∎

11institutetext: R. F. Wimmer-Schweingruber 22institutetext: Institute of
Experimental and Applied Physics, Kiel University, D-24118 Kiel, Germany
Tel.: +49-431-880-3964 Fax: +49-431-880-3968 22email<EMAIL_ADDRESS>kiel.de 33institutetext: National Space Science Center, Chinese Academy of
Sciences, Beijing, China 44institutetext: J. Yu 55institutetext: S. I.
Böttcher 66institutetext: S. Burmeister 77institutetext: H. Lohf
88institutetext: Zigong Xu 99institutetext: B. Schuster 1010institutetext: L.
Seimetz 1111institutetext: A. Ravanbakhsh 1212institutetext: S. Kolbe
1313institutetext: V. Knierim 1414institutetext: H. Woyciechowsky
1515institutetext: Johan L. Freiherr von Forstner1616institutetext:
Shrinivasrao R. Kulkarni 1717institutetext: A. Knappmann 1818institutetext: C.
Büschel 1919institutetext: Institute of Experimental and Applied Physics, Kiel
University, D-24118 Kiel, Germany 2020institutetext: S. Zhang
2121institutetext: B. Yuan 2222institutetext: G. Shen 2323institutetext: C.
Wang 2424institutetext: Z. Chang 2525institutetext: National Space Science
Center, Chinese Academy of Sciences, Beijing, China 2626institutetext: J. Guo
2727institutetext: Institute of Experimental and Applied Physics, Kiel
University, D-24118 Kiel, Germany 2828institutetext: CAS Key Laboratory of
Geospace Environment, Dept. of Geophys. &Planet Sci., University of Science
and Technology of China, Hefei 230026, China 2929institutetext: CAS Center for
Excellence in Comparative Planetology, Hefei 230026, China 3030institutetext:
T. Berger 3131institutetext: C.E. Hellweg 3232institutetext: D.
Matthiä3333institutetext: Institute of Aerospace Medicine, German Aerospace
Center, Linder Höhe, D-51147 Cologne, Germany 3434institutetext: D. Hou
3535institutetext: University of Chinese Academy of Sciences, Beijing, China
3636institutetext: X. Hou 3737institutetext: B. Ren 3838institutetext: Q. Fu
3939institutetext: China Electronics Technology Group Corporation, NO, 18th
Research Institute, Tianjing, China 4040institutetext: Q. Fu
4141institutetext: National Astronomical Observatories, Chinese Academy of
Sciences, Beijing, China

# The Lunar Lander Neutron and Dosimetry (LND) Experiment on Chang’E 4

Robert F. Wimmer-Schweingruber  Jia Yu  Stephan I. Böttcher  Shenyi Zhang
Sönke Burmeister  Henning Lohf  Jingnan Guo  Zigong Xu  Björn Schuster  Lars
Seimetz  Johan L. Freiherr von Forstner  Ali Ravanbakhsh  Violetta Knierim
Stefan Kolbe  Hauke Woyciechowsky  Shrinivasrao R. Kulkarni  Bin Yuan  Guohong
Shen  Chunqing Wang  Zheng Chang  Thomas Berger  Christine E. Hellweg  Daniel
Matthiä  Donghui Hou  Alke Knappmann  Charlotte Büschel  Xufeng Hou  Baoguo
Ren  Qiang Fu

(Received: date / Accepted: date)

###### Abstract

Chang’E 4 is the first mission to the far side of the Moon and consists of a
lander, a rover, and a relay spacecraft. Lander and rover were launched at
18:23 UTC on December 7, 2018 and landed in the von Kármán crater at 02:26 UTC
on January 3, 2019. Here we describe the Lunar Lander Neutron & Dosimetry
experiment (LND) which is part of the Chang’E 4 Lander scientific payload. Its
chief scientific goal is to obtain first active dosimetric measurements on the
surface of the Moon. LND also provides observations of fast neutrons which are
a result of the interaction of high-energy particle radiation with the lunar
regolith and of their thermalized counterpart, thermal neutrons, which are a
sensitive indicator of subsurface water content.

###### Keywords:

Space Radiation Moon Dosimetry Neutrons Exploration

##  1 Introduction

China is currently implementing a series of lunar missions which shall
culminate in a crewed station on the lunar surface. The most recent major step
in this endeavouring is the challenging Chang’E 4 mission to the far side of
the Moon, to the South-Pole Aitken (SPA) basin xu-etal-2018 . Chang’E 4 landed
inside the von Kármán crater at 177.5991∘ E, 45.4446∘ S in selenograpic
coordinates at an elevation of -5,935 m liu-etal-2019 . The SPA basin is the
largest known impact crater on the Moon and one of the largest in the solar
system. It is clear that a record of such a large impact is key to
understanding large impacts in the solar system and thus constrains the impact
history in the solar system potter-etal-2012 . In addition, it gives insights
into the evolution of such large-scale impact basins head-etal-1993 , and
reflects the composition of the lower crust and upper mantle of the Moon.
Inside the SPA basin lies the relatively smooth von Kármán impact crater which
is the landing site for Chinese lunar mission Chang’E 4 ye-etal-2017 ; wu-
etal-2017 . The coordinates of the landing site and its geological context of
the von Kármán crater and SPA basin is discussed in huang-etal-2018 .

In preparation of human exploration of the Moon and solar system, the Lunar
Lander Neutrons and Dosimetry (LND) experiment aboard Chang’E 4 is performing
the first active dosimetric measurements on the lunar surface. Radiation is
one of the main concerns in human space flight and is a potentially limiting
factor for crewed long-term missions such as a mission to the Moon or to Mars
cucinotta-etal-2011 . The complex radiation field of lunar missions is
expected to exhibit large temporal variations in the intensity as well as the
composition of the radiation and is quite different from that measured on the
surface of Earth gordon2004measurement ; haino2004measurements ;
neher1971cosmic ; kremer1999measurements . Therefore, active dosimetry, which
provides time-resolved measurements of the radiation exposure, is a crucial
requirement for human spaceflight in general and equally for human exploration
of the Moon.

The LND experiment consists of segmented silicon Solid State Detectors (SSD)
which form a particle telescope that measures the charged particle radiation.
A new geometrical arrangement and combination with conversion foils allows LND
to also measure the electrically neutral component, neutrons and
$\gamma$-rays. These contribute a non-negligible fraction to the radiation
dose reitz-etal-2012 . The largest part of the absorbed radiation dose comes
from electrically charged galactic cosmic rays (GCR), sporadic solar particle
events, or - inside the Earth’s magnetosphere - from so-called “trapped”
particles in the radiation belts. On the Moon, the latter is unimportant, but
is replaced by an additional, secondary radiation source which is due to the
interaction of the GCR with the lunar soil (regolith). Apart from charged
albedo particles wilson-etal-2012 , this secondary radiation contains neutral
$\gamma$\- and neutron radiation. The latter are highly relevant in a radio-
biological context ottolenghi2013assessment .

Apart from providing information about the temporal variation of the dose
rate, LND also determines the average quality factor $\langle Q\rangle$ by
measuring the Linear Energy Transfer (LET) spectrum of the radiation field.
For calculating $\langle Q\rangle$ from the measured LET spectrum, the LET
dependence of $Q$ as described in ICRP60 and ICRP103 streffer-2007  is used.
This $\langle Q\rangle$ can be folded with the measured energy dose $D$ to
determine the dose equivalent $H$. Radiation measurement with planar Si-SSD
telescopes is a well-established method in dosimetry because it is robust and
easy to handle (see e.g. reitz-etal-2005 ; labrenz-etal-2015 ; berger-
etal-2017 ). As just described, it also provides all required information for
dosimetric measurements. Its disadvantage is that it can not directly measure
the tissue-equivalent dose rate and that its count rate in a non-isotropic
radiation field depends on the orientation of the detector. The multiple
segments of LND allow us to compensate for the latter disadvantage by using
the ratios of coincidence count rates from the various segments, very similar
to what has recently been done for the radiation field on the Martian surface
wimmer-etal-2015 .

Measurements of the radiation field on the lunar surface are crucial to
prepare future human exploration of the Moon. LND determines the required
dosimetric quantities as well as provides measurements of the lunar neutron
and $\gamma$-radiation environment. In this paper we describe the LND,
starting with its scientific objectives and measurement requirements (Sec. 2),
an in-depth discussion of the LND design (Sec.3), LND-internal data processing
(Sec. 4.1) and data products (Sec. 4). Figure 1 shows the LND sensor head (SH)
in the front and the LND electronics box (EB) in the rear.

Figure 1: Photograph of LND which consists of a sensor head (SH, front) and
electronics box (EB, behind), as well as the power and data harnesses which
connect the SH with the EB. The harness to the the instrument control unit
(ICU) is not shown.

##  2 Science Objectives

Despite the aim of landing humans on the Moon in the not too distant future,
radiation measurements in the vicinity of the Moon are remarkably scarce.
Fairly recent measurements in lunar orbit were provided by the Radiation Dose
Monitor (RADOM) on board Chandrayaan-1 dachev-etal-2011 . The spacecraft
reached its operational 100 km circular orbit on November 12, 2008.
Measurements showed a dose rate of 0.227 mGy per day averaged over 3545 hours
of measurement time (20/11/2008 to 18/5/2009). During the last three months of
the mission (20/05/2009 to 28/08/2009) the spacecraft reached a 200 km orbit.
The dose rate increased to 0.257 mGy per day owing to the reduction of the
lunar shadow effect for cosmic rays and to the increase of the cosmic ray flux
related to the reduced solar activity. The minimum of solar activity was
reached shortly after the end of the mission in December 2009 and it was not
expected that significantly larger radiation exposures due to galactic cosmic
rays than the 0.257 mGy per day would occur in these specific orbits reitz-
etal-2012 . This expectation was borne out by measurements in interplanetary
space mewaldt-etal-2010 . Newer measurements have been provided by the Cosmic
Ray Telescope for the Effects of Radiation (CRaTER) instrument spence-
etal-2010  on board the Lunar Reconnaissance Orbiter (LRO). CRaTER measured a
radiation exposure of about $0.22-0.27$ mGy per day in its 50 km orbit spence-
etal-2010b . Chandrayaan-1 and LRO are the only recent missions which have
reported data about the radiation environment of the Moon apart from the
Apollo 17 subsurface measurements of low-energy neutrons by woolum-etal-1975 .

In comparison with these meagre orbital data, there is a real dearth of data
on the lunar surface. The current knowledge about the radiation environment on
the surface of the Moon is based exclusively on calculations using radiation
transport models (e.g.reitz-etal-2012 ) with input parameters from models for
the galactic cosmic ray spectra and for solar particle events. While such
models are based on well-established physical principles, uncertainties in the
inputs and interpretations can result in significant differences in the
predicted total absorbed dose rate or total dose equivalent rate matthiae-
etal-2017  and come with considerable uncertainties mrigakshi-etal-2012 .
Measurements of the lunar neutron density at depths of 20 - 400 g/cm2 within
the lunar subsurface were performed during the Apollo 17 mission woolum-
etal-1975 . These measurements were performed to determine the depth profile
of neutrons in the lunar regolith. This is an important factor if one aims to
determine time scales of the lunar surface mixing processes eugster-etal-1970
. These authors stressed the importance of measuring the spectrum of neutrons
at the lunar surface, but to our knowledge, this has never been done.

The high biological effectiveness of neutrons has been studied by multiple
authors (e.g. ottolenghi2013assessment ; streffer-2007 ; Baiocco2016 ). This
is due to the fact that neutrons can easily interact with nuclei in biological
tissue and produce secondary charged particles. These low-energy short-range
particles interact with the tissue and exhibit a high ionization density and
therefore high potential to damage living cells by the well-known mechanisms
such as direct DNA damage or production of free radicals. Thus, determination
of the neutron spectrum at the lunar surface is a crucial measurement in
preparation of future human exploration of the Moon.

Thus, LND has the following two major science objectives:

  1. 1.

Dosimetry for human exploration of the Moon: Determination of time series of
dose rate and of LET spectra in the complex radiation field of the lunar
surface: Radiation is one of the largest long-term risks in manned
spaceflight. LND will measure the dose for a manned lunar mission as well as
the temporal variation of the dose rate. For the interpretation of these
dosimetric data, the quality factor, $Q$, needs to be known. This is derived
from the LET spectra measured by LND as described in paragraph 2 on page 1. A
novel contribution of LND is to also provide measurements of the neutral
(neutron and $\gamma$-ray) radiation which is an important contribution to the
radiation dose. Measuring the neutron spectrum at the surface also provides
important information to understand lunar surface mixing processes.

  2. 2.

Contribution to heliospheric science: Determination of particle fluxes and
their temporal variations on the far side of the Moon: There are already a
number of spacecraft close to Earth (especially at Lagrange point L1) that
measure the heliospheric particle radiation environment in the vicinity of
Earth. Such a heliospheric ”cluster” of spacecraft is augmented by LND because
it provides an additional, and displaced measurement location. This new data
can contribute to the understanding of particle propagation and transport in
the heliosphere through measurements of the onset times of particle events and
the timing of changes in the energetic particle flux. This is an active field
of research in heliophysics and LND can contribute to it by providing such
data. LND provides data at high cadence (up to one minute) to allow precise
determination of the onset times. Solar particle events have different spectra
than the GCR that do not extend to as high energies, but can nevertheless be a
danger for astronauts on the surface of or orbiting the Moon if their high-
energy flux is sufficiently high (e.g. guo2018generalized ).

In addition to the two aforementioned major science objectives, LND also has a
technological demonstration objective. The extremely large cross section of
gadolinium (Gd) to capture thermal neutrons and subsequently emit a conversion
electron has been exploited for thermal neutron measurements on Earth, but to
our knowledge never before in space (See Sec. 3 for an in-depth discussion.).
Thermal and epithermal neutrons serve as sensitive probes for the shallow
subsurface water (proton) feldman-etal-1998-a ; feldman-etal-1998-b  and FeO
content elphic-etal-1998 . LND’s technological objective is thus to
demonstrate the technological readiness level of this detection technique for
space-based exploration missions. Because of the long and cold lunar nights,
Chang’E 4 has to rely on radioisotope thermoelectric generators (RTG) and
several radioactive heater units (RHU) on the lander and rover, and so the
scientific success of this method can not be ascertained at this point. The
following two science questions illustrate the potential of this measurement
technique.

  1. 1.

Determine the subsurface water content in the South-Pole Aitken Basin:
Subsurface water on the Moon is a precious resource which would be needed for
long-term human presence of humans on the Moon. It is thus critical to
understand the amount of water on the Moon. Because the South-Pole Aitken
Basin has some permanently shadowed regions, it is believed that it may harbor
significant amounts of water feldman-etal-2001 . LND is sensitive to the
subsurface water content and determine the flux of thermal neutrons averaged
over a small area beneath the lander and a larger area surrounding the lander.
See section 3 for a more thorough discussion. At the time of writing this
paper, the influence of the RTG and RHU on this measurement is still being
assessed.

  2. 2.

Determine the FeO content in the South-Pole Aitken Basin: The South-Pole
Aitken Basin is the second largest known impact crater in the solar system. It
is therefore also a “deep hole” in the crust of the Moon and allows us to peer
into mantle material of the Moon. Measurements of Lunar Prospector and
Clementine show different results for the abundance of heavy elements (which
are dominated by FeO) lawrence-etal-2002  which is puzzling, but also of high
importance to understanding the origin of the Moon and thus the solar system.

To achieve the science objectives listed above, LND is designed to perform
several measurements of the lunar radiation environment, which are discussed
in more detail in Sec. 4 and summarized here:

  1. 1.

Time series of the charged and neutral particle dose rate in Si at a cadence
of up to 1 minute.

  2. 2.

Coarse LET-spectra at a cadence of up to 1 minute.

  3. 3.

Coarse charged particle spectra at a cadence of up to 1 minute.

  4. 4.

Coarse energy deposit spectrum of neutral particles at a cadence of up to 1
minute.

  5. 5.

Count rates of thermal neutrons at a cadence of 10 minutes.

  6. 6.

High-resolution measurements of all these quantities as well as heavy ions at
a cadence of 1 hour.

##  3 Instrument Description

LND is mounted inside the $-Y$ payload compartment of the Chang’E 4 lander and
consists of a Sensor Head (SH) and an Electronics Box (EB) (see Fig. 1). The
LND EB connects to the Instrument Control Unit (ICU, not shown) which serves
as the electrical and data interface of LND with the lander. The sensor head
is mounted on a bracket close to the upper deck of the lander which has a re-
closeable opening which allows an unobstructed field of view (FOV) into the
sky. This opening is closed during lunar nights to conserve heat inside the
payload compartment. The LND FOV points approximately 13∘ from the direction
of the normal to the lander deck or along ($\vec{n}=(0.9591,0.0644,0.2772)$ in
(sky, west, south) coordinates.). The small detector signals are pre-
amplified, shaped, and converted to digital signals inside the SH. They are
driven to the EB via UART/LVDS111Universal Asynchronous Receiver/Transmitter,
Low voltage Differential Signaling where further analysis of the signals is
performed. SH and EB are connected by two harnesses, one for power supply,
heater, thermistor and bias voltage of detectors, and the other one for ADCs’
control signals and data readout (see Fig. 1). The design with a separate
sensor head and electronics box was driven by the requirement to keep the
sensor head as cool as possible in the challenging thermal environment of the
Chang’E4 lander.

Figure 2: Functional block diagram of LND. All 10 detectors (indicated by A -
J inside the dash-dotted rectangle marked LND) and their front-end electronics
(pre-amplifiers (PA), shapers (SH), and analog-to-digital converters (ADCs))
are accomodated in the sensor head (left half of the schematic). All other
electronics such as the analog and digital field programmable gate arrays
(FPGAs) low-voltage power supply (LVPS) and are housed in the electronics box
(E-Box, to the right of the dash-dotted vertical line).

Figure 2 shows a functional block diagram of LND. The left-hand side of it
(divided by the vertical dashed line) shows the functions performed in the LND
SH, the right-hand side the LND EB functions. The LND detector system, pre-
amplifiers, shapers and analog to digital converters (ADCs) are all contained
in the LND SH. Twenty charge sensitive pre-amplifiers are integrated onto a
printed-circuit board (PCB) which amplifies trigger signals generated by the
LND detector system. The pre-amplifiers are followed by 30 pairs of shaper and
ADC (analog to digital conversion) circuits which shape and and then sample
the amplified signals before they are sent to the LND EB via the harness. The
digitized values from the SH are pulse-height analyzed (PHA) by the analog
FPGA (Field-Programmable Gate Array) in the EB. The analog FPGA also controls
the ADCs, performs digital filtering, the front-end trigger processing, and
housekeeping data acquisition. The data from the analog FPGA are sent to the
digital FPGA for additional processing and storage before being sent to the
ICU. The additional processing in the FPGAs is discussed in Sec. 4.1. The LND
EB also contains the LVPS board, which supplies latch-up protected power for
LND as well as the bias voltage for the LND SSDs.

###  3.1 Mechanical and Thermal Design Considerations

Figure 3: Schematic view of the LND sensor head in the payload compartment of
the Chang’E 4 lander. LND is tilted by 13 degrees with respect to the top
panel normal, as indicated in this sketch. There is no tilt in the other
direction.

As already mentioned, LND is mounted in the $-Y$ compartment of Chang’E 4
Lander and is tilted by 13 degrees, as shown in Fig. 3. The sensor head sits
on a bracket in order to achieve a unobstructed FOV through the top window of
$-Y$ compartment. Additionally, the position of the sensor head is very close
to the window not only for the purpose of unobstructed FOV but also to radiate
as much heat to the sky as possible via the second surface mirror tape with a
reflectivity to absorptivity ratio of $\sim 8$ which is applied to the front
panel of the LND SH. This keeps the sensor head cool and reduces the
importance of leakage current as a noise source. The size of the top window is
16cm $\times$ 23cm and is open during lunar day time and closed during the
cold lunar night. The LND SH is further insulated from the warm payload
compartment by a “skirt” of MLI (10 layers, emissivity 0.035) which is also
shown in Fig. 3. This connects from the top of the window and completely
surrounds the LND SH, effectively thermally decoupling LND SH from the payload
compartment.

The temperature at the interface of the LND bracket and its mounting panel of
the lander was modeled to vary from -20∘C to +55∘C in the operational case and
-60∘C to +70∘C in the non-operational case. The interface temperature of the
LND electronics box and the lander is expected to lie between -20∘C and +55∘C
in the operational case and -70∘C to +70∘C in the non-operational case. During
the first lunar day, temperatures varied between -7.97∘C and 48.10∘C, with the
highest temperatures occurring on the sensor head analog board, and the lowest
in electronics box.

###  3.2 The LND Sensor Head

This section gives an overview of the LND sensor head, more detailed
descriptions of the different arrangements are given farther down in this
paper, as are several of the figures which are referred to here for the first
time.

Figure 4: The LND telescope consists of 10 segmented 500 $\mu$m-thick Si
solid-state detectors (SSDs), A - J. Detectors B/C, E/F, G/H, and I/J are
mounted in a sandwich configuration, the inner segments of the A and B
detectors, A1 & B1, span the telescope opening. See text for a more detailed
discussion. Angles are measured from the middle to middle of the detector
edges, as discussed on p. 3.3.1.

The LND SH consists of a stack of ten Si solid-state detectors (SSDs) each
with a nominal thickness222Their measured thicknesses are given in Tab. 3.3 of
500 $\mu$m. They are arranged in a charged-particle telescope configuration as
shown in Fig. 4 in which the SSDs are labeled A through J. The measured
thicknesses of the individual detectors are given in Tab. 3.3. Each detector
is segmented into an inner and outer segment with approximately the same
areas, as shown in Fig. 5. This telescope configuration is used to detect
charged particle radiation and identify its composition. Fast neutrons and
$\gamma$-radiation are detected in the inner segment of the C detector in
anti-coincidence with all other detector segments. A 20 $\mu$m thin Gd foil is
sandwiched between detectors E&F and G&H and is used to detect thermal
neutrons. A 250 $\mu$m thick Gd foils is sandwiched between two 500 $\mu$m Al
plates (shown in green) to shield the upward (downward) thermal neutron flux
from the E&F (G&H) detectors and thus allow directional information, as
discussed below in Sec. 3.4.

Fig. 5 shows the detector segments and detailed dimensions.

Figure 5: LND detector layout shows the sensitive areas of LND’s detectors.
The inner segments are referred to as “1”, the outer segments as “2”.
Dimensions are in mm. The area of the inner segment is 440 mm2. The outer
segment and cross-talk ring are connected and their area adds up to 435.6 mm2,
uncertainties in the measurements in this Figure are less than 0.01 mm.

###  3.3 Detectors, Segmentation, and Gain Stages

As already discussed, the detectors on LND are all segmented, some are read
out with two energy gains. Table 3.3 gives the conversion factors from ADC
value to energy (in keV) for LND’s detector segments. For instance, detector
segment A1 is read out at Low gain (A1L) and High gain (A1H), while the two
segments of detector E, E1 and E2, are both read out with one gain. This
information is only needed when analyzing PHA data. The conversion has already
been applied to the published LND data.

detector/ | thickness | gain 1 | gain 2
---|---|---|---
segment | [$\mu$m] | [keV/mV] | [keV/mV]
A1 | 514 | 12.425 | 186.476
A2 |  | 12.530 | 183.837
B1 | 509 | 12.447 | 179.555
B2 |  | 12.800 | 199.022
C1 | 505 | 12.613 | 159.538
C2 |  | 12.400 | 178.805
D1 | 508 | 12.322 | 182.632
D2 |  | 12.480 | 183.416
E1 | 502 | 4.037 | –
E2 |  | 4.142 | –
F1 | 504 | 3.993 | –
F2 |  | 4.051 | –
G1 | 514 | 4.073 | –
G2 |  | 4.070 | –
H1 | 502 | 4.062 | –
H2 |  | 4.065 | –
I1 | 505 | 12.403 | 163.653
I2 |  | 12.144 | 158.402
J1 | 509 | 3.990 | –
J2 |  | 4.025 | –

Table 1: LND detector segments, measured detector thicknesses and gains.

The geometry factors of LND are defined by coincident measurements in A1 and
B1 up to a depth of detector C. For signals in detectors D – J, a coincident
measurement in A1 and D1 is required, as well as a larger energy deposition in
D1 than in D2. This results in a geometry factor of 0.58 cm2sr for A1&B1 and
0.55 cm2sr for A1&D1 with uncertainties less than 1%. The geometric factors of
LND were calculated using GEANT4 agostinelli-etal-2003  for an isotropic flux
of particles, i.e., from $4\pi$. $4\pi$ geometry factors are given here
because there is also a (small) ”return” flux of secondary particles from the
Moon.

For dosimetric quantities shielding by structures in the lander, etc. is not
that important. This allows a larger geometric factor (22.23 cm2sr) by using
the combination of the B (B1&B2) and I (I1&I2) detectors which provides high
counting statistics. Again, the geometry factor given here is calculated for a
$4\pi$ radiation field.

####  3.3.1 Charged-Particle Telescope

A schematic view of the LND SH charged-particle telescope is shown in Fig. 4.
It can be divided into an upper and lower half. The upper four detectors (A–D)
form a detector arrangement similar to the Flight Radiation Environment
Detector (FRED) moeller-etal-2011 ; moeller-etal-2013 ; moeller-etal-2013b
which was based on the Ionizing RAdiation Sensor (IRAS333ESA’s original
Exomars mission included the Humboldt lander with its Pasteur payload. The
Pasteur payload included the Ionizing Radiation Assessment Sensor (IRAS,
wimmer-etal-2008 ), and parts of is design are used in LND. After assembly of
the IRAS prototype, it was reused as FRED in several high-altitude balloon
flights moeller-etal-2013 ; moeller-etal-2013b  and was also qualified for use
in civil aircraft moeller-2013 . FRED used an IRAS-telescope of four 300
$\mu$m Si-SSDs and was calibrated with neutrons at PTB and iThemba
moeller-2013 ; moeller-etal-2013b .) which was developed as part of ESA’s
Exomars program. The lower half of LND (detectors E–J) consists of a closely
packed stack of six more Passivated Implanted Planar Silicon (PIPS) detectors
and an Al-Gd-Al absorber for thermal neutrons. Two pairs (E&F and G&H) clamp a
20 $\mu$m thin Gd foil, while I&J complete the charged-particle telescope.

The full opening angle of 29.4∘ of the LND FoV is determined by the inner
segments of detectors A and B (A1 and B1) and the outer segment of detector J
(J2) as sketched in Fig. 4. Note that this angel is not shown in Fig. 4. The
opening angles (measured from the middle to the middle of the detector edges)
and geometric factors of relevant detector combinations are given above.

This arrangement allows to determine which ions stop in the various detectors
and gives a good estimate of the penetrating particle flux. The resulting
rather longish telescope ensures that the full energy deposit of a particle
which triggers B1 and A1 is measured for stopping ions or that it is
identified as a penetrating ion. The primary energy ranges for ions stopping
in B–I are given in Tab. 6. For dosimetric measurements discussed in
subsection 4.4 a higher count rate is advantageous and both inner and outer
segments of the relevant detectors are used. Because electrons scatter much
more than ions, this telescope configuration is less sensitive to their
primary energy, although some information is still retained as can be seen in
Fig. 13 and discussed there.

The telescope aperture is covered by a layer of thin aluminized Kapton foil
(50.8 $\mu$m Kapton and 25.4 $\mu$m of Al). The size of this window
corresponds to the opening of the telescope spanned by the A1$\cdot$B1
detector segments projected onto the front housing surface of the LND SH. The
energy which particles loose in this protective foil is small compared to the
energy loss in the front detector, A, and has been accounted for in the values
of energy ranges given in Tab. 6.

LND can measure the composition of the charged particles using the combination
of the energy deposited in the front detector (A) and the total deposited
energy in the (B - I) detector stack. This allows LND to measure the
composition of the stopping particles, which is important for dosimetric
purposes but also for heliospheric science. LND provides energy spectra up to
30 MeV/nuc, i.e., above the often-seen “knee” in the interplanetary energy
spectrum. This “knee” is an important indicator of the acceleration process
reames-2014 . Of course the majority of all particles will penetrate LND,
nevertheless, their energy deposit remains proportional to the square of their
nuclear charge and, therefore, LND measures and discriminates all major
minimally ionizing particle species. Knowledge of the particle composition is
important for dosimetry and helps to better understand the LET spectrum (See
Sec. 4.4).

###  3.4 Neutral Particle Detection

LND’s top telescope consists of four segmented Si-SSDs (A - D in Fig. 4). The
three lower detectors (B, C, and D) are packed as close together as possible
using a special process developed by Canberra (now Mirion technologies), the
provider of the SSDs. The inner segment of the C detector, C1, is surrounded
by the B and D detectors as well as the outer segment of the C detector, C2.
Thus, any signal measured in C1 in anti-coincidence with B, D, and C2, will be
due to a neutral particle (neutron or gamma ray). This configuration allows us
to measure neutrons in the energy range $1\lesssim E_{n}\lesssim 20$ MeV with
a maximum energy deposition of $\sim 13\%$ of their primary energy (Fig.
6(b)).

(a) Geometry factor for the detection of gamma rays. Colored dotted lines
indicate various interaction processes discussed in the text.

(b) Geometry factor for the detection of neutrons. The red line shows the
maximum recoil energy transfer. The blue dotted line shows the plasma effect.

Figure 6: Geometry factors for detecting gammas (left) and neutrons (right).
The color scales are the same for both plots. See text for discussion.

This figure shows the geometry factor for the detection of neutrons as a
function of energy. In this plot, incident energy is shown along the $x$-axis,
and the energy deposited in the detector is shown along the $y$-axis. The
geometric factor for the measurement is color coded as shown in the color bar
on the right and was simulated using GEANT4 version 10-1-patch-2444Using the
physics lists QGSP_BERT_HP, G4EmLivermorePhysics, and
G4RadioactiveDecayPhysics. agostinelli-etal-2003 ; allison-etal-2006 ;
allison-etal-2016 . The dashed red line marks the previously discussed elastic
scattering of neutrons with Si-nuclei, it marks the $13.3\%$ maximum energy
transfer. Close inspection shows that the recoil nuclei deposit somewhat less
energy than the allowed maximum which is due to the so-called plasma-effect
tove-and-seibt-1967 ; moeller-2013 . Because the knock-on Si nuclei are highly
ionizing and have only a very short range in Si, the electric field used to
separate electron-hole pairs can not fully penetrate into the region of
ionization and a fraction of the electrons and holes can recombine before they
are separated. This effect results in a small correction which is indicated by
the blue dotted line and is not included in the GEANT4 physics lists. Figure 8
shows the expected measured energy spectrum in C1 only (i.e. in anti-
coincidence with the all other detectors and detector segments).

Continuing the discussion of Fig. 6, we now move to the left-hand panel, Fig.
6(a), which shows LND’s response to $\gamma$-rays. It shows that $\gamma$-rays
can be measured up to approximately 1 MeV. Above that energy, the geometry
factor rapidly decreases. The diagonal line (highlighted with black dots) at
the lowest energies is due to the photo-electric effect in which a
$\gamma$-ray transfers energy to a photo-electron. This effect dominates LNDs
$\gamma$-ray response at low energies because the recoil electrons do not have
enough energy to exit the LND detector and thus deposit all their energy in
the 500 $\mu$m detector. To the right of the photo-electric effect, one sees
the increasing importance of Compton scattering (highlighted with blue dots)
which dominates for energies between $\sim$100 keV and a few MeV. At higher
incident photon energies, the photo effect (shown with red dots) begins to
contribute. LNDs detectors are virtually transparent for higher energies of
$\gamma$ radiation. The horizontal lines which can be seen at low energy
depositions are due to $\gamma$-rays emitted by various materials inside the
LND SH, lead and tin in the electronics, and gadolinium from the Gd foils and
absorber discussed in the following paragraphs. These lines are highlighted by
colored dots and called out in the legend panel. The enhanced response at 17
MeV $<E_{\gamma}<$ 23 MeV (surrounded by a dashed black line) is due to photo-
neutron reactions anderson-etal-1969 .

As has become obvious in the previous discussion, LND can not truly
discriminate between neutrons and $\gamma$-rays. Nevertheless, the different
instrument response functions for $\gamma$-rays and neutrons (panels 6(a) and
6(b) in Fig. 6) result in different sensitivities to the two dominant neutral
particle species. Energy depositions below 1 MeV are dominated by $\gamma$s
whereas at higher deposited energies, neutrons gain in importance.

###  3.5 Thermal Neutrons

We now move on to discuss the lower six detectors (E–J) of LND which are
mounted in two different sandwich configurations. In one, detectors E&F and
G&H clamp a very thin ($\approx 20$ $\mu$m) Gd foil, as shown in red in Fig.
7. The (natural) Gd-foil has a very large cross section555leinweber-etal-2006
and abdushukurov2010  give different values for the cross sections, here we
cite those of leinweber-etal-2006 . (48’800 barn) for thermal ($v_{\rm th}\sim
2200$m/s) neutron capture leinweber-etal-2006 ; abdushukurov2010  and
therefore is used to detect thermal neutrons. The cross section is dominated
by those of the 155Gd (60’700 barns) and 157Gd (254’000 barns) isotopes with
natural abundances of 14.8% and 15.7% leinweber-etal-2006 . After a thermal
neutron has been captured in a 155Gd or 157Gd nucleus, the excited 156Gd or
158Gd nucleus decays via internal conversion emitting a single conversion
electron (in $\sim 80\%$ or $\sim 60\%$ of all cases) or $\gamma$-decay. Most
of the conversion electrons have energies between $\sim 80$ and $\sim 300$ keV
fogelberg-and-baecklin-1972 . The electrons have a range of several microns in
the Gd foil and therefore can escape the foil and hit the neighboring sandwich
detector. Using the other LND detectors as an anti-coincidence, this provides
a clean measurement of thermal neutrons. The $\gamma$-ray from neutron capture
can also be detected in anti-coincidence with surrounding detectors, providing
an independent measurement of the thermal neutrons. The lowermost detector
sandwich (I&J) is a copy of the LND B&C-sandwich and serves as the final
detector in the stack. Detector J serves as a discriminator for particles
stopping in the particle telescope spanned by detectors A – I.

Figure 7: Gd-sandwich detector concept. The very thin Gd foil captures thermal
neutrons and emits conversion electrons. The thick Gd-foil encased in Al
effectively shields the upper Gd-sandwich from thermal neutrons from the soil
and the bottom Gd-sandwich from thermal neutrons from above.

Thermal neutrons emitted from the soil are very slow and a large fraction of
them will return to the Moon because their speeds are less than the escape
speed from the Moon, 2.4 km/s. To discriminate such ballistic thermal neutrons
(which are sensitive to the subsurface proton (water) content) returning to
the Moon from neutrons coming from beneath the lander, the E&F sandwich is
shielded from below by a $\sim 250$ $\mu$m thick Gd foil which is encased in
two 500 $\mu$m thick Al sheets. The thickness of this Gd absorber was
optimized to ensure that less than one in 1000 thermal neutrons can penetrate
through the Gd. The Al encasing is thick enough that the electrons from the
neutron capture cannot escape. Its thickness was also chosen to be the same as
that of the Si-SSDs to also absorb a similar fraction of the $\gamma$-rays
from the neutron capture as in the Si-SSDs. The G&H sandwich then measures
thermal neutrons from below and the E&F sandwich measures thermal neutrons
returning to the Moon from above. Because the return flux averages over a
large area and the primary flux from below averages over a small area, the
difference between the two gives us a measure of the local subsurface
proton666Thermal neutrons are also good tracers of the fluorine content of the
soil, measurements are thus somewhat ambiguous. content. The detector geometry
is summarized in Fig. 7

Figure 8: Modeled spectrum of energy deposits in C1 in anti-coincidence with
all other detector channels. Energy deposits above 1 MeV are dominated by
neutrons.

Model spectra of neutral particles are shown in Fig. 8 and exhibit relatively
low count rates. Integrated over all energies, we expect a count rate of about
1.3 counts per second in the absence of the RTGs/RHUs. At low energies, this
count rate is dominated by gammas. As one can easily see in Fig. 8, neutrons
start to dominate the count rate above energy depositions of about 700 keV, at
energies above $\sim 1$ MeV, we expect only about 0.006 gamma, but 0.06
neutron counts per second 777Building up statistics over time, one may attempt
to invert the neutron and gamma spectra similarly to what was done for the
Radiation Assessment Detector (RAD) on NASA’s Mars Science Laboratory (MSL)
koehler-etal-2011 , albeit with considerably lower counting statistics and
fidelity of the result..

The Chang’E 4 lander and rover are designed to survive many harsh lunar day
and night cycles. Therefore, the lander carries one Radioisotope
Thermoelectric Generator (RTG) for power and three Radioisotope Heater Units
(RHUs). The background from the RTG and RHUs was measured at the 18-th
Research Institute, China Electronics Technology Group Corporation in Tianjin,
China. The results are reported in hou-etal-2019 .

##  4 Data Products

The measurement requirements given in section 2 map to the LND data products
which are summarized in Tab. 2. They are a mix of some data products at high
time resolution (one minute), medium time resolution (10 minutes), and low
time resolution data (one hour). The different cadences of LND’s data products
allow the investigation of rapid variations such as are, e. g., expected
during the onset of a solar particle event. At the same time, no telemetry is
wasted with sending all information at this high cadence. This chapter gives a
detailed description of LND’s data processing and data products.

###  4.1 Data Processing Inside LND

Figure 9: LND’s trigger logic is divided into three levels (L1, L2, and L3).
Processing is distributed into the analog FPGA (L1 & L2) and digital FPGA
(L3).

LND data processing is summarized in Fig. 9 which we discuss from left to
right here. When a particle hits one or more of LND’s detector segments, the
L1 trigger checks which of LND’s 30 detector (gain) channels registered an
energy deposition larger than their trigger thresholds. These are given in the
box beneath the left-most entry of Fig. 9. This information as well as the
measured values are passed on to the L2 trigger which performs a number of
tasks. It checks whether the event has triggered detectors which are relevant
for the LET data product (different detectors can contribute). If so, the
counter for valid LET events (L2$[0]$) is incremented by one. Similarly, if an
event is classified as fulfilling the conditions to contribute to the
determination of TID, the counter for valid TID events (L2$[1]$) is
incremented by one. This is repeated for neutral particles detected in C1
(L2$[2]$) and detectors E – F (L2$[3]$ – L2$[6]$). Such events are valid if
energy was deposited in only one of these detectors, i.e., in anti-coincidence
with all other detectors. Finally, if an event is identified as being due to a
heavy ion, the L2$[7]$ counter is incremented by one. An event which does not
satisfy these trigger conditions is dropped. All processing up to this point
is performed in the analog FPGA (see Fig. 2).

After this processing by the L2 trigger, a valid event is passed on to the L3
trigger which is implemented in the digital FPGA. This trigger further
classifies events and increments the appropriate counters. We being this
discussion with the L3[1] and L3[2] triggers because they are the simplest
ones. An event which was identified by the L2 trigger as an event seen only in
C1 (in anti-coincidence with all other detector segments) is further analysed
and the spectrum of energy depositions in the C1 detector is incremented
accordingly. This is indicated by ”$+1$ fast n histogram” in Fig. 9. The same
is done for events seen in detectors E – H only (L3[2] trigger: ”$+1$ thermal
n histogram”). Because these events only triggered single detectors, their
processing ends here. For all other events, a more complicated processing
chain is applied. An event which satisfies the Ls[0] condition to contribute
to TID has triggered LND’s B detector. Depending on the energy deposited in
detector B, the corresponding histogram counter is incremented by one. While
TID is only a number, LND can not measure it as such. The spectrum of energy
depositions thus accumulated needs to be summed on Earth to derive TID, see
Sec. 4.4. This event is further processed by checking whether it also
triggered detector I, as depicted in Fig. 9. Events which are classified as
L3[3] events have triggered the B detector and at least one other detector,
they are processed in the same manner. The flow chart in the right of Fig. 9
describes the further processing chain.

The histograms which are thus accumulated by LND can be one-dimensional or
two-dimensional. TID and some LET spectra are accumulated in one-dimensional
histograms whereas events that triggered several detectors augment two-
dimensional histograms. We refer to the collection of these histograms as the
Xmas plot (see Sec.4.2 and Fig. 10). The quantities used to calculate the
entry ”pixel” in the Xmas plot are calculated according to the quantities
summarized in Tab. 5, the corresponding energy ranges are given in Tab. 6. The
individual entry types are discussed in the following subsections.

1-minute data products
---
Data product | # counters |  Comments
Protons | 14 |  2 counters for B, one each in C, D, E, F, G, H, and I, 5 for penetrating. See Tab. 6 for energy ranges.
Electronsa | 7 |  4 counters for electrons stopping in B, C, D, 3 counters for electrons stopping in E and F, one for G, H, and I combined. See Tab. 7 for energy ranges.
Neutrals | 4 |  4 counters for $20<E<200$, $200<E<10^{3}$, $10^{3}<E<10^{4}$, $10^{4}<E<10^{5}$ keV
Dosimetryb | 8 |  8 counters for $20<E<95$, $95<E<320$, $320<E<1076$ keV, and $1.076<E<3.62$, $3.62<E<12.2$, $12.2<E<41$, $41<E<138$, $138<E<390$ MeV
LET spectrumb | 8 |  same bins as dosimetry
10-minute data products
Data product | # counters |  Comments
Thermal neutrons | 8 |  1 each for E1, E2, F1, F2, G1, G2, H1, H2, covering $\sim 55<E<\sim 75$ keV
Electronsc | 16 |  16 counters for electrons stopping in E, F, G, H (4 counters for each detector.) See Tab. 7 for energy ranges.
3He | 5 |  3 counters in B, one each in C and D (stopping). See Tab. 6 for energy ranges.
4He | 10 |  3 counters in B, one box in C, D, E, F, G, H, and I. See Tab. 6 for energy ranges.
CNO | 9 |  2 counters in B, one box in C, D, E, F, G, H, and I. See Tab. 6 for energy ranges.
heavy ions | 9 |  2 counters in B, one box in C, D, E, F, G, H, and I. See Tab. 6 for energy ranges.
penetrating | 7 |  3He, 4He, and heavy ions. See Tab. 6 for energy ranges.
60-minute data products
Data product | # entries |  Comments
“Xmas plot” | $150\cdot 64$ |  Full information
PHA words | n/a |  16 PHA buffers of 1 kByte each per hour for diagnostic and calibration purposes.
Table 2: List of LND science data products which are included in telemetry at
1, 10, and 60-minute time resolution as indicated by the headings. aDefined in
Tab. 7. b Bin edges will be adjusted during the course of the mission. c The
counters are defined in Tab. 7.

###  4.2 Figure 10 – the “Xmas Plot”

Fig. 10 shows a ”Xmas plot888We call it the “Xmas plot” because we sent this
data summary plot to colleagues around the world as our Xmas card in 2017. We
had to choose a name for this plot.” which is LND’s principal data product,
all others are derived from it. It contains all data of the particles measured
by LND. The Xmas plot is actually an image of LND’s accumulator memory, the
different regions are explained in more detail in Tab. 3 and are summarized
below. Each pixel of the Xmas plot is a counter which is incremented as
discussed below. LND memory contains two Xmas plots, an active and an inactive
one. Upon measurement of a particle, the active one is updated as described
below. This accumulation is ended after 3600 seconds when the Xmas plot is
turned to inactive mode. At this moment, the counters in the previously
inactive Xmas plot are reset to zero and this memory region (Xmas plot) is
turned to active mode. The previously active Xmas plot is now inactive and is
red out and sent to telemetry over the course of the next hour. Thus the two
Xmas plots alternate between active and inactive mode and provide continuous
data coverage. Regions shaded in cyan in Fig. 10 are not put into telemetry
because they don’t contain physical data and are dominated by noise.

The Xmas plot is divided up column wise into different regions which are
defined in Tab. 3. Each column has 64 rows. Each point in this $274\times 64$
matrix serves as a counter which is incremented when the LND L3 trigger
identifies this to be the correct entry. The integer counters are 4 Bytes, 6
of the 32 bits serve as Hamming-encoding single-even upset correction.

We now proceed to give the explanation of the Xmas plot starting from the left
and moving through it to the right. The left most region of the Xmas plot
contains the accumulators for neutral particles (Sec. 4.3), it is followed
(from left to right) by two regions for the dosimetric quantities total
ionizing dose (TID) and linear energy transfers (LETs) (Sec. 4.4). To the
right of these are memory regions for the accumulation of particles stopping
in LNDs detectors B–I (Sec. 4.5). Penetrating particles are mapped to the
region indicated by “Penetrate J” (Sec. 4.6). The single column on the very
right contains electron data, as does the narrow strip at the bottom of the
plot (Sec. 4.7). The summed counts in the regions indicated by red counters
and white names are read out and telemetered at a cadence of 1 or 10 minutes,
while the entire Xmas plot with the full information is put into telemetry
every hour. The 10 and 1 minute data are explained in more detail in sections
4.9 and 4.10.

Fig. 10 shows an annotated Xmas plot, the annotations are referred to in the
following paragraphs.

Figure 10: LND “Xmas plot”. It is divided into several vertical regions which
contain information about different particle populations. The principal
divisions are indicated in this figure which is based on GEANT4 simulations.
Heavy ions are over-represented to make them visible. The regions indicated
with red boundaries in this Figure will be adapted to reflect updated
calibration values. They are labeled according to the entries given in Tabs.
3, 6, and 7. The regions shaded in cyan are not transmitted back to Earth.

| Columns |
---|---|---
Xmas Plot Region | start | end |
Neutral particles | 0 | 19 |
detected in E1 | 0 | 1 | $E1\cdot\overline{E2}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{F}\cdot\overline{G}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in E2 | 2 | 3 | $E2\cdot\overline{E1}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{F}\cdot\overline{G}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in F1 | 4 | 5 | $F1\cdot\overline{F2}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{G}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in F2 | 6 | 7 | $F2\cdot\overline{F1}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{G}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in G1 | 8 | 9 | $G1\cdot\overline{G2}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{F}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in G2 | 10 | 11 | $G2\cdot\overline{G1}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{F}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
detected in H1 | 12 | 13 | $H1\cdot\overline{H2}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{F}\cdot\overline{G}\cdot\overline{I}\cdot\overline{J}$
detected in H2 | 14 | 15 | $H2\cdot\overline{H1}\cdot\overline{A}\cdot\overline{B}\cdot\overline{C}\cdot\overline{D}\cdot\overline{E}\cdot\overline{F}\cdot\overline{G}\cdot\overline{I}\cdot\overline{J}$
detected in C1 | 16 | 19 | $C1\cdot\overline{C2}\cdot\overline{A}\cdot\overline{B}\cdot\overline{D}\cdot\overline{E}\cdot\overline{F}\cdot\overline{G}\cdot\overline{H}\cdot\overline{I}\cdot\overline{J}$
Dosimetry | 20 | 31 |
TID in B | 20 | 21 |  $B$ (if energy deposit in B is bigger than 40keV)
LET $ABC\overline{I}$ | 22 | 22 | $A\cdot B\cdot C\cdot\overline{I}$
LET $\overline{A}BIJ$ | 23 | 23 | $\overline{A}\cdot B\cdot I\cdot J$
LET $ABIJ$ | 24 | 31 | $A\cdot B\cdot I\cdot J$
Charged particles | 32 | 273 |
stopping in B | 32 | 47 | $A\cdot B\cdot\overline{C}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})$
stopping in C | 48 | 59 | $A\cdot B\cdot C\cdot\overline{D}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})$
stopping in D | 70 | 85 | $A\cdot B\cdot C\cdot D\cdot\overline{E}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
stopping in E | 103 | 117 | $A\cdot B\cdot C\cdot D\cdot E\cdot\overline{F}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
stopping in F | 133 | 144 | $A\cdot B\cdot C\cdot D\cdot E\cdot F\cdot\overline{G}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
stopping in G | 166 | 173 | $A\cdot B\cdot C\cdot D\cdot E\cdot F\cdot G\cdot\overline{H}\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
stopping in H | 198 | 205 | $A\cdot B\cdot C\cdot D\cdot E\cdot F\cdot G\cdot H\cdot\overline{I}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
stopping in I | 228 | 237 | $A\cdot B\cdot C\cdot D\cdot I\cdot\overline{J}\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})\cdot(E_{D1}>E_{D2})$
Penetrating | 246 | 265 | $A\cdot B\cdot I\cdot J\cdot(E_{A1}>E_{A2})\cdot(E_{B1}>E_{B2})$
Electrons | 273 | 273 | stopping in B if $16\cdot\log_{2}((E_{A}+E_{B1})\cdot E_{A}/(8000\cdot 4000))<0$
|  |  | stopping in C if $16\cdot\log_{2}((E_{A}+E_{B1}+E_{C})\cdot E_{A}/(10000\cdot 4000))<-16$
|  |  | stopping in D if $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A}/(1200\cdot 6000))<0$
Table 3: Column ranges for the different regions in the Xmas plot. Each column
contains 64 rows or entries. Columns which are not mentioned in this table are
not transmitted back to Earth and are shaded in Fig. 10.

###  4.3 Neutral Particles

Neutral particle measurements are based on measurements in single-detectors or
detector segments in anti-coincidence with all other detectors/segments. The
energy deposits measured in individual detectors are histogrammed and
telemetered down as part of the Xmas plot, some lower-resolution data products
are sent at higher time resolution, as summarized in Tab. 3. Because the
Chang’E 4 lander has an RTG and three RHUs, small energy deposits in the
single detector are dominated by the background from the lander’s RTG and
RHUs. This needs to be accounted for when interpreting LND’s measurements and
using them to predict human exposure on the surface of the Moon.

####  4.3.1 Thermal Neutrons

The left-most 16 columns contain the histograms of the energy deposits in
detectors E, F, G, and H. Each detector has two segments (1: central, 2: outer
segment), so there are 8 histograms in total. The energy deposit is
accumulated in 128 channels, it is wrapped around once to fit into the format
of the Xmas plot, thus each histogram covers two columns in the Xmas plot. An
example will help understand the structure:

The histogram of energies measured in E1, $E_{E1}$, is shown in the two left-
most columns of Fig. 10 (see also Tab. 3). The 128 bins are accumulated based
on the following formula:

${\rm bin\\#}=16\cdot\log_{2}(E_{E1}/20),$ (1)

where the energy values $E_{E1}$ and 20 are in keV. Such histograms are shown
in Fig. 11 and are shown in a color scale in the Xmas plot. Thus, to extract
the E1 histogram one only needs to extract the two left-most columns of the
Xmas plot. This is fully analogous for all thermal neutron detectors.

Figure 11: Thermal neutron measurements acquired with the LND FS at the
Atominstitut (ATI) in Vienna in September 2017 during one hour. Solid and
dashed lines show measurements in the inner and outer segments (1 and 2) of
LND’s detectors E, F, G, and H. The beam hit LND from the front, so detectors
G and H do not see thermal neutrons. Signatures include X-rays at 43 keV and
internal conversion electrons at 71, 131, and 173 keV.

The number of counts due to thermal neutrons is determined by taking the
differences $E-F$ and $H-G$. We only expect a small fraction of thermal
neutrons to be measured in F and in G, thus these two detectors can serve as
background measurements but at the cost of a somewhat lower efficiency for
detecting thermal neutrons. The number of thermal neutron counts is then
divided by the detection efficiency for thermal neutrons, $\eta_{tn}\approx
1/50$, which was established during the calibration at ATI in Vienna in
September 2017. Together with the area of LND’s detectors (given in Fig. 5)
LND can thus determine the flux of thermal neutrons on the surface of the
Moon.

####  4.3.2 Fast Neutrons (and Gamma Radiation)

The inner segment of the C detector, C1, is also read out in anti-coincidence
with all other LND detectors. It thus responds nearly exclusively to neutral
particles which do not interact with the surrounding detectors and the outer
segment of C, C2. Its energy histogram is stored in 256 bins and is wrapped
around three times in the Xmas plot, see Fig. 10. The histogram bins are
calculated according to eq. 2

${\rm bin\\#}=16\cdot\log_{2}(E_{C1}/20),$ (2)

where $E_{C1}$ and 20 are in keV, i.e., exactly as in eq. 1. Thus the count
rate of neutral particles is easily computed.

Figure 6 shows the geometry factors $G_{\gamma}$ for $\gamma$-rays (Fig. 6(a))
and $G_{n}$ neutrons (Fig. 6(b)) in C1. The vector of differential count rates
in the energy bins of C1, $\vec{z}$, is then given by

$\vec{z}=G_{\gamma}\cdot\vec{J}_{\gamma}+G_{n}\cdot\vec{J}_{n}$ (3)

where $\vec{J}_{\gamma}$ and $\vec{J}_{n}$ are the vectors containing the
differential fluxes of $\gamma$-rays and neutrons, respectively. Inspection of
Fig. 6 shows that an energy deposition in C1 above $\sim$ 1 MeV is very
unlikely to be due to $\gamma$-rays, but much more probable for neutrons with
energies $E_{n}>10$ MeV, as is dicussed in more detail in Sec. 3.4. For energy
depositions below $\sim 1$ MeV, LND can not discriminate between neutrons and
$\gamma$-rays. Inferences about the neutron and $\gamma$ spectra will have to
rely on an extrapolation of the higher-energy neutron spectrum which should be
based on modeling results. The process to obtain fast neutron spectra is based
on similar work already performed for MSL/RAD koehler-etal-2014 ; guo-
etal-2017 .

###  4.4 Dosimetry: Total Ionizing Dose, TID, and Linear Energy Transfer, LET

####  4.4.1 Total Ionizing Dose

While Total Ionizing Dose (TID) is only one number, it can not be computed by
LND and therefore needs to be calculated on ground. To measure TID the energy
spectrum of all particles measured in detector B (i.e., in both the inner and
the outer segments of B, B1 and B2) is accumulated in 128 bins according to
eq. 4.

${\rm bin\\#}=8\cdot\log_{2}(E_{B}/20),$ (4)

where $E_{B}$ and 20 are measured in keV. On ground, TID is then computed
using eq. 5,

${\rm TID}=\sum_{i=8}^{127}\sqrt{E_{i}\cdot E_{i+1}}\ \cdot\ {\rm
counts}_{i},$ (5)

where $i$ is the bin number and

$E_{i}=20\cdot 2^{i/8}\ \mbox{[keV]}$ (6)

Note that the average energy of the bin is expressed here as the harmonic
mean. LND uses logarithmically spaced bins. It could also be expressed by the
usual arithmetic mean, or also by the logarithmic mean which is larger than
the harmonic mean and smaller than the arithmetic mean. Which of these
expressions is used for the average energy of a bin is ambiguous. The choice
should depend on the observed spectrum of energy deposits in B. Values
reported in zhang-etal-2019  are calculated according to eq. 6.

In order to derive the final, physical value of TID, the value calculated
using eq. 5 needs to be converted into Joules and divided by the detector’s
mass, $m=1.04$g,

${\rm TID}_{\rm final}=1.602\cdot 10^{-13}\cdot{\rm TID}/m,$ (7)

where TID from eq. 5 is expressed in keV and $m$ in grams, and TIDfinal in Gy
(J/kg). A coarse value for TID is also given in the LND 1-minute data, see
Sec. 4.10. An example of a TID spectrum is shown in Fig. 12(a) and was
acquired by LND in February 2018 during pre-delivery tests. The threshold of
$\sim 40$ keV is clearly seen, as are the cosmic muons between 100 and 200
keV. The low energy deposits below that of cosmic muons are due to X-rays in
the laboratory which are created by the interaction of high-energy GCR
products with the walls, floor, and ceiling of the laboratory, as well as the
small background activity.

(a) Spectrum of energy depositions in the B detector when LND was standing
upright, pointing at the zenith in our laboratory in Kiel. The threshold of
$\sim 40$ keV is clearly seen, as are the cosmic muons between 100 and 200
keV. The blue curve was acquired using LNDs high-speed streaming mode, the red
dots are data as stored in the “X-mas card”.

(b) LET spectrum acquired with LND standing upright in our laboratory,
pointing at the zenith. The energy deposit of minimally-ionizing muons is
clearly seen around 0.3 keV/micron. Particles with lower primary energy
contribute to higher LETs. The data shown correspond to the LET spectrum
described in line 5 of Tab. 4.

Figure 12: TID (left) and LET (right) acquired by LND prior to re-delivery to
NSSC in February 2018. Higher energy deposits than those visible are expected
for heavy ions (GCRs), but these are only very rarely seen on Earth at sea
level (i.e., in our labs in Kiel).

####  4.4.2 Linear Energy Transfer spectra

The Xmas plot contains three LET spectra defined by the detector combinations
given in the three first lines of Tab. 4. Their locations in the Xmas plot are
given in Tab. 3.

| Det. | # bins |  $\braket{L}$ [$\mu$m] |  $\hat{L}$[$\mu$m] | var($L$) [$\mu$m] | g [mm2sr]
---|---|---|---|---|---|---
1 |  $A\cdot B\cdot C\cdot\bar{I}$ Hi | 64 | 526 | 527 | 367 | 64
2 | $\bar{A}\cdot B\cdot I\cdot J$ | 64 | 619 | 593 | 15055 | 2019
3 | $A\cdot B\cdot I\cdot J$ | $8\times 64$ | 514 | 515 | 962 | 158
4 | $2\cup 3\approx B\cdot J$ | 64 | 611 | 584 | 14774 | 2177
5 | $1\cup 3\approx A\cdot B$ | 64 | 517 | 517 | 823 | 222
Table 4: Properties of the various LET spectra. The first three lines are the
measurements performed by LND while the following two lines are more relevant
from a radiation protection point of view, as discussed in the text. Det.:
detector coincidence used to define the LET. $\braket{L}$: mean path length
through detector, $\hat{L}$: median of path length, var($L$): variance of pat
length, $g$: $4\pi$ geometric factor calculated with GEANT4. $2\cup 3$ and
$1\cup 3$ in rows 4 and 5 indicate the logical union of conditions 2 and 3
($(\bar{A}\cdot B\cdot I\cdot J)\cup(A\cdot B\cdot I\cdot J)$) and of 1 and 3
($(A\cdot B\cdot C\cdot\bar{I})\cup(A\cdot B\cdot I\cdot J)$).

The first three lines in Tab. 4 define the relevant quantities measured by
LND. The combinations in lines 4 and 5 define two LET spectra which are more
relevant from a radiation protection point of view. Line 3 gives the narrowest
viewcone and highest LET resolution, while line 4 gives a slightly wider
viewcone with somewhat higher count rate. The combination given in line 5,
finally, gives a very broad opening angle which is very similar to that of the
Dostel instrument which has been operating on the International Space Station
(ISS) for more than a decade berger-etal-2016 ; berger-etal-2017 . A low-
resolution version (only 8 bins) of the LET spectrum 2 is sent to telemetry
every minute, thus providing high time resolution LET measurements. An example
for an LET spectrum is shown in Fig. 12(b) and was acquired in February 2018
during pre-delivery test. It is based on high-resolution data from the Xmas
plot.

The energy for the LET is measured in the B detector and is converted to bin
number as given in eq. 8,

${\rm bin\\#}=4\cdot\log_{2}(E_{B}/20),$ (8)

where energies ($E_{B}$ and 20) are again measured in keV. Because a high LET
can be due to either heavy ions or to stopping or nearly stopping ions, LND
gives one LET spectrum which allows to discriminate between these two types of
energy deposits in a 2-dimensional LET histogram. It is defined by

${\rm bin\\#}_{x}=2\cdot\log_{2}(E_{I}/E_{A})+4,\quad\quad{\rm
bin\\#}_{y}=4\cdot\log_{2}(E_{B}/20),$ (9)

where energies are again measured in keV. As can be seen in eq. 9, it uses the
energy deposits in the A and I detectors in addition to the energy deposit in
B, so it uses the detector combination with the smallest geometry factor and
smallest path length dispersion, and thus highest resolution. The bins in the
$x$ direction are defined completely analogously to the $x$ axis for the
penetrating charged particles which are described in Sec. 4.6.

To determine the LET spectra, one needs to divide by the average path lengths,
$\braket{L}$, given in Tab. 4. The $x$-axis of the LET spectrum is thus given
by

$x_{i}=E_{i}/\braket{L}=20\cdot 2^{i/4}/\braket{L}\
\mbox{[keV/$\mu$m]},\quad\quad y_{i}=\mbox{counts}_{i}$ (10)

###  4.5 Charged Particles – Ions

LND identifies charged particles by measuring the energy deposition in
different combinations of its SSDs. The mean energy loss per unit path length
of a charged projectile particle with nuclear charge $Z_{1}$ and velocity $v$
in a detector is given by the well-known Bethe-Bloch equation bethe ; bloch ,

$\frac{\rm{d}E}{\rm{d}x}=-\frac{Z_{1}^{2}e^{4}n_{e}}{4\pi\cdot\varepsilon_{0}^{2}\beta^{2}c^{2}m_{e}}\cdot\left[\ln\left(\frac{2m_{e}\beta^{2}c^{2}}{\braket{E_{B}}}\right)-\ln(1-\beta^{2})-\beta^{2}\right],$
(11)

where $\beta=v/c$, $c$ the speed of light, $E_{B}$ is the ionization energy of
the target (173 eV for Si), and $n_{e}$ is the electron density in the target
($6.7\times 10^{29}$m-3 for Si), $m_{e}$ the electron mass, and
$\varepsilon_{0}$ the permittivity of free space. The expression in the square
brackets simplifies to a constant plus a slowly changing $\ln(\beta^{2})$ in
the energy range covered by LND. Thus, we may approximate the energy loss in
the front most detector, A, as

$E_{A}\propto\frac{Z_{1}^{2}m_{1}}{E_{\rm tot}},$ (12)

where $E_{\rm tot}$ is the measured initial energy of the stopping projectile
particle, and $E_{A}$ is the energy deposited in the front detector (A). The
product of the total energy and the energy deposited in A (eq. 12) is then
given by

$Y\doteq E_{\rm tot}\cdot E_{A}\propto E_{\rm
tot}\cdot\frac{Z_{1}^{2}m_{1}}{E_{\rm tot}}\propto Z_{1}^{2}m_{1}\ \approx\
{\rm const.}$ (13)

This quantity, $Y$, only depends on the particle species, i.e, its nuclear
charge, $Z_{1}$, and mass, $m$. Except for some very weak dependencies on
$\ln(\beta^{2})$ all other quantities have canceled out. Thus this quantity
only depends on the particle’s properties which allows us to discriminate even
some isotopes of the various elements. $Y$ as defined in eq. 13 is the
quantity plotted as the $y$-axis of the Xmas plot for particles which stop in
detectors B, C, and D. Stopping particles up to a penetration depth of
detector D are identified by the condition that there is no energy deposited
in detector E. Because the following detectors, F, G, H, I, and J all have
non-sensitive material in front of them, the analogous quantity can not be
used in the same manner. For them, the quantities given in Tab. 5 are plotted
along the $y$-axis of the Xmas plot.

The quantity plotted along the $x$-axis of the Xmas plot is given by the ratio
of the the total deposited energy, $E_{\rm tot}$, and the energy measured in
the front detector, $E_{A}$,

$X\doteq E_{\rm tot}/E_{A}.$ (14)

Using the approximation of eq. 12 this ratio is proportional to $E_{\rm
tot}^{2}/(Z_{1}^{2}\cdot m)$, i.e., is sensitive to the total (primary) energy
of the stopping particle.

For stopping particles, the quantities for the $x$ and $y$-axis are summarized
in Tab. 5. As indicated by red counters in Fig. 10 the combination $(X,Y)$
identifies individual elements or element groups for all particles stopping in
detectors B through I. The grey-shaded strip marked by ”Stop in B” has two
such counters for protons and three each for both He isotopes. Particles with
higher total energy tend to lie at larger values of $X\propto E^{2}_{\rm
tot}$. The neighboring strip marked by ”Stop in C” shows the same kind of data
for particles stopping in C, etc.

Det. |  $x$-axis
---|---
stopping in B | $8\cdot\log_{2}((E_{A}+E_{B})/E_{A})$
stopping in C | $8\cdot\log_{2}((E_{A}+E_{B}+E_{C})/E_{A})-8$
stopping in D | $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})/E_{A})-24$
stopping in E | $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})/E_{A})-24$
stopping in F | $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})/E_{A})-24$
stopping in G | $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})/E_{A})-24$
stopping in H | $16\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})/E_{A})-24$
stopping in I | $2\cdot\log_{2}(E_{I}/E_{A})+8$
Det. |  $y$-axis
stopping in B | $4\cdot\log_{2}((E_{A}+E_{B})\cdot E_{A}/(8000\cdot 4000))$
stopping in C | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C})\cdot E_{A}/(10000\cdot 4000))+4$
stopping in D | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A}/(1200\cdot 6000))-8$
stopping in E | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A})/(1200\cdot 6000))+2$
stopping in F | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A})/(1200\cdot 6000))+7$
stopping in G | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A})/(1200\cdot 6000))+7$
stopping in H | $4\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D1})\cdot E_{A})/(1200\cdot 6000))+8$
stopping in I | $8\cdot\log_{2}((E_{A}+E_{B}+E_{C}+E_{D}+E_{I})/4000)$
Penetrating Particles
$x$-axis | $4\cdot\log_{2}(E_{i}/E_{A})+16$
$y$-axis | $4\cdot\log_{2}((E_{B1}+E_{C}+E_{D})/100)$
Table 5: Quantities used as the $x$ and $y$-axis for the stopping charged-
particle regions of the Xmas plot. Det: Detector in which the particle stops.
The last line gives the quantities used for penetrating particles (column J in
the Xmas plot).

Energetic electrons need to be treated separately because of their high
penetration power. A similar identification scheme is used for them, but their
resulting memory addresses ($(X,Y)$ coordinates) in the Xmas plot are given in
Tab. 7, as explained in section 4.7.

####  4.5.1 Energy Ranges for Stopping Ions

As particles enter the front foil of LND and penetrate the A detector they
loose energy. For a particle to be registered, it must trigger the B detector
which gives the minimum energy it must have in order to be measured by LND. If
it has more energy, it may penetrate the B detector and stop in C, etc. The
stopping energies are given in Tab. 6. They are based on GEANT4 simulations of
the LND sensor and include all relevant layers such as the Gd-absorber, its
surrounding Al-housing, etc. The simulations were performed for an isotropic
source on top of the LND entrance foil.

Stop in | proton |  3He |  4He | CNO | Heavy Ions
---|---|---|---|---|---
| [MeV] | [MeV/nuc] | [MeV/nuc] | [MeV/nuc] | [MeV/nuc]
B dps1 | 9.0-10.6 | 10.6-11.4 | 8.9-9.5 | 16.6-20.5 | 24.6-37.7
B dps2 | 10.7-12.7 | 11.4-12.6 | 9.6-10.9 | 20.5-23.5 | 31.0-46.4
B dps3 | - | 12.9-14.8 | 10.9-12.6 | - | -
C | 12.8-15.7 | 15.0-18.5 | 12.8-15.7 | 25.5-29.3 | 38.2-58.5
D | 15.9-18.4 | 18.7-21.7 | 15.9-18.5 | 31.0-36.4 | 47.5-68.7
E | 18.6-21.0 | 21.7-24.6a | 18.5-21.0a | 37.3-38.6 | 52.1-78.9
F | 21.2-29.2 | 24.9-34.4 | 21.0-29.3 | 42.3-59.1 | 67.1-105.2
G | 29.6-31.3 | 34.8-36.4 | 29.3-31.4 | 54.5-62.6 | 91.6-122.2
H | 31.5-33.0 | 36.9-38.6 | 31.4-32.8 | 57.8-66.4 | 79.8-131.0
I | 33.4-34.5 | 39.0-40.4 | 32.8-34.4 | 61.2-72.8 | 101.6-132.5
Stop in | proton |  3He |  4He | CNO | Heavy Ions
B dps1 | H1 | 3He1 | 4He1 | CNO1 | ions1
B dps2 | H2 | 3He2 | 4He2 | CNO2 | ions2
B dps3 | - | 3He3 | 4He3 | - | -
C | H3 | 3He4 | 4He4 | CNO3 | ions3
D | H4 | 3He5 | 4He5 | CNO4 | ions4
E | H5 | 4He6a | 4He6a | CNO5 | ions5
F | H6 | 4He7 | 4He7 | CNO6 | ions6
G | H7 | 4He8 | 4He8 | CNO7 | ions7
H | H8 | 4He9 | 4He9 | CNO8 | ions8
I | H9 | 4He10 | 4He10 | CNO9 | ions9
Penetrating |  |  |  |  |
pene1 |  | 56.5-182.9 | 48.6-180.8 |  |
pene2 |  |  |  |  $\geq$88.5b |  $\geq$150.4b
pene3 |  |  |  | 95.9-147.0 |  $\geq$111.4b
pene4 |  | 40.7-56.5 | 34.8-45.9 |  |
pene5 |  |  |  | 84.5-91.6 |
pene6 |  |  |  | 70.3-93.8 | 78.9-106.4
pene7 |  |  |  | 75.3-78.9 | 105.2-170.7
H10 |  $\geq$156.2 |  |  |  |
H11 | 42.3-139.2 |  $\geq$198.3 |  $\geq$198.3 |  |
H12 |  |  |  |  |
H13 |  |  |  |  |
H14 | 34.9-40.8 |  |  |  |
Table 6: List of primary energy ranges that protons, 3He, 4He, CNO, and heavy
ions need to have to stop in the LND detectors. “B dpsi”, “pene $i$” and H10 -
H14 refer to the multiple red counters for protons (ions) in the Xmas plot,
Fig. 10, which are discussed in sections 4.9 and 4.10. Example: A proton must
have a primary energy $16.0<E<18.7$ MeV so that it will stop in D. The lower
half of the table shows the name of the corresponding energy bins in the upper
half of this table. The positions of these energy bins in the X-mas plot are
indicated with white labels in Figure 6. The lowest part of the table gives
the minimum energy needed to stop in or penetrate J. a 3He and 4He share the
dps boxes from detectors E to I b 10% of maximum used instead of 50% maximum

###  4.6 Penetrating Charged Particles

The spectrum of energetic particles, especially the GCR, has a substantial
flux of particles with energies which exceed the stopping power of LND. They
are measured in the penetrating channel of LND which is defined by particles
which penetrate all detectors, and stop in or penetrate the J detector. LND
can not discriminate particles stopping in the last detector, J, from
particles that penetrate it because J serves as the anti-coincidence detector
for particles stopping in LND. Most of these penetrating particles are close
to minimally ionizing, i.e., they have a nearly constant energy loss across
LND. Barely penetrating particles have primary energies which result in
smaller energy losses in the front detectors A, B, C, D, than in the rear
detectors I and J. To discriminate barely stopping particles from penetrating
particles, the Xmas plot is redefined as a $32\times 64$ matrix with its $X$
and $Y$ axis coordinates computed according to the rows marked ”Penetrating
Particles” in Tab. 5. This is the definition of the rightmost panel of the
Xmas plot marked as ”Penetrate J”. One easily recognizes the fully
relativistic particles as a nearly straight line from the bottom to the top
and the nearly stopping particles which turn to the right, i.e., towards
larger values of $4\log_{2}(E_{I}/E_{A})$. Particles which veer to the left
move upwards through LND, i.e., away from the Moon. They are part of the
secondary particle population which is created by the interaction of (mainly)
GCRs with the lunar soil. Penetrating electrons lie at the bottom of this
panel and are clearly separated from barely penetrating protons, but not from
fully relativistic protons which is as expected.

###  4.7 Charged Particles – Electrons

The calculation of the $(X,Y)$ addresses for electrons in the Xmas plot
results in vanishing $Y$ values and so most electron data products are plotted
along the $X$ axis ($Y=0$) of Fig. 10. Because electrons are abundant, there
are also one- and ten-minute electron data products. These are indicated in
Fig. 10 by E, F, GHI, and E1,…E4, …H1, …H4. The primary energy ranges
corresponding to these one- and ten-minute data products are given in Tab. 7.
Electrons stopping in the B, C, and D detectors are mapped to the two right-
most columns of the Xmas plot, columns 273 and 274. Those addresses are
calculated as 16$\cdot\log_{2}(T)$, where $T$ is the total deposited energy
(measured in keV). These predominantly low-energy electrons have four one-
minute data products indicated by dps1 – dps4 in Fig. 10, their ranges of
deposited energy is also given in Tab. 7.

Electron channel | bin edges | $E_{\rm dep}$ |  | time res.
---|---|---|---|---
| low | high | [MeV] |  | [minutes]
Column 273 | Row #s |  |  |
$e^{-}$ dps1 | 10 | 17 | 0.5-0.707 |  | 1
$e^{-}$ dps2 | 18 | 25 | 0.707-1 |  | 1
$e^{-}$ dps3 | 26 | 33 | 1-1.414 |  | 1
$e^{-}$ dps4 | 34 | 41 | 1.414-2 |  | 1
|  |  $E_{\rm prim}$ [MeV] |
Row 0 | Column #s | half max | 20% – 20% |
Xmas-E | 97 | 126 | 1.3-2.7 | 1.2-4.3 | 1
Xmas-F | 129 | 158 | 1.9-5.2 | 1.6-8.5 | 1
Xmas-G$\cup$H$\cup$I | 160 | 239 | 3.0-9.0 | 2.7-16.3 | 1
Xmas-E1 | 96 | 96 | 1.5-4.2 | 1.3-9.8 | 10
Xmas-E2 | 97 | 102 | 1.3-2.8 | 1.2-5.4 | 10
Xmas-E3 | 118 | 126 | 1.5-2.8 | 1.3-4.3 | 10
Xmas-E4 | 127 | 127 | 2.0-3.4 | 1.8-4.9 | 10
Xmas-F1 | 128 | 128 | 2.2-6.7 | 1.8-12.3 | 10
Xmas-F2 | 129 | 132 | 2.0-5.3 | 1.7-9.3 | 10
Xmas-F3 | 145 | 158 | 2.1-5.7 | 1.8-8.9 | 10
Xmas-F4 | 159 | 159 | 3.0-6.2 | 2.4-8.5 | 10
Xmas-G1 | 160 | 160 | 3.1-7.2 | 2.7-12.9 | 10
Xmas-G2 | 161 | 165 | 2.8-6.5 | 2.6-10.7 | 10
Xmas-G3 | 166 | 172 | 2.8-6.1 | 2.6-10.2 | 10
Xmas-G4 | 173 | 191 | 2.9-7.5 | 2.7-9.8 | 10
Xmas-H1 | 192 | 192 | 3.6-16.1 | 2.9-29.7 | 10
Xmas-H2 | 193 | 197 | 3.3-12.5 | 2.8-24.7 | 10
Xmas-H3 | 198 | 204 | 3.1-12.2 | 2.8-20.5 | 10
Xmas-H4 | 205 | 223 | 3.3-11.6 | 2.9-22.5 | 10
Table 7: Deposited and primary energy ranges ($E_{\rm dep}$ and $E_{\rm
prim}$) for electrons measured in LND detectors and/or dps counters/counters.
Note that these show very large variability as electrons scatter a lot. The
column half max gives the FWHM range around the modeled maximum, the following
column gives the range between $\pm$ 20% of the maximum. The positions of
these energy bins in the Xmas plot are indicated with black labels in Figure
10. For instance, Xmas-E3 refers to the electron region marked by E3 in the
Xmas plot (rows 118 - 126, column 0). The last column gives the time
resolution at which these data products are put into telemetry.

The increasing penetration depth of electrons with increasing primary energy
can be used for an initial, coarse estimate of the electron spectrum. Figure
13 shows how this works. In the left-hand panel, Fig. 13(a), the simulated
counts are shown for an isotropic, $E^{-1}$ incident electron spectrum. One
easily sees that increasing primary energy of electrons results in increasing
penetration depth into the detector stack. electrons need to have a kinetic
energy of at last 300 keV to trigger the B detector. The results for the F
detector (and to a lesser degree the H detector) appears to “stick out” of the
which is also expected, because the trigger condition is $B\cdot C\cdot D\cdot
E\cdot F\cdot\bar{G}$ and there is the Al-Gd-Al sandwich between the F and G
detectors. The blue curve shows results for penetrating electrons with primary
energies exceeding 3 MeV. The right-hand panel (Fig. 13(b)) shows the response
of the dps1 – dps4 bins of the Xmas plot to the same electron spectrum. It is
dominated by electrons in the primary energy range $0.5<E<2$ MeV. These four
data products are part of the LND 1-minute data, as are those marked E, F, and
GHI in the Xmas plot.

Note that determining the “true” electron spectrum will require an inversion
approach which accounts for the LND instrument response function,
$K_{e^{-}}(E_{\rm det},E_{\rm prim})$, which gives the geometry factors for an
electron of primary energy $E_{\rm prim}$ to be measured at an energy $E_{\rm
det}$. This can be achieved using constrained optimization or other
optimization techniques boehm-etal-2007 ; kharytonovetal2009  which solve the
Fredholm integral given in eq. 15.

$\vec{z}(E_{\rm det})=\int_{0}^{\infty}K_{e^{-}}(E_{\rm det},E_{\rm
prim})f(E_{\rm prim})\rm{d}E_{\rm prim},$ (15)

where $f(E_{\rm prim})$ is the primary spectrum and $\vec{z}(E_{\rm det})$ are
the measured counts in the energy bins $E_{\rm prim}$.

(a) These simulated count spectra show that electrons need at least 300 keV to
be identified in the B, while the probability to be seen in this detector
peaks at approximately 0.7 MeV. This peak depends on the incident spectrum, of
course. “Deeper” detectors have higher detection thresholds, allowing for a
coarse identification of the spectral shape of electrons.

(b) These simulated count spectra show that electrons need at least 0.5 MeV to
be identified in the $e^{-}$ dps1 data product, while the probability to be
seen in this data product peaks at approximately 0.7 MeV. This dps “threshold”
increases with increasing primary energy which allows us to give a very coarse
estimate of the electron spectrum, see also Fig. 13(a).

Figure 13: Electron penetration depths inside LND give information about their
primary energy. The mapping is not 1:1 though, and an inversion process as
described by eq. 15 will be needed to obtain higher fidelity electron spectra.

###  4.8 1-Hour Data Products

The Xmas plot (Fig. 10) is LND’s principal data product and is accumulated
over the course of an hour. As explained in Sec. 4.2, there are two Xmas
plots, one active (i.e., being accumulated) and one inactive (i.e., being sent
to telemetry). It contains the high-resolution data needed to discriminate
between different particle species, especially the rare heavy ions. The data
products contained in the Xmas plot have been discussed in sections 4.2 – 4.7.

###  4.9 10-Minute Data Products

To allow for higher time resolution, LND reads out certain regions in the
active Xmas plot more often than once an hour. These regions are shown as red
boxes in Fig. 10 and we refer to them as boxes or counters in the following.
Because the number of counts in an individual “pixel” in the Xmas plot will
necessarily be small, these large 10-minute boxes contain many Xmas plot
counters to allow us to obtain statistically significant numbers, at least
during large solar particle events. In the case of particles stopping in
detector E, we see that a box is centered on pixel 112 in the $x$ direction
and pixel 20 in the $y$ direction and is marked ”4He6”. This region in the
Xmas plot corresponds to 4He particles stopping in E. Thus, we know that this
particle stopped in E and that it was a 4He particle. Since it takes a
specific energy to penetrate the detectors prior to E and to stop in E (see
Tab. 6) we also know the primary energy of the 4He particles that stopped in
E. This then gives us a point in the differential flux of 4He particles.

The red box which we have placed around the 4He particles stopping in E also
serves as a counter in LND. The LND processing scheduler ensures that the sum
of all the counters in the individual pixels in this box is determined every
10 minutes. This sum is then put into the telemetry. Note that this counter
now contains the number of counts accumulated in this box since the Xmas plot
was last initialized. The number of counts in this box are thus cumulative for
every 10 minute interval in an hour. The total number of counts in the past 10
minutes is thus determined by computing (on ground) the difference between the
latest counter and the preceding one. These differences have already been
computed in the published data. These 10-minute “counters” are 24-bit integer
counters, they are not protected against SEUs since these are unlikely to
happen in any given 10-minute interval. No compression is performed on the
counters. The data products available at 10-minute time resolution are listed
in Tab. 2.

The energy ranges for the various counter boxes are given in Tab. 6. Their
locations can be seen in Fig. 10 and their meanings are obvious from it and
Tab. 6.

###  4.10 1-Minute Data Products

LND also provides data at a time resolution of 1 minute. The logics are
exactly the same as for the 10-minute data, counters are accumulated in boxes
and read out once every minute. They are cumulative, i.e., one needs to take
the difference between the current value and the preceding one to obtain the
count rate. The data products available at 1-minute time resolution are listed
in Tab. 2. The energy ranges for the various ions are also given in Tab. 6,
the positions of these one-minute counter boxes are shown in Fig. 10.

###  4.11 Dead-time corrections

The accumulation of a Xmas plot happens during a full hour, but is stopped for
500 $\mu$s every second. Thus, the accumulation time of the Xmas plot is not
3600 seconds, but 3598.2 seconds. This is a small correction, but mentioned
here for completeness sake. Similarly, the first dps1 data product in every
hour is only accumulated for 59 seconds, all others for 60 seconds per minute,
and, the first dps10 data product in one hour is only accumulated for 599
seconds, all others for 600 seconds every 10 minutes. Corrections for these
small discrepancies are applied to the published data.

In addition to the correct accumulation times of the different data products,
some dead time corrections need to be applied to LND’s data. An approximation
of the dead time that occurs while LND reads out its detectors can be
calculated by multiplying the number of detector readouts by 7 $\mu$s. The
number of readouts can be taken from the L2 trigger counts, but it needs to be
considered which L2 triggers contribute to which data product. This is easiest
to understand by inspecting Fig. 9. The simplest situation is when LND detects
a neutron in detector C1, as this affects only one single detector and
trigger, L2[2]. There is also only one corresponding L3 trigger, L3[1]. The
dead time is then calculated by multiplying the number of L2[2] triggers by a
dead time of 7 $\mu$s. A more complicated dead time correction is that for TID
because it gets contributions from L2[0] (LET) via the L3[3] (LET) trigger,
but also the L2[1] (TID) and L2[7] (heavy ions) via the L3[0] trigger path to
LND’s TID data product (shown in blue in Fig. 9). Thus, the dead time
associated with TID is the sum of the counts in L2[0], L2[1], and L2[7]
multiplied by 7 $\mu$s. Finally, the dead time correction for the thermal
neutron channels in E, F, G and H is done using the sum of the trigger counts
in L2[3] through L2[6]. The eight L2 counters are in telemetry at 1 minute
resolution, so this correction can be made at LND’s highest measuring cadence.
For the data products sent at lower cadence, the L2 counters are summed up
over the respective time intervals to calculate the corresponding dead time.

LND’s accumulation times and dead times are summarized in Tab. 8. They need to
be considered by correcting the nominal accumulation time, $\rm{d}t$ (3600,
600 or 60 seconds, respectively), to

$\rm{d}t_{\rm true}=\mbox{accumulation time}-\mbox{dead time},$ (16)

where the accumulation time and dead time are taken from Tab. 8. Count rates
are thus corrected for dead-time effects using the following expression,

${\rm true\ count\ rate}={\rm measured\ count\
rate}\cdot\frac{\rm{d}t}{\rm{d}t_{\rm true}},$ (17)

where $\rm{d}t$ is the nominal, uncorrected accumulation time for a data
product. Dead time corrections have been applied to the published data.

Type of data product | Accumulation time [s]
---|---
Xmas plot | 3598.2
first dps1 per hour | 59
other dps1 | 60
first dps10 per hour | 599
other dps10 | 600
Type of measurement | Dead time [$\mu$s]
TID, LET, charged particles | (L2[0] $+$ L2[1] $+$ L2[7])$\cdot 7$
Neutrons in C1 | L2[2]$\cdot 7$
Thermal neutrons in E, F, G, H | (L2[3] $+$ L2[4] $+$ L2[5] $+$ L2[6])$\cdot 7$
Table 8: Accumulation times and dead times to be considered when producing LND
data products. The “first” are underlined because this applies only to the
first dps packet per hour. Dead time corrections are discussed in Sec. 4.11.
All counters associated with a data product given in Fig. 9 contribute to its
dead time and thus their sum must be multiplied by 7 $\mu$s to obtain the dead
time.

###  4.12 Calibration of LND

The LND data products are provided in calibrated values, i.e., after all
conversions from instrumental measurement units to the reported physical units
have been applied. The calibration of LND was was performed using the flight
model (FM), the flight spare (FS) unit, and also the engineering model (EM).
Because LND provides very diverse measurements and data products, its
calibration was an extended effort which included a number of facilities in
Europe and China. These are summarized in Tab. 9 and will be published
elsewhere in the literature. LND itself was not calibrated with fast neutrons,
but uses the calibration of the Flight Radiation Environment Detector (FRED,
moeller-2013 ) which also served as a prototype for the fast neutron detection
capabilities of LND. FRED was calibrated with neutrons at the Physikalisch-
Technische Bundesanstalt (PTB) in Braunschweig (5 MeV $<E_{n}<$ 19 MeV) and
with higher energy neutrons at iThemba in South Africa moeller-2013 . FRED
contains near-identical detectors B, C, D in the same stack configuration as
LND. The main difference lies in their thicknesses (300 $\mu$m in FRED and 500
$\mu$m in LND). These are accounted for by modeling the slightly different
responses with GEANT4.

Calibration |  |
---|---|---
facility | purpose | LND Model | Time frame
CAU Kiel | Bi-207 gammas | FM, FS, EM | Summer 2017
CERN/CERF | dose | FM | 2017-06-17 – 2017-06-18
HIMAC | ions: H, He, C, O, Ar | FM | 2017-06-30 – 2017-07-04
ATI | thermal neutrons | FM, FS | 2017-09-25 – 2017-09-28
18th Institute | RTG & RHU background | FS | 2018-07-09 – 2018-07-12
NSSC | electrons | EM | 2018-08-17 – 2018-08-20
Table 9: Overview of calibrations performed with LND.

###### Acknowledgements.

The Lunar Lander Neutron and Dosimetry (LND) instrument is supported by the
German Space Agency, DLR, and its Space Administration under grant 50 JR 1604
to the Christian-Albrechts-University (CAU) Kiel and supported by Beijing
Municipal Science and Technology Commission, Grant No.Z181100002918003 to the
National Space Science Center (NSSC). We would like to thank the following
facilities for allowing us to calibrate LND: CERN/CERF in Geneva, Switzerland;
HIMAC in Chiba, Japan; ATI in Vienna, Austria; SEF in NSSC, Beijing, China. We
thank Oliver Angerer at DLR for his unwavering support of LND. We also thank
the LESEC/CAST their joint effort for LND.

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