[a]European Spallation Source ESS ERIC, SE-22100 Lund, Sweden [b]Hungarian
Academy of Sciences, Centre for Energy Research, 1525 Budapest 114., Hungary
[c]Budapest University of Technology and Economics, Institute of Nuclear
Techniques, 1111 Budapest, Műegyetem rakpart 9., Hungary [d]Dipartimento di
Fisica “G. Occhialini”, Università degli Studi di Milano-Bicocca, Milan 20125,
Italy [e]Istituto di Fisica del Plasma “P. Caldirola”, Associazione EURATOM-
ENEA/CNR, Milan 20125, Italy [f]Physical Chemistry, Lund University, SE-221
00, Lund, Sweden [g]Forschungzentrum Jülich GmbH, Jülich Centre for Neutron
Science JCNS at Heinz Maier-Leibnitz Zentrum, D-85747 Garching, Germany
[h]Data Management and Software Centre (DMSC), European Spallation Source
ERIC, 2200 Copenhagen N, Denmark [i]Mid-Sweden University, SE-85170 Sundsvall,
Sweden<EMAIL_ADDRESS>
# Detector rates for the Small Angle Neutron Scattering instruments at the
European Spallation Source

K. KanakiCorresponding author  M. Klausz  T. Kittelmann  G. Albani  E. Perelli
Cippo  A. Jackson  S. Jaksch  T. Nielsen  P. Zagyvai  R. Hall-Wilton

###### Abstract

Building the European Spallation Source (ESS), the most powerful neutron
source in the world, requires significant technological advances at most
fronts of instrument component design. Detectors are not an exception. The
existing implementations at current neutron scattering facilities are at their
performance limits and sometimes barely cover the scientific needs. At full
operation the ESS will yield unprecedented neutron brilliance. This means that
one of the most challenging aspects for the new detector designs is the
increased rate capability and in particular the peak instantaneous rate
capability, i.e. the number of neutrons hitting the detector per channel,
pixel or cm2 at the peak of the neutron pulse. This paper focuses on
estimating the incident and detection rates that are anticipated for the Small
Angle Neutron Scattering (SANS) instruments planned for ESS. Various
approaches are applied and the results thereof are presented.

BAND-GEM, Boron Coated Straws, Boron10, detector rate, Geant4, He3, McStas,
neutron detector, neutron scattering, SoNDe, transmission monitor

##  1 Introduction

The European Spallation Source [1, 2] aspires to become the most powerful
neutron source in the world, presenting new challenges for the detector
technologies to be used. Fifteen neutron instruments that have been approved
as part of the ESS instrument suite are already challenging the traditional
detection technologies of the neutron scattering field because of the
unprecedented instantaneous counting rates, as well as the requirements for
high spatial resolution [3].

LoKI [4, 5] and SKADI [6, 7] are the two Small Angle Neutron Scattering (SANS)
instruments endorsed for construction at ESS. LoKI is designed to be a broad-
band high intensity instrument with wide polar angle coverage. SKADI offers a
broad range of neutron energies as well, in addition to neutron polarisation
but with a smaller angular coverage, with its detectors placed at a larger
distance from the sample compared to LoKI.

In order to design detectors with the appropriate rate capability and prevent
performance compromises on this front, a detailed analysis of the instrument
requirements and how they translate to detector requirements is vital. It is
also important that such an evaluation be performed with different and
complementary approaches, so as to ensure the reliability of the result within
acceptable limits.

The methods used in this paper aim at acquiring a good understanding of the
rates LoKI and SKADI are going to achieve by looking at how the scattered
neutrons on the sample are distributed in space and time. A realistic worst-
case scenario is reproduced, based on which the detector requirements for rate
capability are extracted and the choice of detector technology is discussed.

In the following sections the tools and methods used are elaborated upon. The
main focus of this evaluation concerns the neutron scattering taking place
within the forward solid angle after the sample, as this happens to be the
primary area of interest for the SANS technique. This translates to a typical
1 m $\times$ 1 m detector area considered for the rate estimates of the
scattering characterisation system (SCS). Various detector technologies are
explored and their traits are discussed with respect to the instrument rate
requirements, as well as the data acquisition (DAQ) design. Last but not
least, a smaller area detector acting as a transmission monitor is placed in
the path of the direct beam and the same analysis is repeated.

##  2 The rate challenge for the ESS SANS detectors

SANS is one of the most widely used experimental techniques for the
investigation of soft matter properties [8]. It uses neutrons that are
elastically scattered on the sample at small scattering angles to infer the
characteristic length scales of the structures present in it. The scale of the
structures of interest that SANS can access is 1–100 nm. Its use of contrast
variation from deuterated samples makes it a very powerful tool especially for
studies of biological and pharmaceutical interest.

The popularity of the SANS technique makes it a ubiquitous tool at every
neutron scattering facility, usually with multiple instruments, targeting both
at high availability for the scientific community, as well as satisfying
complementary scientific requirements. For the same reason, two SANS
instruments have been endorsed at ESS and are currently undergoing different
stages of design.

###  2.1 The LoKI instrument

LoKI (the Low-K Instrument) is a wide simultaneous Q range SANS instrument
designed primarily with the needs of the soft matter, biophysics and materials
science communities in mind. The trend in all of these fields is towards
complexity and heterogeneity. Multi-component systems need to be studied as a
function of multiple environmental conditions with different structures
occurring at different length scales. Small gauge volumes are important to
study both intrinsically small samples and for performing scans of
heterogeneous samples. There is a need to study systems under the sort of non-
equilibrium conditions, such as shear fields, found in real world
applications. The ESS flux will enable more routine access of these conditions
and also permit fast kinetic studies on a wider range of samples than is
possible today. These scientific requirements motivate the requirements that
the detector system have a large angular coverage, have good spatial
resolution, and have a high rate capability.

###  2.2 The SKADI instrument

The Small-K Advanced DIffractometer SKADI is a high-resolution SANS instrument
at the ESS. The scientific areas targeted by SKADI include investigations of
smart materials, biological and medical research, magnetic materials and
materials for energy storage as well as experiments on nano-materials and
nano-composites. As an additional feature SKADI offers a modular sample
environment (3 m $\times$ 3 m) that allows custom sample environments,
especially for in-situ and in-operando investigations. Those will greatly
benefit from the higher flux at the ESS due to lower accessible time scales.
In order to make full use of the higher flux, a high-rate capable detector,
such as the Solid-state Neutron Detector (SoNDe), is necessary.

The detector setup includes three detector banks at different positions (see
Fig. 1). One detector of 20 cm $\times$ 20 cm will be installed at a fixed
position 20 m from the sample. The central detector is a 1 m $\times$ 1 m with
a central 20 cm $\times$ 20 cm aperture that will always be at the collimation
distance to allow for ideal mapping of resolution between aperture and
detector. An identical detector is placed at 1/5 of the middle detector
distance from the sample to allow collecting data from higher scattering
angles. This setup allows covering three orders of magnitude in the Q-space
(reciprocal momentum transfer in the neutron interaction [9], p. 26) in a
single shot experiment to enable the observation of fast sample transitions.

Figure 1: Arrangement of three SoNDe detector banks for the SKADI instrument.
The single modules for the active area are indicated.

###  2.3 Instrument configurations

The chopper settings, collimation length and aperture sizes of a SANS
instrument are experimentally configured depending on the sample and the type
of measurement to be performed. For the rate estimates a few configurations
are selected, aiming at maximising the neutron flux on the sample, in
combination with a sample that strongly scatters within the forward solid
angle.

The instrument and sample settings used for the rate estimates are listed in
Tab. 1. The chopper settings are reflected in the wavelength range, i.e. the
$\lambda_{min}$ and $\lambda_{max}$ values allowed to reach the sample from
the source. The same sample model is used for all instrument configurations.
It is a diblock copolymer with a 4.84% scattering probability, an adequate
choice for the study of the rear detector geometry. The sample size of 1 cm
$\times$ 1 cm matches that of the sample aperture.

Table 1: LoKI instrument configurations for the evaluation of rates. The same sample is used for all scenarios. The divergence represents the direct beam size on the detector and is defined by the collimation settings. config | collimation | $\lambda_{min}$ | $\lambda_{max}$ | source | sample | flux on | divergence
---|---|---|---|---|---|---|---
| length |  |  | aperture | aperture | sample |
| (m) | (Å) | (Å) | (cm $\times$ cm) | (cm $\times$ cm) | (n/cm2/s) | (cm)
1 | 3 | 3.0 | 11.5 | 3 $\times$ 3 | 1 $\times$ 1 | 1.00$\times$109 | 8.4
2 | 5 | 3.0 | 11.5 | 2 $\times$ 2 | 1 $\times$ 1 | 2.02$\times$108 | 4.4
3 | 8 | 3.0 | 10.0 | 2 $\times$ 2 | 1 $\times$ 1 | 8.24$\times$107 | 3.0

In SANS it is typical to match the collimation length to the sample-detector
distance, in order to optimise the resolution capability of the instrument.
For the current study though, this distance is fixed at 5 m to get a cross
comparison among the detector options presented in the following sections.

The contributions to the number of neutrons reaching the detector can be
broken down to the coherent and incoherent scattering components from the
sample, the incoherent scattering from the solvent and the transmitted
neutrons, as in Eq. 1.

$N=coh_{sample}+incoh_{sample}+incoh_{solvent}+transmission.$ (1)

In the current study, only the coherent scattering from the sample is taken
into account, i.e. the actual signal the SANS technique is after. This
provides a lower limit to the rate estimates for the SCS. The transmission
neutrons are studied separately to shed light on the requirements of the
direct beam detector. In the latter case the derived rates serve as an upper
limit.

###  2.4 Rate definitions and analytical estimates

The rate definitions used in this study are listed in [10] (page 14) as
follows:

  * •

Global time-averaged incident/detection rate: the number of neutrons per
second entering/recorded by the entire detector.

  * •

Local time-averaged incident/detection rate: the number of neutrons per second
entering/recorded in a detector pixel, channel or unit.

  * •

Global peak incident/detection rate: the highest instantaneous neutron
incident/detection rate on the whole detector.

  * •

Local peak incident/detection rate: the highest instantaneous neutron
incident/detection rate on the brightest detector pixel, channel or unit.

Knowing the scattering fraction F(%) for a SANS sample model, it is possible
to get an approximate analytical estimate for the time-averaged incident rates
the rear detector is exposed to. The largest portion of the signal-related
scattered neutrons is contained within the forward cone subtended by the rear
detector, which usually has a polar angle coverage of up to a few degrees,
depending on its distance from the sample. As SANS deals with different
degrees of freedom compared to other neutron techniques, the neutrons
scattered at small angles represent long range correlations and carry
information about large distances in real space. The diblock copolymer model
mentioned before has a scattering fraction of about 4.8%. For instrument
configuration 1 this translates to an upper limit of a global incident time-
averaged signal rate of 4.8% $\times$ 109n/s/cm2 flux $\times$ 1 cm2 sample
size = 4.8 $\times$ 107 n/s = 48 MHz. The incoherent contribution from the
sample and the solvent have to be estimated in addition. If 10% of the
incident beam is incoherently scattered in 4$\pi$, then the incident fraction
within the solid angle subtended by the rear detector is 10% $\times$
109n/s/cm2 flux $\times$ 1 cm2 sample size $\times$ 0.04 sr = 4 MHz. A global
time-averaged rate of 52 MHz is to be expected as an upper incident rate limit
for the high flux instrument configuration on the rear detector.

###  2.5 The Monte Carlo approach

Analytical rate estimates are based on several approximations and lack the
more detailed picture that a Monte Carlo (MC) approach can provide. One
fundamental MC tool that is broadly used for instrument design is McStas [11,
12]. It can model all major components of an instrument by sampling an
external neutron source distribution and then propagating neutrons through
guides, choppers, monochromators, collimators etc. until the sample and
beyond. A collection of sample components is also available allowing the
neutrons to scatter based on underlying physics models and then be
histogrammed by monitor components that act like “detectors”. The latter
process is of particular interest for the detector design, as it allows the
visualisation of the neutrons entering the detector geometry accessing at the
same time their full list of properties, e.g. wavelength ($\lambda$), time-of-
flight (TOF), position, scattering angle ($\theta$) and optionally user-
defined flags. These properties are necessary to differentially study the
picture of the impinging neutrons on the detector as a function of time
(within a neutron pulse), wavelength and polar angle.

Both ESS SANS instruments are modeled in McStas as part of the design
progression. In this paper, a baseline LoKI model is used assuming that no
major modifications are anticipated or that future modifications will not
impact the predicted rates in a way that completely resets the detector design
effort. The deduced rate numbers correspond to the butterfly moderator source
(“ESS_butterfly”) [13] with a pulse length of 2.86 ms and reflect the maximum
accelerator power of 5 MW.

###  2.6 Rate derivation method

As the neutron scattering community is transitioning from the traditional 3He
detectors to solid converter detectors and more exotic geometries, it becomes
important to examine incident and detection rates for all the detector
technologies presently evaluated. These scenarios include 3He tubes, Boron
Coated Straws (BCS) by Proportional Technologies, Inc., the SoNDe detector and
the BAND-GEM detector (refs. in respective sections). This practically
translates to a variety of channel and pixel geometries, from the familiar
two-channel tube read out in charge division mode, to two-dimensional (2D)
pixels of rectangular or trapezoidal shape with individual channel readout.

The output of the McStas (2.4.1) simulation that is recorded immediately after
the sample is used as input for a subsequent Geant4 [14, 15, 16] detector
simulation. The latter is performed with the ESS Detector Group Simulation
Framework [17]. The file format facilitating this communication is the Monte
Carlo Particle Lists (MCPL) format [18, 19]. With the combination of the two
software packages it is possible on one hand to take into account the
correlations of neutron properties, like TOF, energy, spatial and momentum
vectors, and on the other hand to reliably evaluate the detector performance.
The Geant4 validation of the latter is addressed elsewhere [20] and is not
discussed in this study.

At a pulsed source the peak rate could be more than an order of magnitude
higher than the time-averaged one. It is thus important for the qualification
of a detector technology for a specific application and impacts the readout
electronics design. The peak rates also dictate the system design for data
collection, aggregation and transfer but as the data are propagated further
down the process chain, it is the time-averaged rates that become more
relevant for data transfer and storage choices.

Another distinction in the current work is between incident and detection
rate. The first would be the upper limit the detector would count, if it had a
detection efficiency of 100%. As the detectors have efficiencies that depend
on the neutron energy, the instance when the number of incident neutrons is
highest is not necessarily the instance of the highest number of detected
neutrons. A detector might be illuminated with a high flux but if it is not
efficient at the respective neutron wavelengths, there is no concern for
saturation. The peak incident rate and peak detection rate do not have to
occur simultaneously.

The incident neutrons arrive at the detector with various TOF and energy
values. As Geant4 continues to count time for the particles it propagates, the
TOF distribution will vary as a function of detector depth. This effect needs
to be taken into account for the estimate of the instantaneous peak detection
rates for those detectors that record depth information [20, 21, 22, 23].

For the derivation of the incident rates, the incident neutron TOF
distribution at 5 m after the sample is used, as depicted in Fig. 2, in order
to select the TOF region which contains the highest number of neutrons.
Similarly, the maximum of the TOF distribution of detected neutrons is used
for the estimate of the highest detection rate.

Figure 2: A typical neutron TOF and $\lambda$ distribution 5 m after the
sample for the three instrument configurations. The global incident rates per
configuration appear in the legend in Hz for a standard 1 m $\times$ 1 m
detector.

The peak number of neutrons can be represented in various ways, e.g. per tube
or pixel. When filling the histograms representing the peak rates, the weight
of every bin is normalised with the accelerator frequency (14 Hz).

##  3 Tackling the ESS flux with tube geometries

One of the options the neutron scattering community has primarily relied on is
3He tube detectors arranged in a single layer, typically with an 8 mm outer
diameter and charge division readout. To satisfy the high rate requirements
the tubes can be arranged in successive layers of possibly lower detection
efficiency, 3He or other technology, in order to distribute the detection
events in a larger volume and reduce event pile-up. The same can be achieved
by reducing the tube size but the increase of dead area compromises the data
quality.

###  3.1 Rates for the 3He tubes

The Geant4 geometry model implemented for the 3He tube (see Fig. 3)
constitutes a typical detector arrangement for many SANS instruments around
the world [24, 25, 26, 27]. The outer tube diameter is 8 mm with a 0.4 mm wall
thickness, a length of 1 m and a total gas pressure of 10 bar with a 3He/CF4
mixture (80/20 by volume) [28, 29, 30]. The material of the vessel is
stainless steel with the crystalline structure of $\gamma$–iron and is
implemented with the help of the NXSG4 library [31]. The physics list used is
QGSP_BIC_HP. In addition, /process/eLoss/stepFunction 0.1 0.001 $\mu$m and
/process/eLoss/minKinEnergy 10 eV are defined. 120 tubes are placed at a 5 m
distance from the sample position, in order to achieve a polar angle coverage
of a few degrees.

(a) The 1 m $\times$ 1 m detector area covered with 120 3He tubes. Primary
neutrons stemming from the sample position appear in red.

(b) Enlarged view of 3He tubes. The stainless steel vessel appears in green
and the counting gas in blue.

Figure 3: The neutron generator is placed at the beginning of the coordinate
system, which coincides with the sample position. Simulated neutrons from
McStas are emitted towards the 1 m2 geometry at 5 m away along the z-axis.
Only neutrons hitting the detector are displayed.

A neutron is counted as incident, when it enters the wall material of a tube.
It is counted as detected, when its conversion products have deposited more
than 120 keV in the counting gas. The threshold is based on the shape of the
experimental pulse height spectrum and has a minor impact on the result of
this study. The TOF and wavelength distributions of incident and detected
neutrons for instrument configuration 1 are shown in Fig. 4. For every
evaluation that follows the TOF maximum is picked from the respective
distribution.

Figure 4: Incident and detected neutron TOF distributions for instrument
configuration 1, including and excluding divergent neutrons. The TOF maxima
can appear at different values for the two cases (left). Incident and detected
neutron $\lambda$ distributions for the same instrument configuration (right).

Fig. 5(a) depicts the time-averaged global and local rates for both incident
and detected neutrons. The number cited in the legend corresponds to the
global time-averaged rate, while the maximum of each histogram corresponds to
the local one. In order to extract the peak rates, a 1 ms TOF slice is
selected from the respective distribution and only neutrons within this slice
are plotted (see Fig. 5(b)). The counts are per tube and ms but are converted
to Hz when cited in the summary Tab. 2. The inclusion or exclusion of
divergent neutrons amounts to a 5% difference only for the first configuration
and the particular sample model, and as such it is not presented as a separate
case.

(a) Time-averaged rates per 3He tube.

(b) Peak rates per 3He tube.

Figure 5: Global (in legend) and local, incident and detection rates for a 3He
detector and instrument configuration 1.

The same analysis is repeated for all instrument configurations of Tab. 1 and
the results are summarised in Tab. 2.

Table 2: Summary table with global and local incident and detection rates, both time-averaged and peak ones, for 3He tubes. config | global average | global average | local average | local average
---|---|---|---|---
|  incident rate |  detection rate |  incident rate/tube |  detection rate/tube
1 | 37 MHz | 25.9 MHz | 1 MHz | 727 kHz
2 | 7.4 MHz | 5.2 MHz | 225 kHz | 152 kHz
3 | 2.9 MHz | 2 MHz | 91 kHz | 61 kHz
config | global peak | global peak | local peak | local peak
|  incident rate |  detection rate |  incident rate/tube |  detection rate/tube
1 | 74 MHz | 48 MHz | 2.9 MHz | 1.8 MHz
2 | 15 MHz | 9.6 MHz | 647 kHz | 381 kHz
3 | 6 MHz | 3.9 MHz | 279 kHz | 175 kHz

The operational limit for a non position sensitive 3He tube is about 100 kHz
[32, 33], dropping at 30-50 kHz for position sensitive tubes. At higher rates
the tube performance deteriorates leading to event pile-up. The spatial
resolution from charge division is sensitive to the position of the detection
event along the tube and is additionally subject to compromise when the
operation parameters are favoured towards high rate capability.

The 3He technology is clearly inappropriate for the SANS instruments at ESS.
Alternative solutions need to be adopted that can serve the scientific case
without wasting the intense ESS neutron pulse. A detector option that
resembles the 3He tube readout but uses a solid 10B4C converter is explored
next.

###  3.2 Rates for the Boron-Coated Straws

A Boron-Coated Straw (BCS) [34, 23] detector is a conventional neutron
detector by Proportional Technologies, Inc., which intends to be a cost
effective 3He replacement technology. A BCS detector consists of an aluminium
tube, containing seven copper straws arranged hexagonally (see Fig. 6(b)). The
tubes are 1 m long with a diameter of 2.54 cm. The straw inner wall is coated
with a 1 $\mu$m thin B4C converter layer enriched in 10B by 95%. They are
filled with an Ar/CO2 mixture (90/10 by volume) at 0.7 atm. Physics list and
eLoss parameters are identical to the 3He tube simulation (see introduction of
section 3.1). The neutron transport in the Al and Cu materials is described
with the help of the NCrystal package [35, 36].

A bias voltage is applied between the tube and resistive anode wires, which
are tensioned in the center of each straw. This makes the straws work in
proportional mode. The charge is read out at both ends of the detector using
charge division to acquire the position information. The tubes can be arranged
in successive layers in order to achieve the desired coverage, uniformity and
detection efficiency.

(a) The primary neutrons (in red) hit the detectors 5 m away from the sample
position.

(b) Enlarged view of the 5 overlapping BCS tube panels. Each aluminium tube
(grey) contains 7 copper straws (orange) arranged hexagonally.

Figure 6: The neutron generator is placed at the beginning of the coordinate
system, which coincides with the sample position. Simulated neutrons from
McStas are emitted towards 5 panels ($\times$ 40 tubes/panel) of BCS tubes
covering 1 m $\times$ 1 m at 5 m away along the z-axis.

In the Geant4 model of the current study 5 layers of BCS detectors, referred
to as panels, consisting of 40 tubes each cover the same 1 m $\times$ 1 m area
as the 3He detector model. Each tube is rotated by an angle of 10∘ around its
cylindrical axis and the adjacent panels are positioned behind each other with
a relative shift of 1.016 cm along the horizontal axis (see Fig. 6(b)) for
performance optimisation reasons.

A neutron detection event is defined the same way as for the 3He tubes, by
applying a 120 keV threshold on the energy deposition of the charged
conversion products in the counting gas. Due to the complex geometry three
different definitions of incident neutrons are used in this section: incident
for the entire detector; incident for a panel; and incident for a straw. A
neutron is counted as incident for the entire detector only once, when it
enters the wall material of a tube for the first time. On the contrary, a
neutron can be counted more than once as incident for a panel but only if it
is scattered back from another panel and enters a tube in the panel of
interest again. Moreover, a neutron is counted as incident for a straw every
time when it enters its copper layer from the outside.

The incident neutron TOF and $\lambda$ spectra per detector panel are depicted
in Fig. 7(a) and Fig. 7(b).

(a)

(b)

Figure 7: Incident TOF (a) and $\lambda$ (b) distributions per panel in depth
for instrument configuration 1. The respective incident rates appear in the
legends.

This approach is important for detectors, which provide depth information, as
every detector layer is exposed to a different neutron distribution (see Fig.
8(a)).

(a)

(b)

Figure 8: $\lambda$ distribution of detected neutrons per panel (a). $\lambda$
dependent neutron conversion and detection efficiency for the entire detector
(b) for instrument configuration 1. The conversion/detection efficiency is the
ratio of the total number of converted/detected neutrons in all straws over
the number of incident neutrons for the entire detector for a particular
incident $\lambda$. The detection rates per panel and the global average
conversion and detection efficiencies appear in the legends.

From the conversion and detection efficiency of the entire detector for
different wavelengths, depicted in Fig. 8(b), it is concluded that the
efficiency for lower wavelengths is lower – as expected – and the global
detection efficiency is 63% with a detection to conversion ratio of 70%.

Figure 9: Detection efficiency per straw for instrument configuration 1.

To get a deeper understanding about the detector system, the detection
efficiency of each straw is shown in Fig. 9. It is defined as the number of
detected neutrons in each straw divided by the number of the respective
incident neutrons. The efficiency of each straw is represented with a two-
dimensional cross-sectional image of the detector geometry similar to Fig.
6(b). The efficiencies of the straws in the first panel indicate that there is
a correlation between the scattering angle and the wavelength and it is clear
that the straws in the front or with clear sight to the sample have much
higher efficiencies than the ones behind them. All straws are identical and so
is their detection efficiency for a particular neutron wavelength, so the
change of the detection efficiency in depth is the result of the hardening of
the neutron spectrum due to the higher absorption cross-section of neutrons
with higher wavelength and the thermalisation of the neutrons via scattering.
This effect in the spectrum is clearly visible in Fig. 7.

Fig. 10 depicts the time-averaged and peak incident rate for each straw
represented the same way as the detection efficiency of the straws. The peak
rates are extracted the same way as for the 3He tubes, by counting neutrons
only from a selected 1 ms TOF slice that results in the highest instantaneous
rates. The tubes with the highest peak incident rates are localised in the
center of the panels because the highest incident rates occur when the
relatively high energy neutrons are scattered on the sample in small angles
and most of them enter the same straws. Fig. 10 gives an enlarged view of
these straws and also shows the peak detected rates of the straws with the
highest values. The highest peak rates appear in the straws of the first panel
for all three configurations. A summary of the estimated incident and
detection rates can be found in Tab. 3.

(a) Time-averaged incident rate for per BCS straw.

(b) Peak incident rate per BCS straw.

Figure 10: Time-averaged and peak incident rate per BCS straw for instrument
configuration 1.

(a)

(b)

Figure 11: Peak incident (a) and detection (b) rates for the central straws for instrument configuration 1. Table 3: Summary table with global and local incident and detection rates, both time-averaged and peak ones, for the BCS detector. config | global average | global average | local average | local average
---|---|---|---|---
|  incident rate |  detection rate |  incident rate/straw |  detection rate/straw
1 | 37.3 MHz | 23.5 MHz | 1.01 MHz | 187 kHz
2 | 7.48 MHz | 4.70 MHz | 211 kHz | 39.0 kHz
3 | 2.91 MHz | 1.82 MHz | 86.3 kHz | 15.0 kHz
config | global peak | global peak | local peak | local peak
|  incident rate |  detection rate |  incident rate/straw |  detection rate/straw
1 | 74.3 MHz | 64.2 MHz | 2.99 MHz | 458 kHz
2 | 15.1 MHz | 13.1 MHz | 651 kHz | 100 kHz
3 | 6.11 MHz | 5.29 MHz | 283 kHz | 47.0 kHz

Similarly to the 3He tubes, the BCS straws are expected to start saturating at
50-100 kHz. For instrument configuration 1 with the shortest instrument
collimation, peak rates as high as 458 kHz for a single straw are derived.
This implies that the operation of such a detector is subject to the same
limitations as a 3He tube.

##  4 Tackling the ESS flux with pixel geometries

The limitations the tube detector geometries are subject to for the ESS SANS
rates can be alleviated with the use of detectors whose anodes consist of 2D
pixels with individual readout, which leads to a more efficient distribution
of the incoming neutron flux. The pixels may vary in shape to accommodate an
even spread of detection events, satisfy spatial resolution requirements, as
well as to geometrically facilitate the polar angle coverage.

In the following sections two different implementations of 2D pixels are
presented, a detector with square pixels (Solid state Neutron Detector
(SoNDe)) and one with trapezoidal pixels (Boron Array Neutron Detector (BAND-
GEM)). These detectors are developed in the context of SANS for ESS and are
the baseline choices for the respective instruments. As these detector
technologies are high rate capable, only the incident rates are considered in
the following evaluation.

###  4.1 Rates for the SoNDe detector

The first approach for handling the SANS rates with 2D anode pixels is the
SoNDe detector [37, 38, 39, 40], adopted by the SKADI instrument. The detector
surface area is covered by multiple scintillator tiles of 6Li-glass (GS20®
[41]) with the respective Multi-anode PMT (MaPMT) placed right behind them.
Each tile is 48.5 mm $\times$ 48.5 cm in size for the chosen MaPMT model
(H12700 [42]) and is served by 64 (8 $\times$ 8) MaPMT pixels. The detector
consists of 400 modules in total, which will be equipping three different
detector banks, as shown in Fig. 1. For the sake of the rate evaluation
though, all 400 modules are assumed to be occupying the rear detector in an
arrangement of 1 m $\times$ 1 m (20 $\times$ 20 modules) placed 5 m after the
sample (see Fig. 12).

Figure 12: Geometry of the SoNDe scintillator tiles in an arrangement of 400
(20 $\times$ 20) modules occupying a 1 m $\times$ 1 m rear detector bank. In
red appear primary neutrons originating from the sample.

An incident neutron is counted the first time it enters the scintillator
glass. The physics taking place inside the scintillator material and beyond is
not included in the Geant4 simulation. Figs. 13 and 14 respectively depict the
incident time-averaged and peak rates per SoNDe module and pixel.

(a)

(b)

Figure 13: Time-averaged incident rates per SoNDe module (a) or pixel (b) for
instrument configuration 1.

(a)

(b)

Figure 14: Peak incident rates per SoNDe module (a) or pixel (b) for instrument configuration 1. Table 4: Summary table with incident time-averaged and peak rates for the SoNDe detector. config | global average | local average | local average
---|---|---|---
| incident rate | incident rate/module | incident rate/pixel
1 | 37 MHz | 1.1 MHz | 21.8 kHz
2 | 5.1 MHz | 167 kHz | 3.6 kHz
3 | 2.9 MHz | 99 kHz | 2.3 kHz
config | global peak | local peak | local peak
| incident rate | incident rate/module | incident rate/pixel
1 | 73 MHz | 3.5 MHz | 90 kHz
2 | 10 MHz | 550 kHz | 21 kHz
3 | 6 MHz | 341 kHz | 14 kHz

The total number of pixels for the current Geant4 implementation of SoNDe is
25600. The SANS technique results in widespread rates over a large number of
pixels, contrary to other neutron techniques. It does not trigger highly
localised detection events in time and space. Thus, it is imperative for the
design of the data acquisition chain to take into account all aspects of the
rate distribution, and to ensure all buffers are adequate for the expected
data patterns.

It is interesting to look at what these values mean in terms of data
throughput. For the highest flux collimation of the instrument, the global
peak incident rate is about 73 MHz. This means that in the hottest millisecond
of the pulse, 73000 neutrons will enter the detector. Assuming that every
neutron triggers a signal over threshold on 1-3 pixels, a 64 bit time-stamp
assigned to every fired pixel and an 8-15 bit pixel ID assigned to pixel
location, the total amount of data the detector pushes out through the optical
fibers per second can be calculated as:

$Data~{}rate~{}\big{(}bps\big{)}=n_{pixels\big{/}neutron}\times
n_{peak~{}neutrons\big{/}s}\times\big{(}timestamp+pixelID\big{)}~{}bits\big{/}pixel$
(2)

and is in the range of 5-17 Gb/s for a 100% efficient detector.

The rate values of Tab. 4 demonstrate the need for operating this detector in
pixel mode and not in Anger camera mode, as the shipping of the ADC values
required by the algorithm would make the data rates forbidding for the DAQ.
Detectors are foreseen to run in different operation modes, e.g. calibration,
diagnostics, standard. In non-standard operation it is anticipated that the
data rate can significantly increase because of the additional information
collected. However, it is common to tolerate pile-ups in this context, as the
DAQ under such circumstances usually serves a different purpose and event
rejection can be applied.

###  4.2 Rates for the BAND-GEM detector

The second detector example of an anode pixel implementation is the Boron
Array Neutron Detector (BAND-GEM) [43, 44, 45, 46, 47]. It is a trapezoidal
GEM module with an intricate cathode design, which consists of consecutive
lamellae forming a Venetian blind (see Fig. 15). In order to achieve the polar
and azimuthal angle coverage for the rear detector of a SANS instrument,
several trapezoidal BAND-GEM modules are assembled together to create a
polygonal cross section as in Fig. 15(a).

(a)

(b)

Figure 15: Rear detector bank composed of eight BAND-GEM modules arranged in a
polygon (a). The anode panels are placed on the back of the detector (red).
The open space in the middle is reserved for the installation of a
transmission monitor. The cathode structure (purple) of a single segment with
gas volumes (green) in between (b). The latter geometry shows a reduced number
of cathodes to allow for better visualisation.

The anode on which the electrical signal is induced is divided in equal slices
of 10∘ in the azimuthal ($\phi$) direction and bands with a constant pitch of
4 mm in the polar angle ($\theta$) direction (see Fig. 16). The shape
introduced for this study does not perfectly match the engineering drawing of
the actual demonstrator but the simplification serves the purpose of the rate
analysis without a significant compromise. Practically, the pixels can be
further subdivided in the azimuthal direction at the outer polar angles to
locally increase the spatial resolution or merged at very low angles, where
their size is below the required spatial resolution to reduce their number.

Figure 16: Anode pad geometry for a BAND-GEM module. In the particular
implementation there are 98 rows of pixels with 10 pixels in each row.

Following the same analysis steps as with the previous detectors, the derived
incident rate estimates are summarised in Tab. 5. Fig. 17 demonstrates the
time-averaged and peak incident rates for instrument configuration 1. The
BAND-GEM technology has been proven to successfully handle thermal neutron
rates of up to 40 MHz/cm2 [43], which renders it an appropriate choice for the
ESS SANS instruments in terms of rate capability.

(a)

(b)

Figure 17: Time-averaged (a) and peak (b) incident rates for the BAND-GEM detector and instrument configuration 1. Table 5: Summary table with incident time-averaged and peak rates for the BAND-GEM detector. config | global average | local average | global peak | local peak
---|---|---|---|---
| incident rate | incident rate/pixel | incident rate | incident rate/pixel
1 | 34 MHz | 13.6 kHz | 68 MHz | 55.9 kHz
2 | 7 MHz | 3.1 kHz | 14 MHz | 18.1 kHz
3 | 2.7 MHz | 1.4 kHz | 5.7 MHz | 12.7 kHz

A single BAND-GEM module contains 980 pixels in the current Geant4
implementation. For the full detector of eight segments, the total number of
channels is 7840. Using Eq. 2 with the assumption of 1-3 triggered
pixels/neutron, 8-15 bits for the pixel ID representation and 100% detection
efficiency the data throughput that 8 segments would push out is approximately
5-16 Gb/s.

##  5 Rates for the transmission detector

Aside from the rate capability of the SCS, the transmission detectors
installed at the ESS SANS instruments need special attention. They are exposed
to a large fraction of the direct beam and the increased neutron flux offers
the possibility for per pulse normalisation. The new operation environment
raises several questions regarding the required spatial resolution, detection
efficiency, stability and longevity of such a detector.

To this end, a square geometry of 6 cm $\times$ 6 cm segmented in 1 cm
$\times$ 1 cm size pixels is placed 5 m away from the sample covering polar
angles up to 0.4∘. The simulated data input uses the same sample model as
before, only this time the transmitted neutrons which do not interact with the
sample are also propagated until the transmission monitor. The total number of
incident neutrons which enter the detector’s active volume are counted and
summarised in the form of global time-averaged and peak rates in Tab. 6 for
all instrument configurations.

Table 6: Summary table with global time-averaged and peak incident rates for a 6 cm $\times$ 6 cm transmission detector. config | global average incident rate | global peak incident rate
---|---|---
1 | 911 MHz | 3.6 GHz
2 | 193 MHz | 785 MHz
3 | 78 MHz | 219 MHz

A non-exhaustive list of implementations is evaluated below; a generic
pixelated anode with a 1 cm $\times$ 1 cm pixel size, a SoNDe-like
implementation based on the H9500 MaPMT model [48] with a 3 mm $\times$ 3 mm
pixel size, a wire gas counter of 15 wires at a 4 mm pitch and an ionisation
chamber operated in current mode. The respective local time-averaged and peak
incident rates are presented in Fig. 18 and Tab. 7.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 18: Incident time-averaged (left) and peak (right) rates for a transmission detector of a 1 cm $\times$ 1 cm pixel size (a, b), a 3 mm $\times$ 3 mm pixel size (c, d) and a wire gas counter (e, f) for instrument configuration 1. Table 7: Summary table with incident time-averaged and peak rates for various implementations of the transmission detector for all instrument configurations. config | local average incident rate | local peak incident rate
---|---|---
| /cm2 /9mm2 /wire | /cm2 /9mm2 /wire
1 | 52 / 5 / 95 MHz | 206 / 22 / 385 MHz
2 | 30 / 4 / 37 MHz | 134 / 19 / 154 MHz
3 | 17 / 3 / 20 MHz | 49 / 11 / 81 MHz

For a 1 cm2 pixel anode, a peak incident rate of 200 MHz/cm2 translates to an
average pulse spacing of 5 ns and a typical detector rise time of 500 ps,
rendering a full efficiency implementation impossible. Assuming a 1% detection
efficiency, the peak detection rate drops to 2 MHz/cm2. A fast detector with a
single converter layer, e.g. a GEM, could satisfy this requirement and
possibly allow for a higher detection efficiency up to 15-20% before it
saturates. The analysis above also demonstrates that the 1 cm2 pixel size is
the upper limit for use in a high flux environment.

A SoNDe-like implementation with a smaller square pixel size of 3 mm $\times$
3 mm, equipped with a fast scintillator like the GS20 glass is thus another
possibility. The upper incident limit estimated here is at 22 MHz/pixel and
given the detector has a high efficiency (¿75% [39]), either the incoming
neutron flux has to be significantly attenuated or the detection efficiency
has to be reduced for the module to operate.

A wire gas counter without position information, covering the same active
area, e.g. with 15 wires at 4 mm pitch, is explored next. With an incident
peak rate of 385 MHz/wire (see Tab. 7) and a detection efficiency of 10-4
(e.g. with N2 as counting gas), the order of magnitude for the peak detection
rate is still around 40 kHz/wire, which poses a challenge for the stability of
such a detector.

Last but not least, a 3He- or 10B-based ionisation chamber can be considered,
if only integrated flux is required from a transmission detector. Both gas and
solid state implementations are used in high flux environments for reactor or
beam monitoring. They are operated in current mode, i.e. the collected charge
is integrated in time. The current is proportional to the direct ionisation
charge released in the active volume, as the chamber is operated with no gain.
This type of detectors have demonstrated operation stability and can perform
over a large dynamic range. However, as they are uncommon in the neutron
scattering field, development is needed to customise them for the particular
use. Similar development steps would be necessary for other more exotic
detector solutions, in order to ensure their performance suitability and
stability [49, 50, 51].

As the transmission detector is exposed to a large fraction of the direct
beam, the outgoing data rates could prove challenging. Indeed, with the
assumptions of a 20% detection efficiency, 1-2 pixels triggered per event, a
64 bit time-stamp per pixel and an 8-10 bit pixel ID, the output data rate is
53-107 Gbps for instrument configuration 1. To stay below the 100 Gbps limit
of the optical fiber, the output data rate can be lowered by further reducing
the detector efficiency, the accuracy of the time stamp or by optimising the
data format to contain a single time stamp per event for all triggered pixels.
A detailed analysis of the instrument requirements with respect to the
detector ones can set the limits of the design parameters.

##  6 Conclusions

As the ESS source will subject the detectors to unprecedented neutron fluxes,
it is scientifically imperative that the new detector requirements are
fulfilled. One of the bigger challenges is the rate capability of detectors
used in SANS techniques, whilst satisfying other requirements. An overview of
the incident and detection rate estimates anticipated for the upcoming SANS
instruments at ESS is presented. The rate capabilities of various detector
technologies are discussed for the rear SCS, as well as for the transmission
detector. Lower and upper limits are respectively set, as only the coherent
signal from the sample is used. The time-averaged SCS rates need to be
corrected upwards by a few % to include the incoherent component, while the
same correction has to be applied downwards for the transmission rates. A more
detailed look at the time dependence of the incoherent signal would be
necessary to adjust the peak rate values. The study is based on a baseline
LoKI instrument model. SKADI is foreseen to operate with longer collimation
lengths compared to LoKI, which immediately relaxes the detection rate
requirements.

It becomes apparent that tube detectors can potentially compromise the
instrument performance for high flux configurations. A standard 3He tube would
saturate already at 100-200 kW source power. A BCS straw is expected to
saturate at 800-1000 kW source power. The tube parameters can be adjusted, so
as to distribute the detection events over multiple layers but such an
improvement cannot adequately lift the saturation limit of this detector type.
Moreover, the addition of multiple detection layers enhances the scattering
effects with a negative impact on the spatial resolution of the detector. A
custom readout electronics design can partially alleviate the saturation but
again at the cost of spatial resolution. Last, both tube technologies explored
in this study employ a closed gas system, which prevents counting gas
purification and impurity filtering, and has consequences on the quality of
operation with sustained high rates over the years. Particularly for BCS, long
term operation under such conditions has not been demonstrated.

Alternative technologies, like SoNDe and BAND-GEM, with 2D anode pixels are a
more suitable choice to exploit the full ESS source power. The pixel size and
shape can be designed for optimal spatial resolution and rate capability. In
the SoNDe case the rate estimates indicate that the detector needs to be
operated in pixelated mode, as the Anger camera mode would result in data
rates too excessive for an affordable DAQ system. In the BAND-GEM case the
open gas system allows for efficient monitoring of the gas quality and
composition, which contributes to the stability and longevity of the detector.
As the amount of channels and data output dramatically increase, special
consideration is needed for the choice of bandwidths and buffers throughout
the DAQ chain.

Last but not least a first glance at the rates for the transmission monitor is
attempted. Few different technologies are discussed in this context. An
important conclusion is that for a position sensitive detector, the pixel size
cannot exceed the 1 cm2 for saturation reasons. Moreover, it turns out that
the output data rate can be more demanding for this detector than for the SCS.
An understanding of the spatial resolution, efficiency and accuracy
requirements from the instrument side is vital for the customisation of the
proposed technologies, as well as the design of the DAQ chain.

Richard Hall-Wilton, Kalliopi Kanaki and Thomas Kittelmann would like to
acknowledge support from the EU Horizon2020 BrightnESS grant (676548). Richard
Hall-Wilton and Kalliopi Kanaki would also like to acknowledge support from
the EU Horizon2020 SoNDe grant (654124). Milán Klausz would like to
acknowledge the supervision of Péter Zagyvai. Computing resources were
provided by the DMSC Computing Centre
(https://europeanspallationsource.se/data-management-software/computing-
centre). The authors would like to thank Richard Heenan for his valuable
comments on the manuscript. Kalliopi Kanaki would like to thank Ramsey Al
Jebali, Morten Jagd Christensen and Jonas Nilsson for the useful conversations
and support with python.

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50 | 0.06875 | 0.34531 | 0.43281 | 0.15313
55 | 0.38125 | 0.00000 | 0.25312 | 0.36562
60 | 0.59375 | 0.00000 | 0.04844 | 0.35781
65 | 0.90312 | 0.00000 | 0.00156 | 0.09531
70 | 0.90000 | 0.00000 | 0.00156 | 0.09844
16.0 | 00 | 0.00000 | 0.93906 | 0.06094 | 0.00000
05 | 0.00000 | 0.98906 | 0.01094 | 0.00000
10 | 0.00000 | 0.96562 | 0.03438 | 0.00000
30 | 0.00000 | 0.99219 | 0.00781 | 0.00000
35 | 0.00000 | 0.99531 | 0.00313 | 0.00156
40 | 0.00000 | 0.89531 | 0.09844 | 0.00625
45 | 0.00000 | 0.78438 | 0.18125 | 0.03438
50 | 0.00000 | 0.41094 | 0.45781 | 0.13125
55 | 0.10625 | 0.00000 | 0.55000 | 0.34375
60 | 0.43281 | 0.00000 | 0.16406 | 0.40313
65 | 0.73594 | 0.00000 | 0.02813 | 0.23594
70 | 0.89062 | 0.00000 | 0.00156 | 0.10781
11.2 | 00 | 0.00000 | 0.99687 | 0.00313 | 0.00000
05 | 0.00000 | 0.99219 | 0.00781 | 0.00000
10 | 0.00000 | 0.98125 | 0.01719 | 0.00156
30 | 0.00000 | 0.99062 | 0.00937 | 0.00000
35 | 0.00000 | 0.99375 | 0.00625 | 0.00000
40 | 0.00000 | 0.99687 | 0.00313 | 0.00000
45 | 0.00000 | 0.94688 | 0.05000 | 0.00313
50 | 0.00000 | 0.72188 | 0.25781 | 0.02031
55 | 0.00000 | 0.38281 | 0.42500 | 0.19219
60 | 0.00000 | 0.00000 | 0.74375 | 0.25625
65 | 0.00000 | 0.00000 | 0.73438 | 0.26562
70 | 0.00000 | 0.00000 | 0.86719 | 0.13281
5.10e21 | 16.0 | 30 | 0.00000 | 0.98091 | 0.01671 | 0.00239
35 | 0.00000 | 0.99523 | 0.00477 | 0.00000
40 | 0.00000 | 0.96181 | 0.03103 | 0.00716
45 | 0.00000 | 0.00000 | 0.99284 | 0.00716
50 | 0.00000 | 0.00000 | 0.90215 | 0.09785
55 | 0.10979 | 0.00000 | 0.62768 | 0.26253
60 | 0.26730 | 0.00000 | 0.34129 | 0.39141
65 | 0.44630 | 0.00000 | 0.00477 | 0.54893
70 | 0.91169 | 0.00000 | 0.00239 | 0.08592

Table 4: Distribution of impactor core material in all iSALE simulations (continued, small-size impactors). Impactor Mass | Impact Velocity | Impact Angle | Escape | Core | Mantle | Vapor
---|---|---|---|---|---|---
(kg) | (km s-1) | (degrees) |  |  |  |
2.78e21 | 20.0 | 00 | 0.00000 | 0.97222 | 0.02778 | 0.00000
30 | 0.00000 | 0.00000 | 1.00000 | 0.00000
45 | 0.00000 | 0.00000 | 0.95833 | 0.04167
50 | 0.00000 | 0.00000 | 0.86574 | 0.13426
55 | 0.02778 | 0.00000 | 0.70833 | 0.26389
60 | 0.41204 | 0.00000 | 0.13889 | 0.44907
65 | 0.50463 | 0.00000 | 0.01852 | 0.47685
70 | 0.89815 | 0.00000 | 0.00463 | 0.09722
16.0 | 00 | 0.00000 | 0.99074 | 0.00926 | 0.00000
30 | 0.00000 | 0.00000 | 0.99074 | 0.00926
35 | 0.00000 | 0.00000 | 1.00000 | 0.00000
40 | 0.00000 | 0.00000 | 0.99537 | 0.00463
45 | 0.00000 | 0.00000 | 0.99074 | 0.00926
50 | 0.00000 | 0.00000 | 0.95370 | 0.04630
55 | 0.00000 | 0.00000 | 0.83796 | 0.16204
60 | 0.10185 | 0.00000 | 0.38426 | 0.51389
65 | 0.34259 | 0.00000 | 0.28704 | 0.37037
70 | 0.79630 | 0.00000 | 0.00463 | 0.19907
11.2 | 00 | 0.00000 | 0.99074 | 0.00926 | 0.00000
30 | 0.00000 | 0.00000 | 1.00000 | 0.00000
45 | 0.00000 | 0.00000 | 1.00000 | 0.00000
50 | 0.00000 | 0.00000 | 0.99074 | 0.00926
55 | 0.00000 | 0.00000 | 0.89352 | 0.10648
60 | 0.00000 | 0.00000 | 0.81019 | 0.18981
65 | 0.00000 | 0.00000 | 0.63889 | 0.36111
70 | 0.00000 | 0.00000 | 0.67593 | 0.32407