events required for more detailed studies. Thus, an “event library” approach
is pursued, where the library consists of thousands of single electron events.
In each case one electron is released at a height of 50 $\mathrm{\mu}$m above
the first GEM with a random position within the primitive cell of the GEM
structure. The electron and its associated avalanche are microscopically
tracked through the system of the two GEMs, and the spatial and timing
information of the produced electrons arriving at 20 $\mathrm{\mu}$m below the
bottom plane of the second GEM are stored, along with the starting position of
the initial electron. For the simulation of large numbers of events, the
ionisation electrons are transported within the drift region until they reach
a distance of 50 $\mathrm{\mu}$m above the first GEM. For each ionisation
electron, its position is projected onto the primitive cell and the spatially
closest electron from the event library is identified. The stored outcome for
this fully simulated library event is retrieved, and the positions of the
resulting electrons (if any) are projected onto the cell of the ionisation
electron. This procedure allows for the benefits of microscopic tracking of
electrons in the ‘end-to-end’ simulation, while keeping the computational cost
for events consisting of hundreds or thousands of ionisation electrons at
manageable levels. For the setup used in the following results, the mean
charge gain after both GEMs is 0.6$\times$105.

###  5.4 ITO strips

Charge-readout signals are simulated with Gmsh [91], Elmer [92] and
Garfield++. Gmsh and Elmer are used to define the geometry of the simulation
space and to calculate electrostatic fields, respectively, while Garfield++ is
used to simulate the electron drift and calculate the resulting ITO strip
signals.

The simulation geometry is a 2D slice through 30 ITO strips, corresponding to
a width along $x$ of 25 mm. The total depth is 11.1 mm, starting at the exit
of the second GEM and ending 5 mm past the ITO plate (this latter region helps
to more accurately model electric-field lines around the ITO strips). A
uniform potential of $-$80 V is considered at the second GEM plane, which
results in the nominal 400 V/cm electric field in the induction gap. The
strips are charged to $+1$ V (individually, for the signal weighting fields),
the bottom is grounded, and the sides are periodic.

The currents induced on the ITO strips by the drifting electrons leaving the
second GEM are convolved with the response of the electronics, including
cross-talk, as discussed in Section 5.5, to generate the expected voltage
signals on each strip. The current signals prior to this convolution are shown
in Fig. 18, for the two benchmark events shown previously in Fig. 16.

Figure 18: The ITO-strip current signals produced by the two example events
shown in Fig. 16 prior to folding in the electronics response. The current
induced on each strip is represented by the height of the strip and its
colour. In each plot the location of the electronic recoil is marked with
“ER”.

###  5.5 Electronics response

The ITO strips exhibit not only significant series resistance (on the order of
6 k$\Omega$/m), but also significant capacitance between strips (65 pF/m).
Thus, any simulation of the response of the detector must include not only the
amplifier and digitiser, but also the ITO strips themselves. This was
implemented by discretising them into 5 segments, and the flat-cable between
the ITO and the amplifier into 3 segments, with the resistance and capacitance
and each segment modelled with a finite-element method. The resulting
electrical circuit was simulated using Cadence Spectre [93].

The simulated response to charge deposited at the midpoint along a strip, and
how this manifests on different channels, is shown in Fig. 19. The plot
highlights a non-negligible amount of coupling between strips; therefore, to
accurately model the digitised signal from simulated events the output from
the electrical model described above was used in Garfield++ to account for
both the shaping of the signals and the lateral smearing due to coupling
between channels. We plan to deconvolve the electronics response function from
the measured waveforms such that the current signals shown previously in Fig.
18 will resemble the data used for further analysis.

Figure 19: Simulated electronics response to charge deposited in the middle of
an ITO strip. The signal depends not only on the charge deposited on the strip
of interest, but also that induced on adjacent strips (up to four strips
either side).

###  5.6 The camera image

Electrons exiting the second GEM stage are used to generate the camera images
of simulated tracks. The photon yield calculated in Section 3.2.1 is assumed
to map onto a geometrically perfect image, which is binned using the
parameters of the CMOS camera described in Section 3.2. Noise is added to each
pixel based on measurements with this camera model for the proposed mode of
operation; the overall signal-to-noise ratio matches that obtained in
preliminary tests. Simulated images of the two Migdal events mentioned above
are shown in Fig. 20.

Figure 20: Simulated camera images of the two benchmark Migdal events shown in
Fig. 16; both NR and ER tracks are visible in each case, with the latter
corresponding to 7.5 keV and 5.0 keV Migdal electrons on the left and right,
respectively. Both images have a realistic sample of camera noise added; the
average (master) dark frame has been subtracted.

###  5.7 Track reconstruction

Tracks are reconstructed in 3D by combining data from the ITO readout, the
camera image and the PMT – initially matched by the MiDAS data reduction
software.

The ITO signals are processed with a 2D deconvolution method similar to that
used in Ref. [94], using the response of the electronics and cross-talk shown
in Fig. 19, to obtain the induced current on each strip. A second 2D
deconvolution is performed using the mean response of a single electron in the
induction gap, obtained from simulation, to find the charge per nanosecond on
each strip. This provides information about the arrival time of each electron
and, using the expected drift velocity, it can be used to estimate the extent
of the track in the $z$ direction.

The camera images also undergo several steps of processing to reconstruct the
2D track information. First, a low-pass filter is applied to remove the GEM
hole pattern from the images (which is visible in Fig. 20). The resulting
image is deconvolved using the Richardson-Lucy algorithm [95, 96] with a 2D
Gaussian point spread function the width of which is estimated based on the
average diffusion at that depth determined from the S1-S2 time delay. The
deconvolved images are input to a track finding algorithm [97] that extracts
the detailed 2D track properties, such as the range, energy loss rate and
initial direction of the particle. The result of this procedure applied to the
simulated Migdal events are shown in Fig. 21.555A grayscale version of Fig. 21
was analysed using ImageJ with plugin Ridge Detection [98].

Figure 21: Reconstructed track for the 5 keV Migdal electron event shown in
Fig. 20 (right), after applying deconvolution and track-finding algorithms to
the camera image; the resultant track ridge is shown in red. The plot in the
lower part of the frame shows the intensity integrated transversally along the
tracks (rather than a straight projection) and is meant to illustrate the very
different energy loss rates along NR and ER tracks.

##  6 Sensitivity

Having described the detector, neutron beam and simulation framework in some
detail, we can now present a more realistic calculation of the signal and
background rates in the fiducial volume. We begin by setting out the expected
number of neutron-induced nuclear recoils and expected Migdal event rates, and
then discuss in detail the background topologies which could affect their
measurement. From the expected signal and background rates an indicative
discovery sensitivity is presented.

###  6.1 Signal acceptance

We expect to operate the experiment for several consecutive days with high
duty cycle, probably limited by the recovery from GEM discharges, progressive
loss of gas purity, and the regular calibrations for gain monitoring. We will
term each few-day long data-taking period at constant operating conditions
(e.g. pressure) a ‘run’.

To maximise duty cycle we will operate the neutron generators in continuous
mode; technical breaks are not deemed necessary by the manufacturer over such
periods. Data can be acquired at the maximum camera speed and transferred from
the DAQ computer to the offline PB-scale storage system with no dead time
envisaged.

The detector stability will be regularly monitored by gas-gain measurements
using the external 55Fe source, and checking the synchronisation between the
camera and the digitiser systems will rely on LED signals. These calibrations
are planned to total 30 minutes every 6 hours, reducing the duty cycle to 92%.

Replenishing the ageing gas and re-biasing the OTPC will take around 30
minutes, and we assume (conservatively) that this will be performed every 6
hours; the above calibrations will be split before and after the gas
replenishing. This will bring the duty cycle down to 84%.

The total number of camera frames recorded in a 5 calendar day run may
approach 40 million (including calibrations), taking up 44 TB of disk storage.

We take the interaction rates in CF4 from Table 1. The fraction of frames with
only one NR interaction in the full active region is $\approx$1/3 for both
generators; we remove frames with more than one interaction ($\approx$15%) –
in many such cases the DAQ will have triggered only once, and there may be
scope for event confusion. In addition, in the first instance the Migdal
analysis will consider only NR tracks fully contained within the smaller
8$\times$8 cm2 fiducial area. With the above considerations, the 5-day run
with 50 Torr of CF4 will accumulate 1.8 and 2.3 million single NR track images
for analysis with the D-D and D-T generators, respectively.

The Migdal probabilities for tracks above threshold fully contained in the
fiducial volume and with ER and NR energies within our ROI are
3.26$\times$10-5 and 8.42$\times$10-5 for the two generators, as set out on
Section 2; these calculations follow Ref. [39].

We must now fold in the efficiency for detecting the Migdal topology in
analysis, including factors such as the highly-variable electron track shape,
energy resolution and other detector effects in the various subsystems. A
detailed study of this topic lies beyond the scope of this paper; instead,
using the simulation framework described in the previous section, we undertook
a blind data challenge to evaluate this efficiency for the worst case
scenario: isotropically-emitted electrons at the nominal 5-keV threshold and
fluorine NR tracks also near their energy threshold. This dataset included a
few hundred events including both Migdal topologies as well as bare nuclear
recoils, in approximately similar numbers; this exercise returned zero false
positives, and an average of 75% of all Migdal events were correctly
identified by the analysers inspecting simulated camera images alone (no ITO
or PMT information). We apply this efficiency to the above Migdal event rates
to arrive at a Migdal detection rate of 8.9 events per calendar day for D-D
neutrons and 29.3 events/day with the D-T generator, or around 44 and 147
events in a 5-day run, respectively. Note that the numbers given in Table 1 do
not include this detection efficiency, single-track frame probability, or the
operational duty cycle.

###  6.2 Backgrounds

We discuss potential backgrounds to this measurement with reference to Table
3, which lists the estimated number of counts per million neutron-induced
recoil tracks in CF4 gas at 50 Torr. Background counts are considered in the
previously-defined ROI, including the 5–15 keV electron energy range; we
consider electron vertices located up to 3 mm from the NR track origin. Signal
rates in the same ROI are also given for comparison. To highlight effects
which we expect to find in the data but that do not necessarily translate into
background counts, we list also the count rate integrated for electron
energies above 0.5 keV; most of these will contribute to the track ‘penumbra’,
but some may cause distinct interactions clearly resolved from the NR track
(e.g. occupying single pixels in the GEM image). In both cases we assume that
the electron detection efficiency is 100%.

In the following it will be confirmed that the sensitivity of the experiment
relies significantly on the long photon attenuation lengths provided by the
low pressure gas – as illustrated in Fig. 5 – and this mitigates against
several backgrounds. A potential major challenge of a different nature comes
from the stochastic nature of the atomic cascades which may develop from the
primary recoil; in particular, a secondary recoil track may be spawned close
to the origin of the initial track to create a fork-like structure which may
be confused with a Migdal vertex in some situations. This background topology
is the most complex and deserves a longer discussion at the end of this
section.

Table 3: Number of background and signal events per million neutron-induced
recoil tracks for D-D (2.47 MeV) and D-T (14.7 MeV) neutrons incident on CF4
gas at 50 Torr. Data are given for $\sim$100 keV nuclear recoil threshold and
$>$0.5 keV and 5–15 keV electron energies, with the electron vertex located up
to 3 mm from the NR track origin. An entry of “0” indicates that the process
cannot occur in the ROI, while “$\approx$0” denotes a negligible rate of
$\ll$0.01 events per million recoils. Individual background components and
topologies are discussed in the text. Signal rates are those from Table 1 for
contained tracks above threshold, normalised per million signal-inducing
events.

Component |  Topology | D-D neutrons | D-T neutrons
---|---|---|---
$>$0.5 | 5–15 keV |  $>$0.5 | 5–15 keV
Recoil-induced $\delta$-rays |  Delta electron from NR track origin |  $\approx$0 | 0 | 541,000 | 0
Particle-Induced X-ray Emission (PIXE) |  |  |  |  |
X-ray emission |  Photoelectron near NR track origin | 1.8 | 0 | 365 | 0
Auger electrons |  Auger electron from NR track origin | 19.6 | 0 | 42,000 | 0
Bremsstrahlung processes† |  |  |  |  |
Quasi-Free Electron Br. (QFEB) |  Photoelectron near NR track origin | 112 |  $\approx$0 | 288 |  $\approx$0
Secondary Electron Br. (SEB) |  Photoelectron near NR track origin | 115 |  $\approx$0 | 279 |  $\approx$0
Atomic Br. (AB) |  Photoelectron near NR track origin | 70 |  $\approx$0 | 171 |  $\approx$0
Nuclear Br. (NB) |  Photoelectron near NR track origin |  $\approx$0 |  $\approx$0 | 0.013 |  $\approx$0
Neutron inelastic $\gamma$-rays |  Compton electron near NR track origin | 1.6 | 0.47 | 0.86 | 0.25
Random track coincidences |  |  |  |  |
External $\gamma$\- and X-rays |  Photo-/Compton electron near NR track |  $\approx$0 |  $\approx$0 |  $\approx$0 |  $\approx$0
Trace radioisotopes (gas) |  Electron from decay near NR track origin | 0.2 | 0.01 | 0.03 |  $\approx$0
Neutron activation (gas) |  Electron from decay near NR track origin | 0 | 0 |  $\approx$0 |  $\approx$0
Muon-induced $\delta$-rays |  Delta electron near NR track origin |  $\approx$0 |  $\approx$0 |  $\approx$0 |  $\approx$0
Secondary nuclear recoil fork |  NR track fork near track origin | – |  $\approx$1 | – |  $\approx$1
Total background |  Sum of the above components |  | 1.5 |  | 1.3
Migdal signal |  Migdal electron from NR track origin |  | 32.6 |  | 84.2

† These processes were evaluated at the endpoint of the nuclear recoil
spectra.

The first potential background listed in Table 3 is that from
$\delta$-electrons produced by the recoiling nucleus; this contribution was
obtained from a GEANT4 simulation of carbon- and fluorine-induced ionisation
for the D-D and D-T recoil spectra. The maximum energy transfer to an electron
at rest in a binary collision is far below the 5 keV threshold. For example, a
4 MeV carbon ion (near the endpoint of the D-T spectrum) transfers a maximum
of 742 eV to a $\delta$ electron; these energies are modified in collisions
with bound electrons, but this is a small effect for light elements. In
conclusion, although this process does produce a significant number of low-
energy electrons which contribute to broaden the NR track, it does not become
a concerning background to the Migdal measurement.

Particle-induced X-ray emission (PIXE) may result in either X-ray fluorescence
(which may be absorbed near the NR track) or the emission of Auger
electrons.666Catalogues of atomic transition energies and yields can be found
in Refs. [99, 100, 101]. For light elements such carbon and fluorine, Auger
yields far exceed X-ray fluorescence yields. The GEANT4 PIXE models [102, 103]
were used to obtain the particle yields. These were validated for these
elements by scaling the proton cross sections in Ref. [104] for the effective
charge of the heavier projectiles and found to be in good agreement. Auger
electron energies have a maximum of 655 eV for CF4 [55] and so PIXE does not
pose a significant background – although it should be noted that this is not
necessary the case for heavier elements with atomic shell energies in the
electron region of interest.

In collisions of recoiling ions with CF4 molecules several Bremsstrahlung
processes may occur. These photons can release a $\sim$keV electron near the
NR track origin (tail), mimicking a Migdal event. Such processes include
Quasi-Free Electron Bremsstrahlung (QFEB) [105], Secondary Electron
Bremsstrahlung (SEB) [106], Nuclear Bremsstrahlung (NB) [107], and Atomic
Bremsstrahlung (AB) (also known as polarizational radiation) [108]. In the
QFEB process an electron of a target atom is scattered by the Coulomb field of
the incident ion and emits bremsstrahlung radiation. In SEB X-rays are
produced by ionised electrons in the Coulomb field of the target nuclei.
Nuclear bremsstrahlung is produced when a NR is accelerated in the Coulomb
field of the target nucleus.777An identically-named process with interest for
dark matter searches [109] refers instead to the photon emission caused by the
electric dipole created between a recoiling nucleus and the atomic electrons;
this phenomenon is rarer than the Migdal effect and is not considered here. In
the AB process, a bound electron of a target atom is excited to a continuum
state by the incident NR and, returning to its original bound state, a photon
is emitted. These Bremsstrahlung processes have been extensively studied in
the context of PIXE as they constitute backgrounds for elemental analysis, and
the corresponding cross sections have been calculated and confirmed
experimentally. In general, the cross sections scale with the charge and the
velocity of the ion and with the atomic number of the target atom [110, 111].
We have calculated a conservative upper limit on the number of electrons
ejected per million carbon recoils with energies at the endpoint of the D-D
and D-T recoil spectra; this involved the scaling the available cross sections
for protons [111, 112], and it took into account the photon absorption
efficiency in the vicinity of NR tracks. Owing to the low velocity of NRs
compared to that of the protons of the same energy, the probability of X-ray
emission in the energy range of interest is extremely low in both the D-D and
the D-T experiments.

A potentially relevant background occurs when a neutron undergoes inelastic
scattering in the active gas volume and a deexcitation $\gamma$-ray interacts
near the NR vertex from the same interaction. This type of event dominates the
background budget in higher pressure experiments [45]. While the mean photon
interaction length is very large at 50 Torr, the Compton scattering of the 110
keV and 197 keV photons from 19F($n$,$n^{\prime}$) is of some concern: their
energy is just right to produce Compton electrons in the ROI – cf. Fig. 5. The
calculation in Table 3 uses GEANT4 to simulate the production and interaction
of these and similar $\gamma$-rays in the 5–15 keV range. The corresponding
background rate is found to be just below 1 event per million NR tracks – we
predict this to be a leading source of background in our experiment, as shown
in Table 3.

A different class of background (with several contributors) occurs when an NR
track and an unrelated ER track are accidentally recorded in coincidence. In
this instance the event topology is similar to that of signal if the electron
is emitted sufficiently close to the NR vertex. These electrons can be caused
by $\gamma$-rays and X-rays produced in different parts of the experiment and
the neutron generator, that reach the active volume. The predicted rate of
coincidence events has been assessed by calculating the photon spectrum
entering the active volume with GEANT4, and then convolving the corresponding
spectrum with the photon probability to yield an electron in the 5–15 keV
window. We assumed that tracks with a separation of 3 mm in camera images can
be well distinguished, while the time resolution is set to the maximum drift
time along the OTPC (230 ns). The total rate of accidental coincidences is
found to be $\ll$0.01 events per million NR with either generator. In most of
these events the NR and the photon are created by two different neutrons (85%
and 77% for D-D and D-T generators, respectively), while the remainder comes
from coincidences where the photon is produced in an earlier interaction of
the same neutron that produces the NR. The volumes where the photon originate
differ between the D-D and D-T experiment configurations. In the former case,
this is dominated by deexcitation X-rays following photoelectric effect in the
cathode (70% of the total), while in the latter case the most significant are
$\gamma$-rays from neutron inelastic scattering occurring in the generator
material placed in the line-of-sight of the active volume (80% of the total).

The previous paragraph discussed accidental coincidences where the origin of
the electron can be traced back to a neutron produced in D-D or D-T fusion.
However, the electric field used to accelerate deuterium ions in these devices
also creates a current of free electrons flowing in the opposite direction,
which produce a significant field of bremsstrahlung photons when stopping. For
the D-D experiment configuration, such bremsstrahlung photons are produced at
a position displaced from the collimator axis, and therefore they are
completely stopped by the shielding before they reach the active volume. For
the D-T experiment configuration, the rate of coincident events from
bremsstrahlung photons has been conservatively estimated using GEANT4
simulations, and we find that this contribution is also negligible. This plus
the preceding contribution correspond to the entry for ‘External $\gamma$\-
and X-rays’ in Table 3. It has also been confirmed that $\gamma$-rays from the
decay of radioisotopes produced by neutron activation only represents a small
contribution to accidental coincidence events (1% and 2% for D-D and D-T
neutrons, respectively).

An additional class of accidental background involves the $\beta$-decay of
trace radioisotopes in the OTPC gas, with low-energy electrons randomly co-
locating with the origin of a NR track. We considered 14C and 39Ar in
CF4-based gas mixtures, both assumed at typical atmospheric concentrations, as
well as 1 mBq of the 222Rn daughters 214Pb and 214Bi, giving a total activity
of a few hundred decays per day. This translates into a negligible coincidence
rate in the electron ROI.

Neutron scattering may produce $\beta$ emitters without additional charged
particles, namely via ($n$,$2n$) or ($n$,$\gamma$) reactions. If the daughter
nucleus decays quickly enough, a two-track topology similar to that of the
signal may be observed. The most relevant case is 19F($n$,$2n$)18F, where the
daughter is produced at a rate of 0.28 nuclei/s with the D-T generator (the
reaction is below threshold with D-D) and has a half-life of 110 minutes. This
specific decay leads to a background rate well below 1 event per million NR
tracks, and other processes such as radiative neutron capture on 19F are even
more unlikely. This background contribution is therefore also negligible.

Finally, atmospheric muons cross the detector at a rate of $\sim$1 per second;
although these have too low an energy loss rate to be observable,
approximately 2% cause $\delta$-ray electrons in the ROI which could
contribute accidental coincidences; this also translates to a negligible
background to the Migdal search.

Next we discuss the more complex issue of atomic cascades in nuclear recoil
tracks and the potential for fork-like events involving secondary recoils to
be confused with the Migdal signal topology.

####  6.2.1 Secondary nuclear recoils

A primary nuclear recoil created in neutron scattering collides along its path
with neighbouring atoms, inducing secondary recoils and initiating an atom
cascade. In a binary collision the secondaries may acquire enough kinetic
energy to produce a prominent fork-like topology, potentially mimicking a
Migdal event. In order to calculate the frequency of such events, we used the
TRIM fast calculations to generate 106 primary recoils from D-D neutrons, with
C and F in the correct proportion. Selected events had secondary recoils
created within the first 1 mm from the primary NR vertex and energies between
11 and 26 keV for carbon and 13.5 and 32 keV for fluorine, both mapping to the
5–15 keVee energy range of the accepted Migdal electrons. Some 10,000 events
met these criteria. The relative rates of such events are summarised in Table
4 for selected primary recoil energies.

Table 4: Relative rates of events with secondary recoils, expressed per million carbon and fluorine primary ions, created within 1 mm from the vertex in 50 Torr CF4, when the energy of the secondary track is in the range 11.0–26 keV (C) and 13.5–32 keV (F), both corresponding to 5–15 keVee. These can be further discriminated from electron tracks as explained in the text. Primary ion | Secondary ion
---|---
Fluorine | Fluorine | Carbon
500 keV | 22,310 | 4,800
400 | 26,840 | 5,930
300 | 36,640 | 7,640
200 | 56,130 | 1,263
170 | 67,040 | 1,418
Carbon | Fluorine | Carbon
500 keV | 6,250 | 1,210
400 | 7,950 | 1,610
300 | 11,380 | 2,310
200 | 17,310 | 3,700
130 | 26,120 | 5,770

Next we assess how many of those 10,000 events might be misinterpreted as
genuine Migdal interactions – and hence determine the background rate from
this source expressed per million primary NR tracks. We simulated more fully
further populations of 10,000 C and F recoils plus 1,000 electrons all with
true energies in the range 4.2–12 keVee: these energies contribute to the 5–10
keVee ROI due to the non-zero energy resolution. In these simulations the NR
tracks are distributed in energy like those induced by the primary NR spectrum
from D-D neutrons, while the electron spectrum follows that expected for the
Migdal electrons. For all tracks we follow the simulation steps described in
Section 5. The resulting deconvolved 2D camera images were used to measure a
2D track range using the method described in Ref. [40]. This was combined with
the $z$ component of the track to calculate an approximate 3D range ($R_{3}$),
which is plotted in Fig. 22 as a function of reconstructed energy.

The average leakage of NR events into the wide ER band was estimated from Fig.
23, which shows the 3D range distribution of NR and ER tracks across the full
ROI. This estimate is derived by simply projecting the events in Fig. 22 onto
the $R_{3}$ axis; a more careful analysis, which corrects for the rise and
larger scatter of the NR band at higher energies, would provide a larger
acceptance of the ERs. We find that 1 NR event lies above $R_{3}$ = 2.80 mm,
with a corresponding acceptance of ER signals of 87%. We note that the 25% of
false-negative events found in the data challenge mentioned in Section 6.1 are
likely to have a strong overlap with events removed by the $R_{3}$ cut, and
hence we do not consider this as an additional source of inefficiency. In
summary, this calculation motivates a total of $\mathcal{O}$(1) event per
million NR tracks in the background tally of Table 3.

Since the probability for secondary-recoil generation within the ROI increases
towards the end of the track (cf. Table 4), it is worth considering whether
‘backward neutrons’ – e.g. back-scattered by the shielding or emitted in
($n$,$2n$) reactions – could contribute significantly to this background by
creating tracks forking near the presumed vertex. As mentioned in Section 4,
the backward neutron flux is of order 1% for neutron energies above 100 keV,
so this would be a small contribution to this background even assuming no
head-tail discrimination at all.

Figure 22: 3D range as a function of reconstructed energy (keVee), showing
separation of low-energy electrons (wide band) from carbon and fluorine
recoils (narrow band) in CF4 at 50 Torr.

Figure 23: Distribution of 3D range in the 5–10 keVee ROI shown in Fig. 22. A
cut at $R_{3}$ = 2.80 mm gives a leakage of 1 background events per million NR
tracks, with a corresponding acceptance of ER signals of 87% (see text for
details).

In conclusion, the number of background events in the signal ROI from the
extensive number of sources considered is small – just over 1 event per
million primary NR tracks – yielding very high signal-to-background ratios for
both generators with CF4 at 50 Torr. The dominant background contributions
come from the interaction of $\gamma$-ray from inelastic neutron scattering
near the NR track vertex, which we assessed realistically via detailed
simulations, plus a comparable contribution from secondary nuclear recoils
mimicking Migdal electrons; the latter calculation has higher uncertainly as
it depends significantly on the quality of the track analyses. Finally, it
should be noted that there are various processes producing backgrounds below
the ER threshold which may come into the ROI for heavier elements: detailed
assessments will be required for other gas mixtures.

###  6.3 Sensitivity

From the knowledge of the signal and background rates and their uncertainties
we may calculate the expected (median) discovery significance for the D-D and
D-T experiments as a function of exposure to the neutron beams: this
quantifies how well one can reject the background-only hypothesis assuming the
nominal signal hypothesis (the Migdal cross sections calculated in Ref. [39]).

Sophisticated statistical analysis techniques will be employed for robust
signal estimation, but a straightforward calculation applicable to counting
experiments will suffice here, this one derived from a Profile Likelihood
Ratio (PLR) test using the Asimov dataset approximation [113]. We consider
initially an uncertainty of 50% on the background rate, assumed to be Gaussian
distributed. This reflects our ability to determine this rate using ancillary
measurements, complemented by Monte Carlo where needed: for example, by
measuring the rates of lone ER and NR tracks to assess random coincidence
backgrounds, or analyse ER vertex locations as a function of distance to the
NR vertex to confirm photon interaction rates near the NR track.

From the signal side, no theory uncertainty has been considered in this
calculation, and neither did we evaluate the uncertainty on our Migdal event
acceptance, as this depends critically on the details of the track analysis.
We recognise that the latter may be significant, recalling that, as indicated
in Table 1, variations in track threshold of 1 mm yield factor of 2
differences in the signal yield. However, given the large signal-to-background
ratios expected this will not hinder the measurement significantly.

Under these assumptions we conclude that both experiments have excellent
discovery potential, achieving 5$\sigma$ median significance in less than one
day of operation: 20 hours for D-D and 4.4 hours for D-T. A more pessimistic
scenario, where we halve the signal rate and increase the background
uncertainty to 70%, yields a 5$\sigma$ discovery in a little over 7 calendar
days for the D-D experiment, while in the D-T case only 7 hours are required
to reach that significance.

In summary, we expect to make conclusive detections with both generators with
a 5-day run in the baseline scenario, even assuming the restrictive parameters
considered here: analysis of camera frames with single interactions fully
contained within a restricted fiducial region, and imposing a conservatively
high electron threshold of 5 keV.

##  7 Migdal in other elements

Measuring Migdal probabilities for different elements, with their particular
electron configurations, will be important to study fully this effect – and
indeed critical should the measured rates disagree with the theoretical
predictions. In future stages of the project we plan to explore CF4-based
mixtures with noble gases, from He to Xe, which include leading elements used
in direct dark matter detection. Krypton may be considered too despite its
radioactive isotopes, which do not pose an insurmountable challenge. Other
elements of interest, e.g. Si and Ge used in cryogenic bolometers, also form
gaseous compounds, e.g. as nonpolar tetrafluorides which have similar electron
transport properties to CF4; however, the dominant contribution of fluorine to
the Migdal rate (due to stoichiometry) must be overcome. Other promising
group-IV compounds include mono-silane (SiH4) and germane (GeH4), which are
expected to have similar properties to methane, a well-known quencher. It must
be noted that the Migdal effect may be subtly different in dense liquids and
solid materials, but our measurements in atomic and molecular species will
provide a sound basis for further study. Table 5 lists neutron cross sections
and calculated Migdal probabilities for these elements [39]. With the
exception of He, the probabilities for emission of a hard Migdal electron are
comparable across the elements considered. Without undertaking a more detailed
study for each element, this provides some initial confidence that the signal
rate in other gases should be comparable to the CF4 rate, which we have found
to be eminently measurable.