Robert F. Wimmer-Schweingruber
Institute of Experimental and Applied Physics, Kiel University, 24118 Kiel,
Germany,
National Space Science Center, Beijing, China<EMAIL_ADDRESS>
# Primary and albedo protons detected by the Lunar Lander Neutron and
Dosimetry (LND) experiment on the lunar farside

Zigong Xu 1,∗, Jingnan Guo 2,3 , Robert F. Wimmer-Schweingruber 1,4,∗ ,
Mikhail I. Dobynde 2, Patrick Kühl 1 , Salman Khaksarighiri 1 and Shenyi Zhang
4,5,6

###### Abstract

## 1

The Lunar Lander Neutron and Dosimetry (LND) Experiment aboard the Chang’E-4
Lander on the lunar far-side measures energetic charged and neutral particles
and monitors the corresponding radiation levels. During solar quiet times,
galactic cosmic rays (GCRs) are the dominating component of charged particles
on the lunar surface. Moreover, the interaction of GCRs with the lunar
regolith also results in upward-directed albedo protons which are measured by
the LND. In this work, we used calibrated LND data to study the GCR primary
and albedo protons. We calculate the averaged GCR proton spectrum in the range
of 9-368 MeV and the averaged albedo proton flux between 64.7 and 76.7 MeV
from June 2019 (the 7th lunar day after Chang’E-4’s landing) to July 2020 (the
20th lunar day). We compare the primary proton measurements of LND with the
Electron Proton Helium INstrument (EPHIN) on SOHO. The comparison shows a
reasonable agreement of the GCR proton spectra among different instruments and
illustrates the capability of LND. Likewise, the albedo proton measurements of
LND are also comparable with measurements by the Cosmic Ray Telescope for the
Effects of Radiation (CRaTER) during solar minimum. Our measurements confirm
predictions from the Radiation Environment and Dose at the Moon (REDMoon)
model. Finally, we provide the ratio of albedo protons to primary protons for
measurements in the energy range of 64.7-76.7 MeV which confirm simulations
over a broader energy range.

##  2 Keywords:

LND, Moon, Lunar radiation environment, Galactic cosmic rays, Lunar albedo
protons, Data calibration, Instrumentation

##  3 Introduction

The charged particle radiation environment on the lunar surface consists of
Galactic Cosmic Rays (GCR), a small contribution from Anomalous Cosmic Rays
(ACR), and a highly variable, sporadic contribution from Solar Energetic
Particles (SEPs). In addition, secondary albedo particles are created
primarily by the GCR interaction with the lunar regolith (Treiman, 1953;
Dorman, 2004; Wilson et al., 2012). In this work we focus on measurements by
the Lunar Lander Neutron and Dosimetry experiment (LND, Wimmer-Schweingruber
et al., 2020) of GCR primary and secondary (albedo) protons and compare them
with state-of-art model predictions (Dobynde and Guo, 2021). The space
radiation measured by LND is a key concern for human space flight and may pose
limits on long-term crewed missions to the Moon or Mars (Cucinotta and
Chappell, 2011).

The interaction of high-energy particles with the lunar regolith results in
the production of secondary particles. Some of these particles can escape from
the soil and can be measured as albedo particles. Obviously, they will also
contribute to the radiation exposure of astronauts on the lunar surface, but
they also provide information about conditions beneath the lunar surface.

Wilson et al. (2012) first distinguished protons measured by the Cosmic Ray
Telescope for the Effects of Radiation (Spence et al., 2010, CRaTER,)
instrument from different directions and constructed the first albedo proton
yield map between 60 and 150 MeV. They found that the ratio of albedo to
primary protons is uniformly distributed over the lunar surface within $\sim$
10% uncertainty and that the average ratio of upward to downward particle
during the minimum between solar cycles 23 and 24 (in 2009-2011) was about
0.38 $\pm$ 0.02. Simulations by Spence et al. (2013) show that such upward
albedo particles can contribute a significant amount ($\sim$ 8.62%) to the
radiation dose with albedo protons accounting for 3.1% of the total dose rate.
Moreover, albedo neutrons have been used to detect and determine the
subsurface hydrogen content (Mitrofanov et al., 2016). Likewise, Schwadron et
al. (2016) used the CRaTER instrument to detect albedo protons and provided
evidence for the existence of hydrated material in the lunar regolith at the
polar regions, based on small variations of the proton yield. A follow-up
study by Schwadron et al. (2017) analyzed the difference of the lunar albedo
protons yield for the lunar sunrise and sunset terminators.

(Looper et al., 2013) presented the CRaTER measurements of radiation
environment near the lunar surface including GCRs and albedo particles. They
also utilized a GEANT4 simulation to model the energy distribution of albedo
particles, and the response of different detectors to various particle species
that reach the instrument on the 50km height lunar orbit.

More recently, Dobynde and Guo (2021) developed the Radiation Environment and
Dose at the Moon (REDMoon) model that describes the detailed radiation
environment both on the lunar surface and in the lunar soil. In this model,
the lunar body is described by concentric spherical layers of different
densities and soil composition is based on Apollo 17 drill core results
(McKinney et al., 2006). The model is based on the GEANT4 Monte-Carlo particle
transport code (Agostinelli et al., 2003) and the FTFP$\\_$BERT$\\_$HP physics
list was used to calculate the GCR-induced radiation environment on and below
the lunar surface. Primary GCRs have an isotropic direction (in the upper
half-sphere) and the output particle types and energy at each soil depth or
zenith angle are recorded. Results from different solar modulation conditions
are also derived.

On January 3, 2019, China successfully landed the Chang’E-4 spacecraft on the
far side of the Moon inside the von Kàrmàn Crater. As one of its scientific
payloads, Lunar Lander Neutron and Dosimetry experiment (LND, Wimmer-
Schweingruber et al., 2020) aboard the Chang’E-4 Lander is a small instrument
with the primary objective of monitoring the radiation level on the lunar
surface. LND consists of ten 500 $\mu$m silicon detectors (labeled A-J) that
are assembled as shown in Fig. 1. The primary data products of LND include
dynamic Total Ionizing Dose rate (TID) and Linear Energy Transfer (LET)
spectra. The radiation dose rate is the radiation energy deposited by incoming
radiation per unit time and unit mass of the absorber and is often measured in
silicon detectors. LET is the energy that an ionizing particle transfers to
the material per unit path length. Knowledge of both of these quantities is
crucial in preparing for human spaceflight and human exploration of the Moon.
Apart from these dosimetric quantities, LND also measures primary charged-
particle energy spectra. Using the energy loss in its individual detectors,
LND measures the primary energy of particles in the energy range between
$\sim$10 MeV/nuc and a few hundred MeV/nuc and distinguishes different
particle species, including electrons, protons, 4He, its isotope 3He, and
heavy ions such as carbon, oxygen, nitrogen, and iron. The post-launch
performance of LND and its capability of measuring protons have been partially
verified through analysis of a weak and impulsive SEP event in May 2019 (Xu et
al., 2020), with proton energy up to $\sim$20 MeV. Moreover, LND measures
upward-directed albedo particles using the same method as was successfully
applied using data from the Radiation Assessment Detector(RAD, Hassler et al.,
2012) on Mars. Appel et al. (2018) determined the flux of albedo particles in
the energy range 100-200 MeV on the Martian surface using a two-dimensional
count density histogram. Here we use a similar method to distinguish upward
proton fluxes from downward ones. .

Zhang et al. (2020) displayed the first measurement of TID and LET spectra
during the first two lunar days after LND was switched on. During the solar
minimum of Solar Cycle (SC) 24/25, the average total absorbed dose rate on the
lunar surface reached 13.2 $\pm$ 1 $\mu Gy/h$. This value is consistent with
the radiation dose that is measured by CRaTER in orbit after the conversion to
the surface in January 2019. A comparison with the radiation level on the Mars
surface shows that the dose rate on the lunar surface is about 15% higher than
that on Mars when GCR intensity reached a maximum during the deep solar
minimum. Furthermore, the lunar surface dose rate is about two times higher
than that measured in the International Space Station (ISS) by the 3D-DOSTEL
instrument (Berger et al., 2020).

More than three years into the Chang’E 4 mission, most of LND’s detectors are
still in good condition and operating well despite the grueling temperature
differences between lunar day and night. Nevertheless, since a mishap on the
dawn of the third lunar day some segments of four of the 10 detectors in LND
have begun to suffer from increased noise levels. We believe that a premature
opening of LND’s lid led to a severe drop in the temperature of LND’s sensor
head. The mounting of LND’s detectors led to unintended thermo-mechanical
stress on the front detector (A) and the three detectors at the end of the
particle telescope (H, I, and J). An adjustment of the thresholds of the
affected detector segments has led to some changes in the LND data products
compared to those presented in Wimmer-Schweingruber et al. (2020). The changes
are described in the appendix.

In this work, we provide a detailed calibration of the GCR proton spectra
measured by LND and present the first measurements of the albedo protons by
LND. The paper is organized as follows: In Section 4, we briefly describe LND,
its measurement principles for primary and albedo protons, data calibration,
the processing of LND data, and the simulation set-up used for interpreting
the data. In Section 5, we present the LND measurements and compare processed
LND data with other available data sets, i.e., the primary GCR measurements by
the Electron Proton Helium INstrument (EPHIN, Müller-Mellin et al., 1995) on-
board SOHO and the albedo protons measured by CRaTER onboard LRO (Wilson et
al., 2012; Schwadron et al., 2016). We compare these measurements with the
numerical cosmic ray model of Cosmic Ray Effects on Micro-Electronics Code
(Tylka et al., 1997, CREME96,), Badhwar-O’Neill 2014 model (BON14, O’Neill et
al., 2015) and the lunar radiation model REDMoon as mentioned above. Section 6
gives a summary and discussion. Finally, the appendix gives a detailed
description of the current LND configuration and calibration parameters.

##  4 Preparation of LND data

Figure 1: Schematic view of the LND sensor head located above the lunar
regolith with a 10-mm Al equivalent shielding (olive) between LND and the
lunar soil. The LND sensor head consists of 10 segmented 500$\mu$m-thick Si
detectors A – J. The Gd (red) and Al (olive) absorbers are designed to detect
uncharged particles. The 10-mm Al sheet is added to mimic the shielding by the
material between the sensor head and the lunar soil. On the lunar surface, the
interaction of high-energy GCR particles (mainly protons) with the soil
generates secondary, upward-moving protons. A more detailed description of LND
is given in Wimmer-Schweingruber et al. (2020).

###  4.1 Instrument and the simulation set-up

A schematic structure of the LND sensor head is given in Fig. 1. It consists
of ten silicon detectors, each with a nominal thickness of 500 $\mu$m.
Detectors are arranged in a charged-particle telescope configuration and
labeled A through J from top to bottom. Each detector is segmented into an
inner and an outer segment (labeled 1 & 2, respectively), each with
approximately the same area. LND uses coincidence measurements to detect the
charged particles which requires particles to pass through the uppermost
detector A and at least trigger the next detector, B. In the middle of the
sensor head, Al and Gd absorbers (shown in olive and red in Fig. 1) are used
to detect the upward and downward flux of thermal neutrons (Gd has a very
large cross-section for thermal neutrons). These absorbers increase the
scattering of particles inside the sensor head and absorb part of the particle
energy without providing a measurement thereof.

Above detector A, the front window is covered by a lid that opens when LND
operates, allowing particles to arrive at the detector without any obstacles.
During lunar nights, the lander closes the lid to keep the sensor head and
detectors warm enough for them to survive the cold lunar night. The payload
compartment of the Chang’E-4 lander which contains other scientific
instruments is located beneath the LND sensor head and thus provides extra
shielding for upward albedo particles before they reach LND. However, the
details of that shielding are unknown and an estimation of 10-mm Al shielding
equivalent was provided by the Chang’E-4 team. We thus add a 10-mm Al sheet
between LND and the lunar soil in our model for estimating the albedo
contribution to LND as shown in Fig. 1. Consequently, the shielding material
raises the lowest energy that albedo protons are required to have in order to
arrive at the LND detector. A more detailed description of LND is given in
Wimmer-Schweingruber et al. (2020).

We employed the GEANT4 toolkit (Agostinelli et al., 2003), version 10.4.1.,
using the QGSP_BERT physics list to simulate the detector response to
different particles from different directions at the relevant energies.

To simulate the particles from above, we placed a square-shaped planar source
right above the front detector A with a size that is larger than the size of
detector A and fully covers the field of view (FOV) of LND, i.e., the inner
dashed line of the combination of A1 and B1 in Fig. 1. Similarly, a square
particle source is placed below the 10mm-Al sheet when simulating upward
particles. The sources are isotropic and the energy spectrum is a power law
with index -1, i.e., logarithmically flat, to allow easy scaling to any other
spectral index 111The “logarithmically flat” spectrum appears “flat” or
horizontal when plotted in a log-log plot. Thus, bins are evenly spaced in a
logarithmic scale and have the same number of counts per bin., as discussed,
e.g., in Guo et al. (2019), but is a standard process. The spectrum is in
differential flux units. We then obtain the averaged geometric factors from
such a simulation and use them to convert detected counts to flux.

Figure 2: The (a) panel displays the ”Xmas plot” of part of the charged
particles stopping between detectors B and I. The empty area represents the
part of the LND memory that is not transmitted to the ground. Panel (b) is the
Xmas plot between columns 246 and 266. The primary proton channels and albedo
proton channel are defined accordingly in those two panels, marked by black
and blue boxes. The quantities used to calculate the entry ”pixel” in the Xmas
plot are calculated according to the quantities summarized in Tab. 5 in
Wimmer-Schweingruber et al. (2020).

###  4.2 Xmas plot

The Xmas plot222We call this plot “Xmas plot” because our group in Kiel used a
similar plot as our 2017 Xmas card. is the primary data product of LND that is
generated onboard and represents the memory space of the LND flight model. All
LND measurements are stored in a 274 $\times$ 64 matrix though not all
elements of this matrix are transmitted to Earth. The memory space refreshes
every hour; hence the time cadence of the Xmas plot is 1 hour. The Xmas plot
can be divided up column-wise into the following regions (from columns 0 to
274): thermal neutrons, fast neutrons, TID, LET, and charged particles. More
details of the data products can be found in Wimmer-Schweingruber et al.
(2020, Sec. 4). In this section, we focus on charged particles and explain the
generation of the corresponding two-dimensional density histogram in the Xmas
plot which is important to understand the calibration of LND data. Part of the
charged particles measurement is displayed in panels (a) and (b) of Fig. 2

The charged particles in the Xmas plot can be further divided up into two
parts, stopping and penetrating particles. The stopping particles have
energies between $\sim$ 8 and $\sim$ 35 MeV/nuc. LND thus measures SEPs, ACRs,
and lower energy GCRs in this energy range. When arriving at LND on the lunar
surface, particles within this energy range can first trigger and penetrate
detector A, then pass the following detectors, depositing (part of) their
kinetic energy. Depending on their primary energy, some of these particles
will stop in one of the detectors between B and I (as indicated by B, C, etc.
along the top of Fig. 2(a)) and hence deposit all of their energy. The higher
their primary energy, the deeper they get in the detector stack. The upper
limit is $\sim$35 MeV/nuc for protons and helium nuclei stopping in detector
I, but different for heavier ions (Wimmer-Schweingruber et al., 2020). A small
uncertainty in their primary energy remains due to noise in the individual
detectors. Particles with energies above 35 MeV/nuc will penetrate detector I
and stop in detector J or penetrate it, i.e., all detectors from A to J are
triggered. Penetrating particles may come from above or below. Panels (a) and
(b) of Fig. 2 show those parts of the Xmas plot that belong to stopping and
penetrating particles. A precise description of the quantities used to
populate the Xmas plot are given in Tab. 5 of Wimmer-Schweingruber et al.
(2020), but a short summary is given here for convenience. For particles
stopping between detectors B and H, the values along the x axis are a
monotonous function of the ratio Etotal/EA. The y axis is ordered according to
the product E${}_{total}\cdot$EA. The ratio and product are mapped to row and
column values internally in the instrument. Thus, the column regions marked by
B, C, D are similar to traditional d$E$/d$x$ \- E plots, but rotated and
compressed into d$E$/d$x$ $\cdot$ $E_{\rm total}$ vs. d$E$/d$x$ / $E_{\rm
total}$ space. In this space the ”1/E” energy loss appears as a horizontal
line and the penetrating particles do not show up because they are detected in
the next detector. The horizontal (energy) axis is compressed by the division
by EA. Particles stopping in detectors E, F, etc. are treated somewhat
differently, see Wimmer-Schweingruber et al. (2020) for more details. The
quantities used for penetrating particles and particles stopping in detector I
are similar. The x axis is ordered by $E_{I}/E_{A}$ and the y axis is ordered
by the sum of energy depositions in detectors B, C, and D (see sec. 4.4.1 for
the exact definition of penetrating particles). Stopping particles populate
columns 32 – 240, while penetrating particles are between 246 and 266. The
data in the empty regions in Fig. 2 (a) are not transmitted back to Earth.

The proton channels that are used in this work are outlined by the black boxes
in panels (a) and (b) of Fig. 2 and further indicated by H1 - H14. We call
them DPS boxes, where DPS stands for “data product scheduler”. Count numbers
inside DPS boxes are read out from memory every minute. Therefore the cadence
of primary proton data is 1 minute. These high-time-resolution proton data are
important during the onsets of SEP events (Xu et al., 2020). The pixels with
high count rates around row 20 in Fig. 2(a) are 4He counts. Heavier ions would
lie at even higher rows.

One of the advantages of the Xmas plot data product is that one can define
one’s own data product. For this work, we defined a mask for upward-moving
protons. It is marked by the blue box in panel (b) of Fig.2. The positions of
those pixels were determined manually based on simulation results. Because
such particles are rare, the one-hour time resolution of the Xmas plot is more
than sufficient. In the following sections, we explain this data product in
depth.

The Xmas plot in Fig. 2 was accumulated between the 7th and the 20th lunar day
(from June 27, 2019 to July 26, 2020) 333One lunar day is approximately 28
Earth days long. The periods when LND was on are listed in
https://www.ieap.uni-kiel.de/et/change4/data_by_lunar_day/info. This was a
period in the deep solar minimum between solar cycles 24 and 25. The minimum
solar modulation and solar activity during that period led to the highest GCR
flux since space age (Fu et al., 2021). It offers the opportunity to validate
LND’s performance using GCR data without the interruption by SEPs. As
discussed above and in the appendix, the thresholds of several detectors had
to be increased, the period we use for this work begins after all these
changes have been made.

###  4.3 Detection of downward-moving protons

####  4.3.1 Stopping and penetrating protons

Stopping and penetrating protons populate DPS boxes H1 - H14, their geometry
factors are shown in panel (a) of Fig. 3. The DPS boxes H1 - H9 count the
protons that stop in detectors B to I. 444Note that channel H9 has a
relatively narrow energy range (bin width) and a smaller geometry factor than
the other channels. The reason for this is an error in the definition of the
corresponding DPS box (between columns 224 and 240) which does not contain the
bulk of the particle population stopping in detector I. As shown in panel(a)
of Fig. 2, nearly half of the pixels with higher density lie outside of the
black box, leading to the reduced geometry factor. This defect was not
resolved in time for the flight model and hence the updated geometry factors
given in the appendix should be used to make use of this channel. DPS boxes
H10 - H14 record penetrating protons with energies above $\sim$ 35MeV. The
energy bins in H10, H11, and H14 are used in this paper for the first time,
they extend the measurement capability of LND beyond the energy of stopping
particles. Unlike those for stopping particles, the geometry factors of
penetrating particles partially overlap, as can be seen in panel (a) of Fig.
3. Moreover, the measurement of penetrating channels has a larger uncertainty
due to uncertainties in the determination of the background as will be
discussed in Sec. 4.3.3. Currently, data from the penetrating channels are not
yet publicly available because they still require a better calibration. With
the onset of solar activity, we expect this to be achieved with some large SEP
events with energies above $\sim$ 35 MeV.

####  4.3.2 Calculation of Fluxes

Figure 3: The geometry factors for both downward protons in (a) stopping
channels (H1-H9) and penetrating ones (H10, H11, H14), and albedo protons in
(b) are based on an input spectrum with power index $\gamma$=-1

.

The differential flux, ${\rm d}F$ is calculated according to equation 1 which
is valid for all particle species, including albedo protons,

${\rm d}F=\frac{N}{{\rm d}E\cdot\bar{G}\cdot{\rm d}t},$ (1)

where N is the number of counts in the DPS boxes, ${\rm d}E$ is the energy bin
width determined from the response functions shown in panel (a) of Fig. 3,
${\rm d}t$ is the accumulation time of the whole measurement, and includes
possible dead time corrections (Wimmer-Schweingruber et al., 2020), and
$\bar{G}$ is the weighted geometry factor of each energy bin. The method that
was used to calculate the averaged geometry factors is given in the appendix
and their values are given in table S3. The geometry factors of primary
protons and albedo protons as a function of energy are given in panels (a) and
(b) of Fig. 3.

We note that, despite the intention of the concept of geometry factors, the
averaged geometry factors derived via Eq. S1 in the supplementary material do
depend on the input spectra. As explained in appendix, the contribution of
high-energy particles results in non-negligible contributions in the count
rates for low-energy channels. Thus, the spectral shape beyond $~{}\sim 100$
MeV affects the count rate in the penetrating channels. The stopping channels
are less affected, as discussed in the appendix.

In table S3 we provide the averaged geometry factors derived for two different
input spectra; one is a power-law spectrum with index -1 (column 3), where the
particles are uniformly distributed in logarithmic energy space. The other one
is the numerical CREME96 GCR model spectrum (Tylka et al., 1997) for the 2019
solar minimum (column 4).

####  4.3.3 Correction of the contribution from 4He and heavy ions to the
proton flux

Close inspection of panel (a) of Fig. 2 shows that 4He and heavy ions
contaminate the proton DPS boxes H1 - H9. While 4He is well separated from
protons (its counts can be seen to populate the Xmas plot around row number
20), the Xmas plot entries between 4He and protons are clearly populated by a
substantial background. This background which mainly affects the low-energy
proton DPS boxes is primarily due to high-energy He and heavier ions which
create secondary particles after they interacted with detector A. The
secondary particles trigger B after which A is read out. Because the geometry
factor for interaction with A is large and the flux of high-energy (GCR) ions
is also high, this process happens sufficiently often to result in this
background.

The penetrating channels shown in panel (b) of Fig. 2 are affected by the
noisy detector segments A2,I1&I2, and J1. The effect of this malfunction has
been accounted for by increasing the thresholds of these detectors and
disabling A2 in the LND level-3 data processing logics (see Wimmer-
Schweingruber et al., 2020, for a discussion). This results in the asymmetry
shape seen in panel (b). In the supplementary material, we give the detailed
explanations of this asymmetric structure. Moreover, minimally-ionizing
protons are affected more than 4He because of their smaller energy deposition
in the detectors. Thus the detection efficiency for minimally-ionizing protons
(measured in H10) is reduced because of the increased thresholds in I and J.
The minimally-ionizing protons populate primarily H10, whereas minimally
ionizing 4He populates primarily H11. Thus, as can be seen in panel (a) of
Fig. 3 the protons measured in H11 are strongly affected by minimally-ionizing
4He (dashed line in Fig. 3).

In order to quantify these different sources of contamination and reduced
detection efficiencies, we ran extensive GEANT4 simulations of LND. We used
the simulation setup introduced in sec.4.1 to model elements from hydrogen to
iron, thus including all relevant GCR species. Instead of calculating the
geometry factors for detecting these elements in their instrument channels
(i.e., in the appropriate boxes in the Xmas plot), we derived the geometry
factors for measuring them in the proton channels (H1 - H14) as a function of
energy. These simulation data were then analyzed using the current LND
configuration(incl. thresholds). Thus we could estimate the contamination of
the H1 - H14 proton channels by high-energy (GCR) helium and - to a lesser
extent - heavy ions. Of course, 4He is rarer than hydrogen, but the
contribution of GCR 4He to the stopping proton channels (H1 - H7) is on the
order of a few percent, but larger for H8 and H9 (cf. Tab. S3 of supplementary
material). Similarly, minimally-ionizing 4He affects the penetrating, but not
minimally-ionizing protons in H11, only 36% of all particles in H11 are
protons (see respective entry in Tab. S3 of supplementary material).

To check the influence of different GCR models on the correction factors, we
compare the results of the CREME 96 (Tylka et al., 1997) and BON14 GCR models
(O’Neill et al., 2015). The correction factors are given in columns 5 and 6 of
Tab. S3 of supplementary material. Both models have comparable values, except
for the factor of channel H1, which measures protons with energy of about 10
MeV. CREME96 suggests that about 95% of particles measured in H1 are protons,
while this percentage for the BON14 is about 87%. This discrepancy is likely
due to the different spectral shapes for protons below 10 MeV. CREME96
includes low-energy (solar) particles while BON14 only includes GCR protons
(and heavier ions). Thus, the ratio of ”true” protons in H1 to ”background
protons” is larger for CREME96 than for BON14.

We note that the contamination from GCR ions discussed above is negligible
during SEP events because of the higher fluxes at low energies (softness of
the spectra) and the higher proton abundance compared to heavier ions.
However, the same contamination processes will affect the measurements, but to
a different extent that depends on the exact spectra of the solar particles.
Because the GCR-induced background is always present, we can subtract the
background which was measured before the SEP event from the measurements taken
during the event.

###  4.4 Detection of albedo protons

####  4.4.1 Measurement principle and response function

As alluded to in Sec. 4.2 both downward and upward pointing particles
contribute to the “penetrating” channels in the Xmas plot between columns 246
and 266 (panel (b) of Fig. 2). The extent of the $y$-axis shown covers
penetrating protons and 4He nuclei, heavier nuclei do not contribute to the
region shown here.

The x and y axes in panel (b) of Fig. 2 are defined as
$4\cdot\mathrm{log_{2}(E_{I}/E_{A})}+16$ and
$4\cdot\mathrm{log_{2}((E_{B1}+E_{C}+E_{D})/100)}$ respectively, where
$E_{I},E_{A},E_{C},E_{D}$ represent the total energy deposited in both the
inner and outer segments of the corresponding detectors, and $E_{B1}$ is the
energy deposition in the inner segment of detector B. The row number is
determined by the total energy deposited by particles in detectors B1, C, and
D. The Bethe-Bloch equation (Bethe, 1930; Bloch, 1933),
$dE\propto\frac{Z^{2}}{ME}$, gives the energy deposited by particles in the
silicon detectors; high-energy particles tend to deposit less energy than
lower-energy particles ($E$ less than $\sim$ 1 GeV) and heavy ions deposit
more energy than light elements due to their higher nuclear charge, $Z$.
Therefore, in the Xmas plot, the row number of protons with high primary
energy is smaller than the low energy proton, and the protons are at the
bottom of the 2D histogram. 4He and heavy ions are located above them.

The column number of a particle in the Xmas plot depends on the $E_{I}$ to
$E_{A}$ ratio. Suppose particles in particular the minimum ionizing particles,
deposit similar energy in the front detector A and the bottom detector I, i.e.
$E_{I}\sim E_{A}$, particles will be placed in the middle column of the
penetrating histogram, i.e., in column 256. When the particle deposit more
energy in detector I than detector A ($E_{I}>E_{A}$), the quantities for the
x-axis are larger than 256, and those particles will be added to the pixels in
the right half of panel (b). On the other hand, if a particle deposits less in
detector I than in detector A, it will be placed in the left half of panel
(b). In principle, the former corresponds to particles moving downward, since
particles first trigger detector A with larger incident energy and trigger I
in the end with smaller incident energy after they lose their energy in the
previous detectors, and the latter represents particles moving upward. Here we
only focus on particles with energies of up to a few tens to a few hundred
MeV/nuc and for which their average energy loss in silicon detectors decreases
with the increased primary energy.

From simulations we thus determine the region marked in blue in panel (b) of
upward-moving protons and calculate the corresponding geometry factor as shown
in the panel (b) of Fig. 3. The energy range of this albedo proton channel is
(64.7 – 76.7MeV), with an average geometry factor of $\mathrm{0.18\ cm^{2}sr}$
for an ${\rm d}J/{\rm d}E\propto E^{-1}$ spectrum. The energy range is defined
by the 10%-of-maximum criterion, and the uncertainty in these limits was
estimated at the 5% and 10% of maximum and 90% to 95% of maximum levels. Given
the steep flanks of this energy channel, these uncertainties are realistic.

Fortunately, our simulations show that the noise issue and the changes in LND
configuration do not affect LND’s response to albedo protons. They are too
much away from the affected region in the Xmas plot, as can be seen in panel
(b) of Fig. 2.

####  4.4.2 Background subtraction

The count rates of albedo protons between 64.7 MeV and 76.7 MeV in the Xmas
plots are affected by a background which is caused by high-energy protons from
both directions and needs to be subtracted. To better visualize this
background, we plot the distributions of the count rates with statistical
uncertainties as error bar along the Y-axis from columns 246 to 253 in the
different panels of Fig. 4. The blue dots are the averaged counts per hour in
each pixel, and the orange dots are the count rates of albedo protons in the
relevant pixels.

We model the background along the y-axis with a Gaussian distribution. The
fitted results are plotted as red dashed lines in Fig. 4. Each panel is fitted
separately with different parameters. Finally, the backgrounds of the albedo
protons are estimated based on the fitted model and subtracted from the albedo
proton data points (shown as orange data points) to determine the flux of
albedo protons.

Figure 4: The distribution of count rates along the Y-axis between columns 246
and 253”Xmas plot”. The blue dashed lines are the measurements and the red
dashed lines are the fitted Gaussian distributions. The error bars are
statistical uncertainties. The difference between the orange dots and the
background gives the albedo proton-contributed count rates.

##  5 Measurements and comparison with Model

Following the calibration processes mentioned before, we derived the averaged
primary proton spectrum between 8 MeV and 368 MeV and the averaged albedo
proton flux between 64.7 MeV and 76.7 MeV for the lunar days between June 2019
and July 2020, i.e., when LND was on. No solar energetic protons were observed
by LND on the lunar surface.

###  5.1 GCR primary proton spectrum

The obtained LND GCR proton differential flux is plotted as empty blue circles
in Fig. 5. The error bars in the $x$ and $y$ directions correspond to the
widths of the energy bins and the flux uncertainty, respectively (The
numerical values are also given in the last column of table S3 of appendix).
The nine lowest energy channels (H1-H9) are the averages of the 1-minute data
products of stopping protons in the energy range between 9 and 35 MeV. The
rightmost three proton channels (from left to right, H14, H11, H10) show the
penetrating proton flux with energy above 35 MeV. The detailed information of
the bins is given in table S3. We only show the statistical uncertainties of
the differential flux. Since each channel accumulated a large number of
particles during this one-year measurement reported here, the statistical
errors of each channel are small, especially for the penetrating channels.
Hence the error bars of those three channels are almost invisible. Moreover,
as we explained in Sec. 4.3.3, the contamination caused by GCR ions has been
subtracted.

Besides the measurements of LND, we also plot SOHO/EPHIN (grey square)
measurements in Fig. 5. SOHO/EPHIN provides measurements of protons with
energies between 4.3 and 53 MeV. In this work, we use the EPHIN daily averaged
level 3 proton fluxes derived from the PHA data according to the methods
developed by Kühl et al. (2020). Those data have 16 energy bins provided by
the SOHO/EPHIN team. The periods of EPHIN data are the same as those during
which LND operated, i.e., to the times when Chang’E 4 was on during local
lunar daytime. One sees that the proton spectrum drops in the energy channels
above 50 MeV. As explained by the EPHIN team, this change is unexpected and
might not reflect the actual proton spectrum in space555P. Kühl, private
communication, 2022.. As shown in Fig. 5, the GCR proton spectrum measured by
LND agrees well with that measured by SOHO/EPHIN in the energy range below 40
MeV.

Moreover, we also compare the LND measurement of GCR protons with the CREME96
and BON14 cosmic ray models. CREME96 is a widely-used program that can
simulate the ionizing-radiation environment in near-Earth space and predict
the cosmic ray flux, based on the semi-empirical model of Nymmik et al.
(1992). Their solar quiet model includes GCR, ACR, and a low-energy component
below $\sim$10 MeV that originates from the sun and interplanetary space.
Likewise, BON14 is based on GCR measurements from particle detectors and can
predict the GCR variations related to solar modulation which is an input
parameter of the model. In Fig. 5, we only plot the CREME96 cosmic ray spectra
of 2019 as dashed blue lines since the BON14 predicts a very similar proton
flux during solar minimum. The lower curve is the original spectrum generated
by the CREME websitefor this period. Obviously, the GCR model underestimates
the proton flux at a few tens of MeV during solar minimum 24/25, and the
measurement is about 48%$\pm$2% higher than the model spectra. This percentage
is the averaged ratio between the measurement and the mode. The comparison
with BON14 leads to the same conclusion. Therefore, we multiplied the CREME
spectrum by a factor of 1.56 for the limited energy range which fits the LND
measurement best. This implies that the actual solar modulation during the
solar minimum 24/25 may be weaker than the modulation used in numerical
models. A similar disagreement between models and experimental data has been
reported by Mrigakshi et al. (2012) during the solar minimum 23/24 and further
discussed by Matthiä et al. (2013). They discuss that the averaged sunspot
number is not an accurate predictor of GCR fluxes during solar minimum and
show substantial differences between the GCR ISO model (ISO, 2004) (which is a
later version of the Nymmik et al. (1992) model) and the BON model. In fact,
solar modulation has been reported to be reduced in 2019-2020 and GCR
intensities at 1 au during this period reached the highest record in the space
age (Fu et al., 2021).

###  5.2 Albedo protons

As discussed in Sec. 4.4, LND can resolve albedo protons and determine their
flux between 64.7 and 76.7 MeV. This is shown as the red circle in Fig. 5 for
the same time period as the GCR spectra. The background has been subtracted
and the error of the flux is the resulting systematic uncertainty which is
larger than the statistical error. The averaged flux at $\sim$ 70.5 MeV is
about $1.12\mathrm{\pm 0.09\times 10^{-4}(cm^{2}\ s\ sr\ MeV)^{-1}}$ which is
remarkably close to the primary GCR proton flux measured by LND in this energy
range. Albedo protons are the product of high-energy GCRs which interact with
the lunar soil. A small fraction of the reaction products can escape from the
soil and thus forms the albedo population. This interaction is modeled by the
REDMoon code (Dobynde and Guo, 2021) which then predicts the lunar proton
albedo as shown by the red lines in Fig. 5 and discussed in the following
paragraph.

Here the REDMoon model takes the CREME GCR model as input to calculate the
angle- and energy-resolved surface particle flux on the Moon. The result for
the time period reported here is given in Fig. 6 which shows the isotropically
distributed downward flux (zenith angle 90-180 deg) at the lunar surface in
the upper half of the figure. The lower half shows the angle- and energy-
resolved upward flux of (albedo) protons, the black rectangle marks the energy
range which LND measures. The albedo protons are primarily due to GCR protons,
but GCR helium and heavier ions contribute a small fraction. The REDMoon
results shown as dashed red lines in Fig. 5 were calculated with the unscaled
CREME model as well as a CREME input spectrum scaled by a constant factor of
1.56, as discussed above. The region between these two model predictions is
shaded in pink and represents the upward proton flux that is expected to be
measured by LND. The decrease of the albedo protons flux at energy higher than
$\sim$100 MeV reflects that the generation efficiency of secondary particles
drops with energy.

The lower panel of Fig. 5 shows the ratio of upward (albedo) to downward (GCR)
proton flux as derived by taking the ratio of REDMoon and CREME simulation
results. Note that the ratio is the same for the scaled and non-scaled inputs
of CREME spectra and that it is computed at the same energy of downward and
upward propagating protons. The ratio peaks around 20 MeV, where the albedo
protons are more than two times higher than the primary GCR protons in that
energy range. Above it, the ratio drops as the GCR flux increases and the
albedo flux decreases. The high ratio ($>1$) is the consequence of the high-
energy GCR making the main contribution to the low-energy albedo protons.

We determined the ratio of albedo protons to the primary protons in the energy
range between 64.7 and 76.7 MeV, as measured by LND. The average primary
proton flux is estimated from the scaled GCR spectrum that fits the LND
measurements. We found that the ratio is about 0.64$\pm$0.07 which means that
the albedo protons are a significant contribution to the particle flux on the
lunar surface in this energy range. Thus, about 39% $\pm$6% of all protons
around 70 MeV are secondary albedo particles emitted from the lunar regolith.
The second data point shown in magenta dots is the ratio reported by the
CRaTER team (Wilson et al., 2012). The REDMoon simulation results agree well
with the both the LND and CRATER measurements in their energy ranges.

The CRaTER data point was only reported by Wilson et al. (2012) as a ratio of
the number of upward (albedo) protons to that of downward protons measured
within the same FOV and the same energy range for both particle populations.
They found a value of 0.38$\pm$0.02 for this ratio which is different from the
one reported by LND in this work. It is important to note that the CRaTER
measurements are sensitive to a different energy range than LND, i.e., between
60 and 150 MeV (with an average energy higher than the LND-seen albedo
protons) and were obtained between 2009 to 2011. This time period also
corresponds to a solar minimum and we don’t expect the ratio of upward to
downward protons to depend strongly on the detailed differences in the two
solar minima between solar cycles 23/24 and 24/25.

Primary (GCR) protons interact with the lunar surface and can produce the
albedo population reported here. Schwadron et al. (2017) discuss the various
generation mechanisms in more detail. The overall shape of the ratio of albedo
to primary proton can be understood without sophisticated modeling: Albedo
protons necessarily must have lost a significant part of their energy in the
uppermost layers of the lunar regolith. Because the primary (GCR) proton flux
increases with energy in and beyond the energy range covered by LND, the ratio
of albedo/primary proton flux must decrease with energy. This simple
explanation is supported by REDMoon model calculations and were also obtained
by Looper et al. (2013) in their simulation of the radiation environment on
the lunar orbiter of 50km height. This also explains why the LND observations
of the albedo to primary ratio is nearly two times higher than that of
LRO/CRaTER. In Tab. 1, we list the ratios of different cases, including the
ratios from LND in 2019, CRaTER in 2009, and the ratio from the simulation
averaged over different energy. We always use the GCR spectrum of 2019 as the
input spectrum in the simulation. Ignoring the time difference, we can
directly compare the simulation with measurements in the same energy range.
The modeled albedo to primary proton ratio averaged between in the LND energy
range (65-76 MeV) is 0.8, which is slightly higher than LND’s measurement, but
the albedo flux falls within the pink shaded band in the upper panel. For
CRaTER one needs to average the model over a wider energy range which is given
by CRaTER’s energy range. Thus folding the model function with the CRaTER
energy range, we obtain a value of 0.33, which is comparable with the CRaTER’s
result.

Wilson et al. (2012) only report the albedo to primary proton ratio, but not
the upward proton flux. This can easily be estimated by multiplying the scaled
CREME model flux in the appropriate energy range with the reported albedo
ratio and is shown as the magenta point in the upper panel of Fig. 5. The
albedo proton flux that is calculated using the original (unscaled) GCR
spectrum can be taken as a lower limit. LND measurements, CRaTER measurements,
and the REDMoon simulation are consistent within the reported uncertainties.

Figure 5: (Top) The GCR primary proton spectra including both measurements (LND in empty blue circles and SOHO/EPHIN in grey triangles) and modeled results (blue dashed lines). Albedo proton spectra are drawn in reddish colors. The simulation results from REDMoon are within the transparent red area. The LND measurement of albedo protons is the red circle. The error bar is the systematic uncertainty as defined in sec. 4.4. The estimated albedo proton flux that we derived using the ratio of albedo to primary proton measured by LRO/CRaTER is the magenta data point. (Bottom) The ratio of albedo to primary flux versus proton energy. The red and magenta points are the ratio of albedo to primary proton flux derived from LND data in this study and that from LRO/CRaTER data (Wilson et al., 2012), respectively. The black line shows the prediction from the REDMoon model. The detailed explanations are given in the main text, the values for the LND data pints are given in Tab. S3 of supplementary material. Figure 6: (left) The angular distribution of protons on the lunar surface including both albedo protons (0-90 degree) and GCR primary protons (90 - 180 degree). The plot is modified from panel (a) of Fig. 4 in Dobynde and Guo (2021). (right): Albedo proton flux as a function of primary protons shows a maximum around albedo energies of 80 MeV. These albedo particles are produced by primary protons with much higher energies. Both albedo particle distributions are derived by REDMoon model. Table 1: The ratio of lunar albedo protons to primary protons. LND(64.7-76.7MeV) | CRaTER(60-150MeV) | simulation(65-76MeV) | simulation(60-150MeV)
---|---|---|---
2019-2020 | 2008-2009 | 2019 | 2019
64$\%\pm 7$ | 38$\%\pm$2 | 80$\%$ | 33$\%$

##  6 Summary, Discussion and conclusion

We have performed and reported a careful re-analysis of the LND calibration.
LND data in the energy range between 9 MeV and 368 MeV agrees well with data
from the SOHO/EPHIN instrument. LND data up to 35 MeV are for well-resolved
protons stopping in LND’s detector stack; the remaining three data points are
for penetrating protons.

Furthermore, we compared LND’s proton spectrum with the CREME96 GCR model. We
find that the CREME96 predictions underestimate the proton flux during
reported time period in the solar minimum 24/25. The average ratio between LND
measurements and the CREME96 model predictions is $\sim$1.48$\pm$0.02. This
may be due to the much weaker solar modulation during the deep solar minimum
24/25. In fact, GCR intensities at 1 au during this time period reached the
highest recorded fluxes in the space age (Fu et al., 2021).

With its stack of 10 silicon detectors, LND is capable of measuring both the
downward as well as the upward proton flux. Such albedo protons are the result
of the interaction of high-energy GCR particles with the lunar regolith. The
bulk of the albedo particles is created by the high-energy portion of the
primary GCR protons, as shown in the right hand panel of Fig. 6. This part of
the GCR spectrum is less affected by solar modulation than the low-energy
part. Therefore, when considering the effect of solar modulation on the ratio
of upward to downward particles one needs to consider that this ratio is
calculated at the same primary energy of the upward and downward-pointing
particles. Because the low-energy part of the GCR spectrum is strongly
affected by solar modulation, the up/down ratio is primarily affected by the
low-energy downward flux and much less so by the upward flux which is
primarily determined by the high-energy downward-pointing flux, as reported by
Wilson et al. (2012). This effect is especially important during solar
particle events. Comparing the measured upward to downward differential fluxes
we find a ratio of $0.64\pm 0.07$ in the energy range between $64.7-76.7$ MeV.
This ratio is shown as the red data point in the lower panel of Fig. 5.
Because of the additional shielding from beneath provided by the Chang’E 4
lander, the energy ranges resolved by LND differ for the upward and downward
particle populations. Furthermore, we scaled the upward to downward flux ratio
reported by the CRaTER team using data prior to solar minimum 23/24 to the
time period investigated here. We used the scaled CREME96 downward flux to
determine the upward flux expected in the CRaTER energy range. The resulting
upward flux (shown as the magenta data point in the lower panel of Fig. 5)
agrees well with LND’s measurement and the REDMoon predictions, despite being
valid for a different energy range ($60-150$ MeV).

As already stated, the REDMoon simulation tool provides the upward (albedo)
differential proton flux. We compare the REDMoon model results with the
downward flux from the scaled CREME96 model to derive the ratio of upward to
downward differential flux shows as the dash-dotted line in the lower panel of
Fig. 5. At energies below $\sim$ 50 MeV, the ratio is above 1 and it has a
peak value above 2 near 20 MeV. With increasing energy, the ratio decreases as
the generation of albedo protons at this energy decreases. We observe that the
modeled energy dependence of the albedo proton flux is confirmed by the
combination of the LND and (scaled) CRaTER data.

LND is the first high-energy charged-particles telescope to be working on the
lunar surface. We have presented measurements of low-energy cosmic ray protons
in conjunction with albedo protons and that the latter contribute
significantly to the particle flux on the lunar surface. We also show that the
albedo proton flux is energy dependent, and that both primary and albedo
proton fluxes are in good agreement with measurements from LRO/CRaTER.
Obviously, due to their high flux and relatively low energy, albedo protons
are an important contribution to the radiation to which astronauts would be
exposed to on the surface of the Moon. Albedo protons are energetic enough to
penetrate a space suit and have sufficiently low energy do stop in the body of
an astronaut, thus depositing all their energy in the astronaut’s tissue. The
Sun is now becoming more active and future data from large solar particle
events will be critical to understand their effect on the lunar radiation
environment and its effect on human exploration of the Moon.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

ZX led the data analysis and paper writing. RW and JG advised on the data
analysis and improved the paper writing. MD provided the simulation data of
the REDMoon model, and PK offered SOHO/EPHIN data. SK and SZ provided valuable
information and suggestions. All authors read the paper and approved its
submission.

## Funding

The Lunar Lander Neutron and Dosimetry (LND) instrument was funded by the
German Space Agency, DLR, and its space Administration under grant 50 JR 1604
to the Christian-Albrechts-University (CAU) Kiel as well as the Beijing
Municipal Science and Technology Commission (grant no. Z181100002918003) and
NSFC (grant no. 41941001). JG and MD are supported by the Strategic Priority
Program of the Chinese Academy of Sciences (Grant No. XDB41000000) and the
National Natural Science Foundation of China (Grant No. 42074222, 41941001).
We acknowledge financial support by Land Schleswig-Holstein within the funding
programme Open Access Publikationsfonds.

## Acknowledgments

We thank the two anonymous reviewers for their thorough reviews which helped
to improve this paper and the many individuals who were involved in
conceiving, designing, building, testing, and launching LND and Chang’E 4.

## Supplemental Data

The data calibrations and the LND configuration changes are given in the
supplementary material.

## Data Availability Statement

The scientific data of Lunar Lander Neutron and Dosimetry Experiment are
provided by China National Space Administration.

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