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University of Southern California Dissertations and Theses
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Interactions of planetary surfaces with space environments and their effects on volatile formation and transport: atomic scale simulations
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Interactions of planetary surfaces with space environments and their effects on volatile formation and transport: atomic scale simulations
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Content
Interactions of Planetary Surfaces with Space Environments and
Their Effects on V olatile Formation and Transport: Atomic Scale
Simulations
by
Ziyu Huang
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ASTRONAUTICAL ENGINEERING)
August 2023
Copyright 2023 Ziyu Huang
Acknowledgements
First and foremost, I would like to express my deepest gratitude to my advisor, Prof. Joseph Wang.
Your unwavering support, insightful critiques, and patience throughout this journey have been
invaluable. You constantly pushed me to become a better researcher and I am profoundly grateful
for your mentorship.
I would also like to extend my appreciation to the members of my dissertation committee, Prof.
Mike Gruntman, Prof. Aiichiro Nakano and Prof. Ken-ichi Nomura. Your feedback and guidance
have been essential in shaping my research. Your rigorous standards and insightful comments have
helped me refine my work and broaden my understanding of the subject. I also want to thank Liam
S. Morrissey for all the helpful discussions on the simulation.
My sincere thanks also go to all the members of the ASTE department and my colleagues, who
provided valuable insights, engaging discussions, and moral support. Their encouragement and
friendship made this academic pursuit all the more rewarding.
Lastly, I would like to express my heartfelt gratitude to my family and friends for their uncon-
ditional love, encouragement, and patience throughout this endeavor. Their unwavering support
and belief in my abilities kept me motivated during challenging times.
ii
Table of Contents
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Lunar V olatile Observation . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 Lunar Water Formation Mechanisms Induced by Space Environment . . . . 3
1.1.3 Lunar V olatile Transport and Lunar Exosphere . . . . . . . . . . . . . . . . 5
1.1.4 Exploration of Icy Moons . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Solar Wind Implantation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Micrometeoroid Impact Generated Water . . . . . . . . . . . . . . . . . . 12
1.2.3 Deep Dielectric Charging and Breakdown . . . . . . . . . . . . . . . . . . 16
1.2.4 V olatile Transport Model: Exosphere Modeling . . . . . . . . . . . . . . . 18
1.2.5 Hypervelocity Ice Impact: Exploration of Icy Moons . . . . . . . . . . . . 19
1.3 Motivations and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Chapter 2: Methods and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1 Molecular Dynamics Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.2 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2 Interacting Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.1 Reactive Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.2 Ziegler-Biersack-Littmark and Electronic Stopping Energy . . . . . . . . . 28
2.3 Machine Learning Algorithm: Maxwellian Mixture Model . . . . . . . . . . . . . 28
2.3.1 Derivation of Maxwellian Mixture Model . . . . . . . . . . . . . . . . . . 28
2.3.2 Numerical Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 3: Solar Wind Implantation and Its Contribution to Lunar OH/H
2
O . . . . . . . . 34
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
iii
3.2 Formula and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Saturation of Solar Wind Implantation . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Chapter 4: Deep Dielectric Breakdown: Formation of Water Molecules . . . . . . . . . . . 49
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Formula and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.4 Conclusion and Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter 5: Micrometeoroid Impact: Lunar Water Retention . . . . . . . . . . . . . . . . . 63
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Formulation and Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3 Retention and Release of Water Molecules . . . . . . . . . . . . . . . . . . . . . 68
5.4 Generation of O
2
and its implication of Hematite on the lunar surface . . . . . . . . 73
5.5 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 6: The Influence of Lunar Surface Hydration Status on the Exosphere Transport . . 80
6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.2 Machine Learning Fitting of Velocity Distribution Function . . . . . . . . . . . . 83
6.3 Direct Comparison of Si− OH Substrate and SiO
2
− H
2
O Substrate . . . . . . . . . 84
6.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Chapter 7: Implications of Water-Surface Interactions to the Measurement of Icy Grains . . 90
7.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
7.2 Simulation Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.4 Implications for Ice Impact Velocity Measurement . . . . . . . . . . . . . . . . . . 102
7.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Chapter 8: Unraveling Impact Generated Exosphere of Icy Surfaces: the Role of Clustering 106
8.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
8.2 Method and Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
8.2.1 Mixed Maxwellian Distribution for Water Clusters . . . . . . . . . . . . . 110
8.2.2 Validation of multiple Maxwellian Distribution . . . . . . . . . . . . . . . 111
8.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8.3.1 Dependence on the Escape Velocity . . . . . . . . . . . . . . . . . . . . . 113
8.3.2 Sensitivity Test of Power Index . . . . . . . . . . . . . . . . . . . . . . . . 116
8.3.3 A General Model for All Exosphere Species . . . . . . . . . . . . . . . . . 117
8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Chapter 9: Summary and Recommendation for Future Studies . . . . . . . . . . . . . . . . 121
9.1 Summary of Lunar Water Cycle Modeling . . . . . . . . . . . . . . . . . . . . . . 121
9.2 Discussion: Contribution of Dielectric Breakdown to the Water Formation in a
Grain Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
iv
9.3 Discussion: Timescale and Spatial Scale of Dielectric Breakdown and Microme-
teoroid Impact . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
9.4 Recommendation for Future Studies on Lunar V olatile Modeling . . . . . . . . . . 127
9.5 Summary of Hypervelocity Ice Impact Modeling . . . . . . . . . . . . . . . . . . 128
9.6 Recommendation for Future Studies on Hypervelocity Ice Impact Modeling . . . . 130
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
v
List of Tables
1.1 Summary of Previous Experimental Studies on Solar Wind Implantation . . . . . . 10
4.1 Simulation parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.1 Simulation Cases and Statistics of Water Molecules after Impact . . . . . . . . . . 68
vi
List of Figures
1.1 Plumes, ice crust and internal ocean of Europa, credits: JPL . . . . . . . . . . . . 8
1.2 Europa Clipper Missions, credits: JPL . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Distribution of impact velocity of micrometeoroid impact on the moon . . . . . . 14
1.4 Timescale of discharge on lunar surface related to temperature [1] . . . . . . . . . 17
2.1 Velocity distribution of two groups of molecules with T
1
(in red) and T
2
(in blue)
and the mixture of the two groups (in purple). Histogram of random data with a
distribution of f
s
(v) obtained by acceptance-rejection method is shown in blue bins 32
2.2 Red dot: ω
1
andσ
1
, blue dot: ω
2
andσ
2
, green diamonds are two groups ofω and
σ identified by Maxwellian Mixture Model. . . . . . . . . . . . . . . . . . . . . . 33
3.1 Snapshots of molecular structure at N=1 and N= 2743 and 8679 implantation
events. N is the number of implantataion events. Red particles are oxygen atoms,
yellow particles are silicon atoms and black particles are hydrogen atoms. . . . . . 41
3.2 Column density of molecules and chemical groups during implantation. Top
panel: the total column density of molecules in the simulation box. Middle panel:
The column density of molecules under the surface. Bottom panel: The column
density of molecules above the surface. . . . . . . . . . . . . . . . . . . . . . . . 42
4.1 Snapshots of the molecular structures in the simulation. Figure(a): initial
configuration of Simulations 1 and 2A. Figure (b): the end of Simulation 1. Figure
(c): the end of Simulation 2A and beginning of Simulation 2B. Figure (d): the
end of Simulation 2B. Red particles represent oxygen atoms, yellow particles
represent silica atoms and blue particle represent hydrogen atoms. . . . . . . . . . 55
4.2 Detailed bond structures at the beginning of Simulation 2A (Figure 4.2 a) and at
the end of Simulation 2B (Figs. (b) and (c)). Figure (a): SiO
4
tetrahedra of the
silica nanoparticle. Figure (b): water molecules attached to silica surface. Figure
(c): hydrogen bonds between water molecules at the silica surface. Red particles
represent oxygen atoms, yellow particles represent silica atoms and blue particle
represent hydrogen atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
vii
4.3 Comparison of the number of molecules in Simulations 1 and 2A: Number of
water molecules (Figure 4.3 a); Number of SiO
4
tetrahedra (Figure 4.3 b); and
Number of OH group molecules (Figure 4.3 c). . . . . . . . . . . . . . . . . . . . 62
4.4 Comparison of the number of water molecules, SiO
4
tetrahedra, and hydrogen
molecules in Simulations 2A and 2B. . . . . . . . . . . . . . . . . . . . . . . . . 62
5.1 Snapshots of the impact process for Case 1. (a) t = 0 ps. (b) t = 10ps. (c) t =
20ps. (d) t = 80ps. The upper panels show the micrometeoroid and lunar surface
(generated from simulation results using OVITO [2]). The lower panels show
zoomed in molecule structures. Red particles: O atoms. Yellow particles: Si
atoms. Blue particles: H atoms. (In the lower panels, the plots are sliced through
the center of the crater to show the molecule structures.) . . . . . . . . . . . . . . 66
5.2 Closer look at the molecular setup for micrometeoroid impact simulation. . . . . . 67
5.3 Time history of the H
2
O molecules in simulation. (a) Total molecules in the
system N
H
2
O
total
. (b) The ejected molecules N
H
2
O
e jected
. (c) The molecules that remain
locally at the impact surface N
H
2
O
local
. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Ejecta Analysis (Case 1). (a) The ejection velocity distribution. The blue dot line
is at V
1
, and the red dot line is at V
2
. (b) PDF of the height in the exosphere H
exo
.
(c) PDF of the transport distance from the impact site D
trans
. . . . . . . . . . . . . 77
5.5 Time history of the SiO
4
tetrahedra in simulation. (a) Total tetrahedra in the
system N
SiO
4
total
. (b) The ejected tetrahedra N
SiO
4
e jected
. (c) The tetrahedra that remain
locally at the impact surface N
SiO
4
sur f ace
. . . . . . . . . . . . . . . . . . . . . . . . . 78
5.6 Time history of the O
2
molecules in simulation. (a) Total molecules in the system
N
O
2
total
. (b) The ejected molecules N
O
2
e jected
. (c) The molecules that remain locally at
the impact surface N
O
2
local
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1 Machine Learning Fitting of Velocity Distribution Function from [3] . . . . . . . . 84
6.2 (a) Setup of SiO
2
− OH and (b) Setup of SO
2
− H
2
O . . . . . . . . . . . . . . . . 85
6.3 3D snapshots (upper panel) and 2-D Top-views (lower panel) of the temperature
contour during micrometeoroid impact with V = 20 km/s at t = 0, 20, 100fs. Color
coded by kinetic energy (10 atoms neighbour average) . . . . . . . . . . . . . . . 85
6.4 (a) Velocity Distribution Function of Ejected H
2
O in SiO
2
− OH case and (b)
Velocity Distribution Function of Ejected H
2
O in SiO
2
− H
2
O . . . . . . . . . . . 88
7.1 Left: simulation setup and molecular structure of an ice cluster. Right: cluster
analysis of the resulting ejecta (a) monomers and dimers (b) trimmers (c) large
clusters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
7.2 Number of clusters after hypervelocity ice impact against the magnitude of velocity 96
viii
7.3 Size of the largest cluster after hypervelocity ice impact against the magnitude of
velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.4 Number of clusters after hypervelocity ice impact against vertical component of
the velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
7.5 Size of the largest cluster after hypervelocity ice impact against vertical component
of the velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
7.6 Pseudo Mass Spectra of Cluster after Hypervelocity Ice Impact with i= 60
◦ . . . . 99
7.7 Power-law index (n
2
which is usueal) fitting against vertical component of the
velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
7.8 Number of molecular hydrogen (H
2
) generated and ratio of H atoms in H
2
from H
2
O103
7.9 Number of molecular oxygen (O
2
) generated and ratio of O atoms in O
2
from H
2
O 103
7.10 Yield of molecular hydrogen (H
2
) and molecular oxygen (O
2
) against vertical
component of the impact velocity . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.11 Relative ratio of molecular oxygen(O
2
) yield and molecular hydrogen (H
2
) yield
from H
2
O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
8.1 Validation of Mixed Maxwellian Distribution by Reactive Molecular Dynamics
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
8.2 Velocity distribution function for Single Maxwellian (dashed curves) and Mixed
Maxwellian (solid curves). Black dashed line indicates the escape velocity of
Europa, the Moon and Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.3 Cumulative distribution function for Single Maxwellian (dashed curves) and
Mixed Maxwellian (solid curves). Black dashed line indicates the escape velocity
of Europa, the Moon and Mercury . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.4 (a) Difference of surface bounded portion between single Maxwellian distribution
and mixed Maxwellian distribution (b) Relative difference assuming single
Maxwellian distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.5 Relative Ratio of Mixed Maxwellian distribution compared with single
Maxwellian distribution for Mercury, Moon, Europa and Triton . . . . . . . . . . . 118
8.6 Relative Ratio of Mixed Maxwellian distribution compared with single
Maxwellian distribution for Ceres, Tethys and Enceladus . . . . . . . . . . . . . . 118
9.1 Water weight ratio when scaling up to the radius of lunar dust grain from 0-100 µ m 123
9.2 Water weight ratio when scaling up to implantation depth of 0-20 nm . . . . . . . . 124
9.3 Comparison between timescales of solar wind implantation saturation, microme-
teoroid impact and dielectric breakdown in a crater. . . . . . . . . . . . . . . . . . 126
ix
Abstract
The origin of lunar volatiles is a long-standing problem. As the moon does not have a global
magnetic field and a sustainable atmosphere, solar wind particles, micrometeoroids, and energetic
particles can interact directly with the lunar regolith surface. Such interactions have been proposed
to play a critical role in the formation of lunar water. This dissertation presents the first atomic
scale simulation study of the dynamics and chemical reactions of lunar surface-environmental
interactions and their contributions to lunar water formation and the lunar exosphere.
Reactive molecular dynamics simulations are carried out to model solar wind implantation on
the lunar surface, micrometeoroid impact on the lunar surface, and dielectric breakdown of lunar
regolith due to space weather effects, and to understand how these processes affect the lunar wa-
ter formation cycle. The solar wind implantation simulation study closely replicates the energy
and flux conditions of solar wind particles. The results show an efficient formation of hydroxyl
groups (-OH) and molecular hydrogen (H) but relatively weaker water synthesis. Additionally, a
saturation feature of hydroxyl due to solar wind implantation is identified for a timescale of 1 to
1000 years. The micrometeoroid impact simulation study resolves both the chemical reactions and
physical collisions during impact on the hydroxylated regolith surface, as well as the dynamics of
the released water molecules. The results reveal that water molecules are both generated and lost
during micrometeoroid impacts and that water retention is significantly affected by the impact ve-
locity significantly affects water retention, with higher velocities resulting in greater water loss to
space. The dielectric breakdown simulation study resolves the effect of the electric field from deep
dielectric charging in regolith grain due to space weather events. The results show that such deep
dielectric charging can break the Si-O bonds in regolith grain and facilitate the formation of water
x
molecules, which are subsequently preserved as water ice attached to the regolith. The combined
results from these simulation studies show that, while solar wind implantation can lead to the for-
mation of some hydroxyl groups and water molecules, the contribution by the implantation process
itself is not significant enough to account for the observed lunar water content. Micrometeoroid
impacts and dielectric breakdown provide the required energy or catalyst for water formation reac-
tions. For all the cases considered, micrometeoroid impacts always produce more water molecules.
However, a comparison of the time scale of implantation saturation against that of micrometeoroid
impacts (10
4
years) and dielectric breakdown (10
3
years) indicates that dielectric breakdown ex-
hibits a higher efficiency in converting the hydrogen from solar wind into water molecules. This
provides further evidence that the permanently shadowed regions are ideal locations for both water
formation and water preservation.
The results of chemical bond calculations are further combined with transport simulation to
study the dynamics of released water molecules from the lunar surface. Machine learning is applied
to identify the different sources of water molecules in the ejected water molecules. The results
show that the original water molecules and the newly formed water molecules have very different
velocity distributions, and thus have a distinct contribution to the exosphere. This suggests the
need for a clear identification of the form of water on the lunar surface in exosphere studies.
While the focus of this dissertation is on lunar water formation, the simulation methodology
is also extended to study hypervelocity ice impact to support future exploration of icy moons.
The results reveal a two-stage fragmentation pattern as we increase the impact velocity, the inter-
molecular fragmentation and inter-atomic fragmentation. The inter-molecular fragmentation stage
shows a consistent power-law size distribution while the inter-atomic fragmentation stage shows
a correlation between the generation of molecular hydrogen and molecular oxygen. We proposed
that the chemical reactions products in the inter-atomic fragmentation stage could be used as a
velocity probing method for icy moon exploration missions. An examination of the dynamics of
the water molecules generated by hypervelocity impact also shows that, when there are significant
clusters of water molecules, the overall velocity distribution function of the ejected water should
xi
be modeled by mixed Maxwellian distributions rather than a single Maxwellian distribution for
impact generated surface bonded exosphere. Thus, future exosphere modeling should include the
effect of clustering and need to integrate surface chemistry with transport dynamics.
xii
Chapter 1
Introduction
1.1 Overview
V olatiles on the moon are of increasing interest to both scientific research and exploration of space.
The moon is the closest airless body to our planet and the most accessible place to investigate the
history and evolution of the universe. Understanding the origin of lunar volatile is helpful to en-
lighten the discovery of other planets in the future. For the upcoming ARTEMIS-1 mission to
the moon, finding the origin of lunar volatiles is essential to NASA’s In-Situ Resource Utilization
(ISRU) plan. H
2
O, H
2
, and O
2
are part of the high-priority resources for human exploration. An
”Origin-first” concept was proposed by Farrell et al. [4] to understand the origin of the volatiles
before making any irreversible damage to the volatile system. The origin of those molecules deter-
mines their renewability, which provides guidance for us to collect or reproduce them under lunar
environment. This section presents an overview of the background and recent studies regarding
lunar volatiles.
1.1.1 Lunar Volatile Observation
Lunar volatiles holds a lot of information about the moon regarding its origin and evolution. Sev-
eral past and future human explorations of the moon are bonded with the existence and abundance
of lunar volatiles. As one of the most basic and essential species, the discussion of water is a
1
major area of interest. The existence of lunar water has been much debated since the Apollo era.
Several studies[5, 6, 7, 8] predicted that water molecules might be condensed on the lunar surface
but returned lunar samples during the Apollo mission indicate that the moon is lack of water[9]. A
dry moon concept was accepted by most scholars for many decades until 2008. With the advance-
ment in secondary ion mass spectrometry, Saal et al. [10] found a considerable amount of water in
lunar volcanic glasses. Followed by that, several spacecrafts have found in-situ evidence of 3-µm
band (− OH/H
2
O) on the moon including Lunar Reconnaissance Orbiter (LRO) [11], Lunar Crater
Observation Sensing Satellite (LCROSS)[12] and Chandrayaan-1 [13].
The confirmed detection of − OH/H
2
O had led to a renewed interest in the discussion of lunar
volatiles. Many questions remained unanswered regarding the origin, abundance and distribution
of lunar volatiles. Especially the origin which directly determines the abundance and distribution
of volatiles. Both endogenous and exogenous sources are proposed to contribute to the formation
of lunar water[14]. For instance, endogenous sources include volcanism and outgassing events
from the lunar interior. Exogenous sources include solar wind, micrometeoroid impact, or water-
rich comet impact. The physical form and the evolution of the water generated by each mechanism
have shaped the observed water features on the lunar surface.
Observational data provides possibilities to investigate the spatial distribution of lunar water.
Sunshine et al. [15] shows that water is distributed widely on the lunar surface by analyzing Deep
Impact extended mission (EPOXI) data. Both M
3
[16, 13] and LCROSS [17] found concentration
of water at permanently shadowed regions (PSRs). On a smaller scale, Hayne et al. [18] found that
micro cold traps generated by the surface roughness are shown to have the capacity to hold as much
water as large PSRs. Most recently, the surprising data obtained by NASA/DLR Stratospheric
Observatory for Infrared Astronomy (SOFIA)[19] have found evidence of widespread hydration
at sunlit regions. More and more evidence shows that water exists on the lunar surface despite the
extreme space environment.
2
1.1.2 Lunar Water Formation Mechanisms Induced by Space Environment
Hapke [20] proposed that the bombardment of solar wind on the lunar surface might lead to hy-
droxylation or even water formation. This hypothesis has been proved by many recent experiments
[21, 22, 23, 24]. Although the results of these experiments are not the same as will be discussed
in the literature review section, they all showed that solar wind implantation is a major contributor
to the hydrogen cycle. It was also used to explain the 3-µm band absorption feature detected by
remote sensing. Indeed, lacking an atmosphere and magnetic field, the moon is directly exposed to
solar wind plasma and magnetotail. The surface of the moon has been altered continuously by the
solar wind plasma. Based on regular solar wind conditions (V
sw
≈ 400 km/s and n
sw
≈ 10 cm
− 3
),
Hurley [25] estimated that solar wind provides hydrogen to lunar surface at a rate of 30 g/s. Given
that the age of the moon is around 4.5 Ga, the solar wind has provided 9.46× 10
17
g of hydrogen
that could contribute to water molecules.
Except for its direct contribution to lunar water, solar wind implantation is also the prior step
for many other exogenous processes. Some studies believe that solar wind implantation itself is not
able to generate water molecules directly. Instead, it generates hydroxyl groups that can be reacted
to form water molecules. Those hydroxyl needs more energy from other exogenous processes
to become water molecules. Understanding solar wind implantation will be critical to investi-
gate subsequent processes since hydrogen’s implantation depth and distribution can significantly
change the outcome of subsequent mechanisms.
One of the subsequent mechanisms following solar wind implantation is micrometeoroid im-
pact. Micrometeoroid impact has been considered a significant triggering mechanism for lunar wa-
ter formation. The process to convert hydroxyl to water molecules, recombinative desorption(RD),
requires a typical temperature of 450 K[26] while the maximum temperature of the lunar surface is
only about 400 K. Zhu et al. [27] showed that the heat released by impact could provide sufficient
energy to start the reaction. In the same paper, it was also shown that the impact liberated water
molecules at the same time. This motivates us to think about the net contribution of micromete-
oroid to the observed water molecules or water retention.
3
Many factors influence the retention of water generated by an impact. The heat released during
an impact may generate and liberate water molecules at the same time. Mechanical collisions may
also create ejecta containing water molecules. Of all the liberated water molecules, they can be
transported to other locations on the lunar surface, exosphere, or outer space, depending on their
velocity. Those with a velocity larger than the moon’s escape velocity will be lost and never return
back to the lunar surface. In order to investigate the formation and loss of water molecules during
the impact, It is necessary to investigate how the velocities of the released molecules change with
impact conditions.
Impacts are also likely to change the molecular structure of the surface, which could affect the
retention of water. For instance, a porous structure can trap more solar wind protons and have a
larger capacity to hold water molecules. The thermal and dielectric properties of the lunar surface
will be changed as well. As solar wind particles and micrometeoroids continuously bombard the
lunar surface, it’s expected that the surface has been altered repeatedly. The change of the structure
will in return affect the next implantation or impact.
As mentioned previously, the interaction between solar wind implantation and micrometeoroid
impact has been a subject of interest. While numerous studies have extensively examined these
phenomena individually, few have explored the combined effects of these two mechanisms. Gillis-
Davis et al. [28] tested the space weathering effect of the combination of micrometeoroid impact
and electron bombardment. The results of the combination case are much more significant than
only conducting a single space weathering process. These findings emphasize the need to focus on
the combined effect, particularly when considering the involvement of chemical reactions.
Another subsequent mechanism discovered recently is the dielectric breakdown on the lunar
surface. If the solar wind conditions are not quite as usual, some energetic events might occur
on the lunar surface. Jordan et al. [29] proposed that at lunar PSRs, since the temperature is as
cold as 40 K, the dielectric constant of the regolith change significantly under this temperature.
During solar energetic particle (SEP) events, an extremely high electric field might be built up.
The magnitude of this E field might be as high as 10
6
–10
7
V/m. Under this high electric field, the
4
hydroxylated regolith grain might experience a dielectric breakdown event, and nearby hydroxyl
groups might be combined to form water molecules. The mechanism indicates that the formation
of water molecules is likely connected to space weather conditions.
In summary, solar wind plasma and the space environment of the moon are believed to make
large contributions to the formation of water. However, limitations of experiments and observa-
tions prevent further investigation of the relative contribution. For instance, the change of molec-
ular structure is hard to be captured by experiments. Achieving hypervelocity is also an obstacle
for experiments. It is hard to compare the relative contribution without knowing the exact chem-
ical reactions and physical processes during each mechanism. A model is missing to reveal the
information of geophysical processes on an atomic scale.
1.1.3 Lunar Volatile Transport and Lunar Exosphere
The exosphere of the moon is another window to investigate lunar volatiles. The concept of the
lunar exosphere is similar to the atmosphere but it’s too thin to be an atmosphere. Molecules are
still bonded by the gravity of the moon. The formation of the lunar exosphere is mostly attributed to
geophysical processes that release volatile molecules from the surface, including micrometeoroid
impact and sputtering by solar wind plasma or photons. Based on the data from Lunar Atmosphere
and Dust Environment Explorer (LADEE)[30], Benna et al. [31] observed an active water cycle in
the exosphere. The in-situ observation data shows the dynamics of near-surface water on the lunar
surface, indicating water on or even beneath the lunar surface might also be active. The exosphere
is also part of the lunar volatile transport model (VTM). Transport of volatiles on the lunar surface
is induced by either thermal heating of the surface or the space environment. Within the exosphere,
radiation and photo-dissociation might also be significant to the dynamics of the molecules. A
better understanding of the transport model is able to provide insights into the volatile on the lunar
surface.
All the water formation mechanisms introduced in the last section could induce water loss. For
instance, micrometeoroid impact vaporizes and ejects many water molecules on the lunar surface.
5
A large amount of the ejecta will become part of the exosphere. On the other hand, water molecules
in the exosphere can also be transported back to the lunar surface and become the source of water
retention. Water molecules are desorbed from the surface at lower latitudes in the daytime and
condensed to form ice in cold regions. Hayne et al. [18] suggests that water from the exosphere is
one of the major sources for ice in the cold traps based on thermal models.
The transport of water between the surface and exosphere builds a lunar water cycle. The loss
and sink of water make the exosphere very unsteady. Many observed features of lunar water are
attributed to this transport. For instance, the diurnal change of water has been observed by Hendrix
et al. [32]. The temperature on the surface drives the huge latitude variation of water abundance.
However, what physical processes trigger the change and how the exosphere participates in this
change is unclear. All of the questions would attribute to the most fundamental question: how water
molecules interact with lunar regolith and how geophysical processes initiate water desorption.
1.1.4 Exploration of Icy Moons
Enceladus and Europa are two of the most fascinating objects in our Solar System, each with
the potential to harbor extraterrestrial life. Both moons are thought to have subsurface oceans
that potentially house the necessary ingredients for life, including water, organic compounds, and
energy sources. Additionally, these moons have been found to exhibit geysers, or plumes, which
consist of water vapor and other materials ejected from the surface (see Figure 1.1). These plumes
are of great interest to scientists, as they provide a unique opportunity to study the subsurface
environments of these moons without the need for direct access. Numerous studies and missions
have been conducted to study the plumes on Enceladus and Europa, such as the Europa Clipper
Mission (see Figure 1.2).
Previous missions for the exploration of icy bodies include the Galileo and Juno missions. The
flyby of the Juno mission has brought us extremely useful data regarding Europa. While the Juno
mission is primarily focused on studying Jupiter, it has also provided valuable insights into some
of its moons, including Europa and Enceladus. Notably, Juno has provided data that suggests the
6
moon Europa has a magnetic field, potentially indicating a salty ocean beneath its icy surface.
Similarly, Enceladus, a moon of Saturn, has also been of interest for its potential to support life.
Juno’s observations have revealed evidence of water vapor plumes erupting from the moon’s south
pole, providing further evidence for the presence of an ocean beneath its icy crust. Juno’s continued
exploration of Jupiter and its moons promises to shed further light on these fascinating worlds and
their potential for habitability.
The discovery of plumes on Enceladus can be attributed to the Cassini-Huygens mission.
Launched in 1997, the Cassini spacecraft arrived in orbit around Saturn in 2004 and commenced
an extensive exploration of the planet and its moons. One of its most significant discoveries, doc-
umented by Porco et al. [33], was the presence of water-rich plumes erupting from the south polar
region of Enceladus in 2005. This groundbreaking revelation revolutionized our understanding of
this enigmatic moon. These plumes originate from the so-called ”tiger stripes,” which refer to four
prominent fractures in the moon’s icy surface [34]. Composed of water vapor, ice particles, and
other gases and particles, these plumes can reach heights of over 100 kilometers above the moon’s
surface [35].
While the discovery of plumes on Enceladus represented a groundbreaking achievement, it
also aroused interest in the possibility of similar phenomena on other moons in the Solar System.
Among Jupiter’s largest moons, Europa emerged as a prime candidate due to its icy surface and
the potential existence of a subsurface ocean. The first evidence of plumes on Europa was detected
in 2012 using the Hubble Space Telescope (HST), which observed faint emissions of hydrogen
and oxygen above the moon’s southern hemisphere [36]. This initial observation was followed
by multiple detections of potential plumes using the HST in 2014, as well as a revisit of data
collected by the Galileo mission in 1997 [37, 37]. In 2018, additional support for the existence of
plumes on Europa was provided by a study that used HST data to detect evidence of a plume-like
feature above the moon’s surface [38]. While the evidence for plumes on Europa is still somewhat
circumstantial and controversial, these observations have sparked significant interest and debate in
the scientific community, prompting plans for future missions to explore this intriguing moon in
7
more detail. Most recently, with the launch of James Webb Space Telescope (JWST), there are
more evidence of the plumes on icy moons. Villanueva et al. [39] used the NIRSpec instrument
and captured the largest plume ever detected on Enceladus.
The discovery of plumes on Enceladus and Europa has not only provided new insights into
the geological processes of these moons, but also has significant implications for astrobiology
and the search for extraterrestrial life. NASA’s upcoming Europa Clipper mission [40], set to
launch in 2024, will study the moon’s composition, geology, and potential habitability in detail.
Likewise, there are plans for future missions to Enceladus, including the Enceladus Life Finder
[41], a proposed mission that would land on the moon’s surface and directly sample its plumes to
search for signs of life. As our understanding of these moons and their plumes continues to grow,
it is clear that they represent some of the most promising targets for astrobiological exploration in
our Solar System.
Figure 1.1: Plumes, ice crust and internal ocean of Europa, credits: JPL
1.2 Literature Review
This section provides an overview of recent studies on the formation and transport of lunar water
and hypervelocity ice impact. It will be organized into four parts. First, we will introduce the solar
wind implantation mechanism, focusing on previous experimental research conducted in this area.
Second, we will review the role of micrometeoroid impacts as a significant contributor to lunar
8
Figure 1.2: Europa Clipper Missions, credits: JPL
water. Third, we will discuss a newly proposed mechanism involving deep dielectric charging in
the permanently shadowed regions. A short discussion of lunar water transport will be provided
to understand how the formation mechanisms affect the exosphere of the moon. Lastly, we will
explore recent hypervelocity impact experiments and modeling efforts aimed at enhancing our
understanding for future icy moon exploration missions.
1.2.1 Solar Wind Implantation
Numerous laboratory experiments have been conducted to investigate solar wind implantation.
However, various conclusions are drawn based on different experimental conditions and samples.
A summary of the experiments and their conditions is presented in Table 1.1. Schaible and Baragi-
ola [23], Ichimura et al. [21], Burke et al. [22], McLain et al. [24] show that no water molecules are
detected after irradiation and the implantation only contribute to hydroxyl groups, but Managadze
et al. [42], Bradley et al. [43], Zeng et al. [44] found that water molecules are formed after the irra-
diation. While most of the experimental results prove that solar wind hydrogen at least contributes
to the formation of hydroxyl, Burke et al. [22] did not find any significant increase of OH/H
2
O
in their experiment, indicating that implantation itself is not able to generate hydroxyl nor water
molecules.
9
Reference Material Implanted ions E
imp
E
imp
E
imp
Burke et al. [22] Terrestrial minerals H
+
1–100 keV
Managadze et al. [42]
1.SiO
2
2. Olivine
D
2
+
3 keV
Ichimura et al. [21]
1. Highlands Sample [62241]
2. Mare Sample [70051]
H
+
/D
2
+
1.1 keV
Schaible and Baragiola [23]
1. Amorphous SiO
2
2. Olivine
H
+
2–10 keV
Crandall et al. [45] Olivine D
2
+
2.5 keV
Chrbolkov´ a et al. [46]
1.Olivine
2.Pyroxene
H
+
, He
+
, Ar
+
5–40 keV
McLain et al. [24]
1. Apollo 17 [78421]
2. Crushed fused silica
H
+
2
2 keV
Tang et al. [47]
1.Olivine
2.Pyroxene
3.Plagioclase
4.V olcanic glass
H
+
7 keV
Zeng et al. [44] Plagioclase H
+
5 keV
Nakauchi et al. [48] Serpentine and Saponite H
+
2
10 keV
Table 1.1: Summary of Previous Experimental Studies on Solar Wind Implantation
10
As shown in the table, the conflicting results and conclusions are mainly due to the energy of the
beam used in the experiment. To simulate solar wind plasma conditions, most of the experiments
used energy equivalent to or slightly above 1 keV , but some of them were limited by the instrument
and used different energy. However, previous studies have shown that irradiation is very sensitive
to energy. Anders and Urbassek [49] found that the energy associated with the particles will
heat up sample locally the moment the particles collide with the surface atoms. Remote sensing
also provides evidence of that. The diurnal change [32] of water molecules reveals that water
is thermally unstable even with the temperature change between daytime and nighttime. Different
energies of the beam could thermally release water molecules with different desorption rates, which
could alter the results.
While experiments can qualitatively simulate the interactions of solar wind particles and the
lunar surface, some limitations remain. First, all the experiments provide the fluence of the beam
and convert it to equivalent years of implantation considering solar wind flux, but few of them
notice the difference of flux . Indeed, to simulate the flux of solar wind particles would require
years of experiment, which is impossible. However, the flux might actually be a critical condition
to be considered. On the lunar surface, the implantation process is coupled with cooling, especially
in high latitude areas. A high flux particle beam is very likely to accumulate energy on the surface
which means the beam will heat the surface without cooling. Similarly to high energy particles, the
water desorption rate due to unnecessary heating under laboratory conditions might be significantly
higher.
Theoretical studies have also tried to understand solar wind implantation. Stopping and Range
of Ions in Matter (SRIM)[50] is the most frequently used model to determine the implantation
depth of irradiation. However, with a minimal chemical model in it, one cannot tell the physical
form of the implanted ions. For instance, whether the implanted hydrogen exists as single atoms
or turned into – OH or even H
2
O is unknown, especially for – OH and H
2
O, which is also a
question for the observation side. The remote sensing observation of lunar water has a long-
standing question that the spectral absorption around 2.8–3.0µm indicates both – OH and H
2
O
11
and it’s hard to distinguish between them. Until 6µm detection, which is the vibration band for
H
2
O alone by the Stratospheric Observatory for Infrared Astronomy (SOFIA) [19], the existence of
pure water molecules are confirmed. Nevertheless, it is still hard to tell the ratio between – OH and
H
2
O and find out the exact outcome of solar wind implantation. This is critical to understanding the
hydrogen cycle on the lunar surface as well as collecting hydrogen for ISRU. Also, as more solar
wind particles are implanted, the surface will become “mature,” acting differently from the “fresh”
surface. This dynamic process with a change of maturity was not considered by experiments and
SRIM simulation.
The detailed process of solar wind implantation could reveal more information about the hydra-
tion on the lunar surface. This is the first step to understand the water and hydroxyl cycle induced
by the moon’s space environment. As discussed in Ichimura et al. [21], the implantation is a dy-
namic process [21]. The amount of – OH will reach an equilibrium state or saturation state during
the implantation of solar wind protons, indicating that the formation and the loss of – OH occur si-
multaneously. Hydroxyl formed on the surface can be turned into water molecules during extreme
space weather events like micrometeoroid impact. After the impact, most hydroxyl groups will
become water molecules either gardened to a deeper depth or released from the surface, leaving a
clean surface with minimal hydroxyl left. How long it takes for the surface to be saturated again,
which is still yet unknown, is essential for understanding the contribution of solar wind to water
formation.
1.2.2 Micrometeoroid Impact Generated Water
The contribution of micrometeoroid impact to lunar water formation is mainly due to the tempera-
ture rise after the impact. Zhu et al. [27] designed an experiment to prove this. They first exposed
olivine to a 5-keV D
2
+
to simulate solar wind implantation. No water molecules are detected at
this step. After that, they exposed the irradiated sample to a pulsed infrared CO
2
laser to simulate
micrometeoroid impact. The laser can heat the sample locally to 1400 K and trigger the recom-
binative desorption process. Finally, they designed a temperature-programmed-desorption (TPD)
12
experiment to liberate potential trapped water inside the regolith. Secondary electron images of
the irradiated samples show that pits and lids are formed after the TPD experiments. In compar-
ison, they did not detect pits and lids on the original olivine or samples only irradiated by ion or
laser. The pits and lids are signs of molecules or gases once trapped beneath the surface that are
desorbed rapidly. Combined with the m/Z = 20 (D
2
O
+
) signal found by a mass spectrometer,
they believed that micrometeoroid impact could create a significant amount of water molecules. A
similar paper by Zhu et al. [51] also shows that micrometeoroid impact can provide re-generative
water molecules on the asteroid surface.
The experiment provides strong evidence that micrometeoroid impact is able to generate water
molecules on the lunar surface. However, on the other hand, the heat generated by impact can also
liberate water molecules, leading to the loss of water content on the lunar surface. For instance,
Benna et al. [31] show that by analyzing data from LADEE, strong water release from the surface
is associated with meteoroid streams events. They concluded that the moon is losing water due to
the impact. Impacts of comets deliver water to the surface, but the strong energy during the impact
will evaporate and release a significant amount of water to the exosphere or to the space [52, 53].
The comprehensive understanding of lunar water retention and its connection to micromete-
oroid impacts necessitates a detailed investigation into the intricacies of the impact process. Nu-
merous parameters influence the outcomes of these impacts. On the impactor’s side, both mass and
impact velocity magnitude determine the kinetic energy, which subsequently converts to thermal
energy upon collision.
The impact velocity distribution of micrometeoroid is described in [54]:
f
m
(v
m
)=κ
v
m
q
v
2
m
− v
2
mEe
+ v
2
Ee
3
e
− γ
√
v
2
m
− v
2
mEe
+v
2
Ee
(1.1)
where v
m
is the velocity of the impactor, v
mEe
is the escape velocity of the moon and v
Ee
is the
escape velocity of earth. After fitting over 2 × 10
4
meteors data[55], the constants κ and γ are
13
chosen as 3.81 and 0.247 respectively. The distribution is plotted in Figure. 1.3 which shows that
the velocity is concentrated between 4 and 20 km/s with a focus at 12 km/s.
Figure 1.3: Distribution of impact velocity of micrometeoroid impact on the moon
The impact angle i of the impactor ranges from 0
◦ to 90
◦ . Shoemaker [56] shows that assuming
the moon as a spherical body, the probability density of an object impacting the surface with
incident angle i is:
dP= 2sinicosidi= 2sin2idi. (1.2)
This shows that i= 45
◦ has the highest probability, a finding which holds true on a global scale.
However, when applying this distribution, one must take into account the size of the impactor. For
large impactors, such as meteoroids or comets colliding with flat lunar regions, this distribution is
effective. Yet, when the target is situated on a crater wall, the distribution might be shifted by the
tilt angle of the wall. This consideration is also crucial for smaller impactors like micrometeoroids,
which measure in the micrometre scale or even smaller. The roughness of the surface upon im-
pact also needs to be factored in, as local surface roughness may shift the distribution. Bandfield
14
et al. [57] calculated surface roughness using the Thermal Infrared (TIR) on the Lunar Recon-
naissance Orbiter (LRO). Numerous studies have explored shadowed regions and local micro cold
traps caused by surface roughness, but few have examined their effects on micrometeoroid impact.
Numerous methods exist for understanding hypervelocity impact, both experimentally and nu-
merically. A variety of studies have leveraged laboratory experiments [58, 59, 60] and macro-
scopic simulation models, such as Smooth Particle Hydrodynamics (SPH) [61, 62], to simulate the
process of micrometeoroid impact. However, these macroscopic simulation models fall short in
simultaneously resolving chemical reactions and mechanical collisions. Current experimental lim-
itations make precise measurements of water generation and retention due to hypervelocity impact
unfeasible, as the induced chemical reactions occur on a timescale of nano- or sub-nano-seconds.
Holmstr¨ om et al. [63] utilized a classical MD model to simulate the deformation of silica glass
under hypervelocity impact. Their research extended the scope of impact studies to a nanometer
scale, fully resolving the details of deformation by observing atom displacement. This inspires fur-
ther investigation of micrometeoroid impacts on an atomic scale. At this scale, a chemical reaction
is characterized as a sequence of bond formations and breakages. Any alterations in surface shape,
porosity, and amorphous structure can also be meticulously captured.
In summary, the contribution of micrometeoroid impact could be largely affected by the pa-
rameters of impactors and target materials, but few of current studies has noticed that. The net
production of water after micrometeoroid impact needs to be studied on an atomic scale. With
the help of MD, we can ask and answer more questions in detail about the impact process. For
instance, how much energy is turned into thermal energy through inelastic collision for the water
formation process? How do the fragments from impact vary with impact parameters, and where
do all the fragments go?
15
1.2.3 Deep Dielectric Charging and Breakdown
There have been extensive studies of plasma charging of the lunar surface (see, for example, [64,
65, 66, 67, 68, 69, 70] and references therein). Due to its relatively low average energy (10–
10
3
eV), the solar wind plasma interacts mostly with the surface, causing surface charging. While
the solar wind protons typically penetrate the surface within a depth of dozens of nanometers (nm)
[50], the much more energetic particles from solar flares or coronal mass ejections (10
6
–10
10
eV),
i.e., solar energetic particles (SEP) (ions and electrons), and galactic cosmic rays (GCR) (10
8
–
10
20
eV) can penetrate further beneath the surface to a depth of a few millimetres (mm).
The charges deposited by SEP and GCR particles cause charging in the subsurface region,
i.e., deep dielectric charging. It is well established that the enhanced flux of SEPs during a space
weather event can deposit a significant amount of charges to generate a strong, localized electric
field in dielectric materials such as SiO
2
[50]. If the electric field strength exceeds a threshold
value in the regolith, dielectric breakdown will occur.
The study of deep dielectric charging caught attention because of the breakdown and arcing
events in spacecrafts [71, 72]. Later on, Lemelle et al. [73] show that deep dielectric charging
is possible to lead to dielectric breakdown and then cause space weathering effects on olivine.
This indicates that dielectric breakdown may also occur on airless bodies. A series of studies of
Jordan [74, 29, 1, 75, 76, 77] analyze the dielectric properties of lunar regolith and concluded that
dielectric breakdown occurs on lunar regolith as an energetic event and may occur at the same rate
as micrometeoroid impact.
For dielectric materials, the time scale for the charge to be dissipated is:
τ =ε/σ
c
(1.3)
whereε is the the permittivity andσ
c
is the conductivity of the material. The dielectric constant k of
lunar regolith within the temperature range of lunar regolith is around 2 [78]. Then the permittivity
16
isε≈ 2ε
0
whereε
0
= 8.85× 10
− 12
F· m
− 1
. The conductivity of lunar regolith changes significantly
with temperature:
σ
c
=σ
c0
e
αT
(1.4)
where σ
c0
= 6× 10
− 18
S/m and α = 0.0237 K
− 1
. As a result, the relationship between the dis-
charge time scale and the temperature isτ =
2ε
0
σ
c0
e
αT
and it is plotted in Fig. 1.4
Figure 1.4: Timescale of discharge on lunar surface related to temperature [1]
The timescale is in the order of days when the temperature of the regolith is low. On the
lunar surface, especially at PSRs, the temperature could be as low as 40 K [79]. Interestingly, the
PSRs, which are believed to be rich in water, have a larger possibility to experience deep dielectric
charging and dielectric breakdown. Based on the lunar surface temperature map, Jordan et al. [1]
estimated the spatial distribution of the discharge timescale based on the temperature map from
Paige et al. [80]. The distribution of discharge time scale (Figure 3 in [1]) matches the distribution
of water at the north and south pole. This motivates us to wonder if the dielectric breakdown events
contribute to the formation and retention of lunar water.
Jordan [76] estimated that deep dielectric charging caused by a typical SEP event could estab-
lish a localized electric field in the lunar regolith on the order of 10
6
to 10
7
V/m, a value exceeding
17
the breakdown threshold of silica. Recently, Shusterman et al. [81] found laboratory evidence of
dielectric breakdown with high electron flux irradiated olivine using lunar conditions. The break-
down creates dendritic channels, which are plasma channels during the breakdown. Amorphous
rims, pits which are typical signs of space weathering, are also detected by SEM. More experimen-
tal studies on the chemical alternation are planned to be performed in the future.
1.2.4 Volatile Transport Model: Exosphere Modeling
Watson, Murray and Brown[8, 7] proposed that the existence of the exosphere help transport many
free water molecules to cold traps. This section reviews recent studies of the dynamics of the re-
leased particles from the lunar surface. As mentioned in the previous section, most of the mecha-
nisms that contribute to water formation might also lead to the loss of water. Those water molecules
are either migrated to other locations on the lunar surface by ballistic trajectories, released to the
lunar exosphere or escaped to space. The interactions between the exosphere and surface might
shape the distribution of volatiles on the lunar surface.
For those released particles that follow ballistic trajectories, the distance of the trajectory is :
D=
2v
∥
v
⊥
g
moon
(1.5)
and the flight time of the molecules is:
τ =
2v
⊥
g
moon
(1.6)
Most of the previous studies [82, 83] assumed the released molecules are thermally balanced
with the surface. The velocity distribution function is then is Maxwellian distribution:
f(v)=
r
m
2πkT
e
− mv
2
2kT
(1.7)
where T is the local temperature. Combining Eq. 1.5–1.7 and temperature map of lunar surface,
one can derive the spatial distribution of water after ballistic trajectories. Qualitatively, warm
18
regions lose more water, and cold regions lose less water. From the point of view of receiving water,
cold regions receive water from both cold and warm regions, while warm regions only receive
water from other warm regions. This makes water concentrated in cold regions. Schorghofer [84]
used a random-walk method to model the dynamics of ballistic trajectories as Markov processes.
He then found that the results can be well-fitted to a diffusion process. A continuum model is
derived to find the evolution and steady-state distribution of water concentration.
While the model works well qualitatively, some approximations might lead to divergence—for
instance, the velocity distribution of released particles. Farrell et al. [85] implemented a similar
Monte Carlo method but used two different velocity distribution functions based on the processes
that cause the release. Micrometeoroid impact vaporization follows a Maxwellian distribution
for velocity, while solar wind sputtering exhibits a different distribution known as the Sigmund-
Thompson distribution [86], characterized by a longer tail. This model makes it possible to quan-
titatively compare the contribution of solar wind sputtering and micrometeoroid impact. However,
if the ejected molecules are not thermally mixed with the surface, then the Maxwellian distribution
might not be a good assumption. The atomic-scale model might provide more information by in-
cluding different parameters such as impact angles, surface conditions (roughness, amorphization,
porosity) and solar wind conditions.
1.2.5 Hypervelocity Ice Impact: Exploration of Icy Moons
Over the past few years, the University of Colorado Boulder’s hypervelocity dust accelerator has
been leveraged extensively to study the impact of dust. A key advancement was recently made in
the study of hypervelocity impacts and their effects on extraterrestrial cryo-environments, as doc-
umented in Nelson [87]. With the development and implementation of an experimental apparatus
replicating the extreme conditions of space, Nelson [87] managed to study the impacts of microm-
eteoroids on various cryogenic materials under controlled conditions. This innovative approach
has provided valuable insights into the processes and outcomes of micrometeoroid collisions with
cryogenic surfaces, like those found on icy moons and other celestial bodies. This study’s findings
19
significantly contribute to our broader understanding of hypervelocity impacts in space, and their
potential implications on the formation and evolution of extraterrestrial icy bodies.
Recent studies have started exploring hypervelocity ice impacts to support future missions to
icy moons. In one such study, Ulibarri et al. [88] delved into the detection of the amino acid his-
tidine and its breakup products in spectra obtained from hypervelocity impact experiments on ice
samples. The authors employed a combination of experimental data and computational models to
detect and analyze the spectral signatures of histidine and its fragments. Their findings confirm the
detectability of histidine in spectra derived from hypervelocity ice impacts. This provides pivotal
insights into the possible existence of amino acids in extraterrestrial icy bodies and their potential
survival in extreme impact conditions. The study additionally contributes to our comprehension of
the astrochemical processes that potentially facilitate the formation of complex organic molecules
in space.
Miller et al. [89] centered their study on the mass spectral characterization of ice grain ana-
logues, akin to those found on Enceladus - one of Saturn’s icy moons, after hypervelocity impacts.
By performing a series of impact experiments and examining the consequent mass spectra, the au-
thors offer valuable insights into the processes and outcomes of hypervelocity collisions involving
icy grains. This study enhances our understanding of the potential ramifications of such impacts
on the geophysical and astrochemical evolution of Enceladus, and other celestial bodies of similar
nature. Furthermore, the findings emphasize the necessity of exploring hypervelocity impacts on
icy grains to achieve a more comprehensive understanding of the formation and evolution of icy
celestial bodies in the Solar System.
In addition to experimental studies, theoretical modeling has also delivered valuable insights
into this field. Jaramillo-Botero et al. [90] centered their research on the process of hypervelocity
sampling for detecting biosignatures during space missions. The research explores the challenges
and opportunities tied to this approach, and its potential to identify extraterrestrial life. The au-
thors, by analyzing the technical aspects, instrumentation, and mission design, provide valuable
insights into the feasibility and effectiveness of hypervelocity sampling for biosignature detection
20
in extraterrestrial environments. This study emphasizes the need for advancing our understand-
ing of hypervelocity sampling techniques, which holds significant promise in unveiling evidence
of life beyond Earth. Therefore, it contributes to the broader scientific comprehension of life’s
origins and distribution in the universe.
1.3 Motivations and Objectives
As we continue to observe and investigate lunar volatiles, more fundamental questions arise. For
example, among all the possible water formation mechanisms, which one contributes the most
to the observed water on the lunar surface? How do the physical properties and forms of lunar
volatiles affect their retention, loss, and transport processes on the moon? While the combination
of observational and experimental studies has yielded many insights into these questions, there is
still much to learn. In particular, theoretical studies at the atomic scale can provide valuable infor-
mation that is beyond the reach of experiments. The goal of this dissertation is to investigate the
fundamental physical properties of lunar volatiles at the atomic scale using first-principle meth-
ods. We will model chemical reactions and geophysical processes that are relevant to lunar volatile
behavior. In particular, we will focus on two important processes: solar wind implantation and
micrometeoroid impact. In addition, we will investigate any possible chemical reactions process
during extreme space weather conditions which could lead to dielectric breakdown.
Although previous studies have examined the effects of solar wind implantation on lunar
volatiles, many geophysical conditions have been overlooked due to instrumental limitations.
Atomic-scale simulations can provide a more comprehensive understanding of the impact of these
conditions on the behavior of lunar volatiles. We will also simulate micrometeoroid impact us-
ing the reactive force field (ReaxFF) MD model, which can resolve both chemical reactions and
21
dynamics of molecules. By comparing the water abundance before and after impact, we can de-
termine whether impacts contribute to water formation or cause the loss of water. Mostly impor-
tantly, we will compare the timescale between solar wind implantation and micrometeoroid impact
to quantify the efficiency of H delivery by solar wind.
To broaden the scope of our study beyond lunar volatiles, we will also investigate hypervelocity
ice impact in the solar system. Using atomic-scale simulations, we will gain a better understanding
of the physical processes and chemical reactions that occur during micrometeoroid impact on ice.
Specifically, we will use first-principle methods to simulate the inter-molecular and inter-atomic
fragmentation processes that occur during hypervelocity ice impact. This part of the study aims
to provide a theoretical basis for the Surface Dust Analyzer (SUDA)[91] on the Europa Clipper
mission as well as future missions that aims to explore icy grains in our solar system. SUDA will
use ice grain speed probes with a wide range of velocity magnitudes and impact angles to study
the surface and subsurface of Europa, one of Jupiter’s moons.
Furthermore, our investigation of hypervelocity ice impact will also have implications for the
transport of individual molecules and clusters in the exosphere of icy bodies in the solar system. By
simulating the inter-molecular and inter-atomic fragmentation processes that occur during hyper-
velocity ice impact, we can gain insights into the mechanisms that govern the transport of volatiles
in the exosphere. Building on our simulations and experimental data, we will develop an improved
impact-generated vapor model and compare it to previous classical models. This model will be
able to better predict the amount and distribution of vapor generated by impact events and was
bounded by gravity on icy bodies in the solar system. The results of this study will not only im-
prove our understanding of the behavior of volatiles on the moon and in the solar system but will
also have practical applications for future space missions. By providing a more accurate model of
impact-generated vapor, we can better predict and interpret data collected by instruments such as
mass spectrometers and ion probes.
The objectives and contribution of this dissertation is summarized below:
22
• Atomic-scale simulations are used to investigate the contribution of solar wind implantation
to water formation on the lunar surface.
• We then investigates the chemical reactions that lead to the formation of volatiles on lunar
polar shadowed regions (PSRs) during extreme space weather conditions that could possible
lead to dielectric breakdown.
• We implement physical-chemical models using molecular dynamics simulations to investi-
gate the chemical reactions together with dynamics during the micrometeoroid impact pro-
cess.
• We employ machine learning techniques to identify the complex velocity distribution func-
tion of impact-generated vapor, providing a more detailed understanding of the behavior of
volatiles in the exosphere of icy bodies.
• We explore the two-stage fragmentation process of hypervelocity ice impact and its im-
plications for the Europa Clipper mission. By simulating inter-molecular and inter-atomic
fragmentation processes, we aim to provide a theoretical basis for the surface dust analyzer
(SUDA) on the Europa Clipper Mission.
• We develop a comprehensive model to understand the effect of clusters on the surface-
bounded exosphere of icy bodies induced by impact. By accounting for the behavior of
individual molecules and clusters, we can improve our understanding of the transport of
volatiles in the exosphere.
23
Chapter 2
Methods and Models
This chapter presents the models used in this dissertation, primarily leaning on molecular dynamics
simulation. We used a range of interaction potentials, which will be discussed in detail. For
a deeper analysis of the results, a Maxwellian Mixture Model (MMM) was constructed. This
model based on the Gaussian Mixture Model (GMM) and is designed to decompose different
sources of water molecules released during a micrometeoroid impact event (Chapter 5), and the
vapor composed of both molecules and clusters in a hypervelocity ice impact (Chapter 8). We
delineate how the optimization process of MMM differs from the conventional GMM and provide
a numerical test to verify its accuracy.
2.1 Molecular Dynamics Simulation
2.1.1 Overview
Molecular dynamics simulation is a computational technique that allows researchers to study the
behavior of molecules and materials at the atomic and molecular scale. It involves numerically
integrating Newton’s equations of motion to simulate the trajectories of individual particles within
a system. This simulation technique provides valuable insight into the thermodynamic and kinetic
properties of materials and their response to external conditions such as temperature, pressure,
and electric fields. Molecular dynamics simulations are widely used in various fields, including
24
chemistry, materials science, and biophysics. They offer a powerful tool for studying the behavior
of complex systems and predicting properties, making them an essential tool for the design of
new materials and drugs. In materials science, for example, molecular dynamics simulations are
used to investigate the mechanical, thermal, and electrical properties of materials, as well as their
responses to external stresses and deformations.
Molecular dynamics simulation starts with the input of atoms’ positions⃗ r
i
=(x
i
,y
i
,z
i
). These
positions are usually derived from the crystal structure of the materials or from stable molecular
structures. Subsequently, velocity and acceleration are calculated as the derivatives of position and
velocity:
⃗ v
i
(t)=
˙
⃗ r
i
(t)=
d⃗ r
dt
≡ lim
δt→0
⃗ r
i
(t+δt)− ⃗ r
i
(t)
δt
(2.1)
⃗ a
i
(t)=
¨
⃗ r
i
(t)=
d
2
⃗ r
dt
2
=
d⃗ v
i
dt
≡ lim
δt→0
⃗ v
i
(t+δt)− ⃗ v
i
(t)
δt
(2.2)
The numerical integration of Newtonian equations above is achieved by Velocity Verlet Algo-
rithm. By defining timestep δt, the position and velocity are updated step by step:
(⃗ r
i
(0),⃗ v
i
(0))7→(⃗ r
i
(δt),⃗ v
i
(δt))7→(⃗ r
i
(2δt),⃗ v
i
(2δt))7→··· (2.3)
The velocity-verlet algorithm proivdes the following form for integration
⃗ r
i
(t+∆)=⃗ r
i
(t)+⃗ v
i
(t)∆+
1
2
⃗ a
i
(t)∆
2
+ O
∆
4
⃗ v
i
(t+∆)=⃗ v
i
(t)+
⃗ a
i
(t)+⃗ a
i
(t+∆)
2
∆+ O
∆
3
(2.4)
The pseudocode for velocity-verlet algorithm is shown in Algorithm. 1
25
Algorithm 1 Velocity Verlet Algorithm
1: procedure VELVERLET((
⃗
r
N
,
⃗
v
N
) ▷ Positions and velocities of N atoms as input
2:
⃗
a
N
← ⃗
r
N
3: while t < T do ▷ Integration from t = 0 to t = T
4: ⃗ v
i
← ⃗ v
i
+⃗ a
i
δt
2
5: ⃗ r
i
← ⃗ r
i
+⃗ v
i
δt
6:
⃗
a
N
← ⃗
r
N
7: ⃗ v
i
← ⃗ v
i
+⃗ a
i
δt
2
8: end while
9: end procedure
2.1.2 Boundary Conditions
Periodic boundary conditions (PBC) are commonly used to simulate bulk materials with a small
number of atoms. In this approach, the entire MD box is replicated in the assigned dimensions, and
the atoms located near the edges of the box interact with atoms in the replicated images. Equation.
2.5 shows the position transformation when implementing PBC. If an atom’s coordinate becomes
larger than the MD simulation box size, the box size should be subtracted from its coordinate.
Similarly, if the coordinate of an atom becomes less than zero, the MD simulation box length
should be added to its position. In other words, if an atom moves out of the box, its periodic image
enters the simulation box from the opposite side:
x
i
← x
i
− SignR
L
x
2
,x
i
− SignR
L
x
2
,x
i
− L
x
y
i
← y
i
− SignR
L
y
2
,y
i
− SignR
L
y
2
,y
i
− L
y
z
i
← z
i
− SignR
L
z
2
,z
i
− SignR
L
z
2
,y
i
− L
z
(2.5)
where
SignR
L
x
2
,x
i
=
L
x
2
x
i
> 0
− L
x
2
x
i
≤ 0
(2.6)
26
2.2 Interacting Potentials
2.2.1 Reactive Molecular Dynamics
The simulations of this study applies the recently developed reactive force field (ReaxFF), a first-
principle informed force field that models the bond strength in chemical reactions [92]. The bond
energy is explicitly modeled by the inter-atomic potentials. The chemical reactions are modeled
by analyzing the bond formation and bond breaking process. The application of the ReaxFF sig-
nificantly reduces the computational cost while retaining an accurate description of the energy
landscape obtained from quantum mechanics calculations. The potentials included in the ReaxFF
MD simulation model is shown in Eq(1). The force field used in the simulation is developed by
[93] and has been tested for the silica-water system.
E
ReaxFF
({⃗ r
i j
},{⃗ r
i jk
},{⃗ r
i jkl
},{q
i
},{BO
i j
})= E
bond
+ E
l p
+ E
over
+ E
under
+
E
val
+ E
pen
+ E
coa
+ E
tors
+ E
con j
+ E
hbond
+ E
vdWaals
+ E
Coulomb
(2.7)
where the total energy E
ReaxFF
is a function of the inter-atomic distance between an atomic pair,
⃗ r
i j
, triplets,⃗ r
i jk
, and quadruplets,⃗ r
i jkl
, as well as atomic charges q
i
and bond orders BO
i j
be-
tween an atomic pair. The valence interactions include the bonding energy E
bond
, lone-pair energy
E
l p
, overcoordination energy E
over
, undercoordination energy E
under
, valence-angle energy E
val
,
penalty energy E
pen
, 3-body conjugation energy E
coa
, torsion-angle energy E
tors
, 4-body conjuga-
tion energy E
con j
, and hydrogen bonding energy E
hbond
. The noncovalent interactions comprise
van der Waals energy E
vdWaals
and Coulomb energy E
Coulomb
, which are screened by a taper func-
tion. The simulations of this paper utilize a fully parallel ReaxFF MD code, the RXMD. A detailed
description of the code and the model can be found in Nomura et al. [94].
27
2.2.2 Ziegler-Biersack-Littmark and Electronic Stopping Energy
We investigate solar wind implantation on the lunar surface and volatile formation using MD sim-
ulation. When the energy of the particles is too large, an additional repulsive force needs to be con-
sidered in addition to the one in reactive molecular dynamics (RMD). For instance, the irradiation
simulation requires the incorporation of two specific potentials to gain a more detailed description
of the interaction. To resolve both the chemical reactions and the physical interactions arising
from high energy impact during implantation, we apply the Large-scale Atomic/Molecular Mas-
sively Parallel Simulator (LAMMPS) [95]. This utilizes the reactive molecular dynamic (RMD)
model [92], the ZBL potential [96], and electronic stopping energy [97, 98].
The ZBL potential and electronic stopping energy is included to simulate high energy particle
impact and transport. The ZBL term is [96]:
E
ZBL
i j
=
1
4πε
0
Z
i
Z
j
e
2
r
i j
φ
r
i j
/a
(2.8)
where e is the electron charge,ε
0
the electrical permittivity of vacuum, and Z the nuclear charge of
the atom. The parameters a=
0.46850
Z
0.23
i
+Z
0.23
j
and functionφ(x)= 0.18175e
− 3.19980x
+0.50986e
− 0.94229x
+
0.28022e
− 0.40290x
+ 0.02817e
− 0.20162x
are from [96]. The electronic stopping energy is given by:
⃗
F
i
=
⃗
F
0
i
− ⃗ v
i
∥⃗ v
i
∥
· S
e
(2.9)
where where
⃗
F
i
and
⃗
F
0
i
are the updated force and original force, electronic stopping energy depends
on the velocity and S
e
is the stopping coefficient calculated by SRIM[50].
2.3 Machine Learning Algorithm: Maxwellian Mixture Model
2.3.1 Derivation of Maxwellian Mixture Model
We conducted a machine learning study of the molecules generated by micrometeoroid impact.
Machine learning offered insightful findings based on the data from both atomic scale simulations
28
and planetary scale modeling of the exosphere. Our model is based on a conventional machine
learning algorithm known as the Gaussian Mixture Model (GMM).
The Gaussian Mixture Model (GMM) is a statistical method for density estimation and clus-
tering, representing a probability distribution as a weighted sum of Gaussian components. GMMs
are valuable for tasks like image segmentation, speech recognition, and anomaly detection, with
applications across finance, computer vision, and natural language processing. Here we apply this
model to the analysis of our data. The major task is to identify different components of distributions
from a mixed distribution. Identification includes the weights of each component and the param-
eters of each distribution. In our case, we assume the mixed distribution is a sum of two or more
Maxwellian distribution, thus the objective is to find the weights ω
i
and temperature T
i
of each
Maxwellian distribution. We substitute the Gaussian distribution with Maxwellian distribution and
performed several tests to validate the model.
The log-likelihood of the Gaussian Mixture Model is:
log p(X|θ)=
N
∑
n=1
log
K
∑
k=1
π
k
N (x
n
|µ
k
,Σ
k
)
!
(2.10)
where X is the set of observed data points, θ represents the set of parameters in the GMM,
N is the number of data points, K is the number of Gaussian components in the mixture model,
π
k
is the mixing coefficient of the k-th component with ∑
K
k=1
π
k
= 1, andN (x
n
|µ
k
,Σ
k
) is the
multivariate Gaussian probability density function with mean µ
k
and covariance matrixΣ
k
. When
switching from the Gaussian distribution to Maxwellian distribution, several gradient decent fac-
tors need to be changed during the expectation-maximization(EM) process. As the expectation
part of EM remains the same except for substituting the distribution, we will focus the derivation
on the maximization process.
The M steps starts by maximizing Eq. 2.10 withN (x
n
|µ
k
,Σ
k
) replaced byM(x
n
|σ
k
) ,
whereM(x
n
|σ
k
) has the form of:
M(v)=
1
2πσ
3/2
4πv
2
e
− v
2
2σ
(2.11)
29
Here we used a latent variable z
n
to estimate the classification of each clusters and q
n
(t) is the
distribution of z
n
calculated in the estimation step:
q
(t)
n
(z
n
= k)= p
z
n
= k| x
n
;θ
(t)
∝ p
x
n
,z
n
= k;θ
(t)
= p
z
n
= k;θ
(t)
p
x
n
| z
n
= k;θ
(t)
=ω
(t)
k
M
x
n
|σ
(t)
k
(2.12)
The maximization of log-likelihood is:
argmax
θ
Q
θ,θ
(t)
= argmax
θ
N
∑
n=1
E
z
n
∼ q
(t)
n
[ln p(x
n
,z
n
;θ)]
= argmax
θ
N
∑
n=1
E
z
n
∼ q
(t)
n
[ln p(z
n
;θ)+ ln p(x
n
| z
n
;θ)]
= argmax
{ω
k
,µ
k
,Σ
k
}
N
∑
n=1
K
∑
k=1
γ
nk
(lnω
k
+ lnM(x
n
|σ
k
))
(2.13)
To find the ω
i
, we take the derivative of the equation above respect toω
i
:
argmax
ω
N
∑
n=1
K
∑
k=1
γ
nk
lnω
k
(2.14)
and get
ω
k
=
∑
n
γ
nk
N
(2.15)
The optimalσ
k
can be obtained by taking the derivative w.r.tσ
k
:
argmax
σ
k
N
∑
n=1
γ
nk
lnM(x
n
|σ
k
)= argmax
µ
k
,σ
k
∑
n
γ
nk
3
2
ln
1
σ
k
− (x
n
)
2
2σ
2
k
!
. (2.16)
which leads to:
∑
n
γ
nk
− 3
2σ
k
+
x
n
x
T
n
σ
3
k
!
= 0 (2.17)
30
σ
2
k
=
2
3∑
n
γ
nk
∑
n
γ
nk
x
n
x
T
n
(2.18)
The result is very similar to the standard GMM optimal σ
k
taking µ
k
= 0 with an additional
factor of
2
3
due to the
1
2πσ
3/2
term in Maxwellian distribution function. The pseudocode is shown
in Algorithm.2.
Algorithm 2 EM for Maxwellian Mixture Model
1: procedure MMM(⃗ x
n
,θ) ▷ Raw data and parameters
2: Initializeω
k
,σ
k
▷ for each k∈[K]
3: while not converged do
4: updateγ
nk
= p(z
n
= k| x
n
)∝ω
k
N(x
n
|µ
k
,Σ
k
)
5: updateω
k
=
∑
n
γ
nk
N
6: updateσ
2
k
=
2
3∑
n
γ
nk
∑
n
γ
nk
x
n
x
T
n
7: end while
8: end procedure
2.3.2 Numerical Validation
We assumed two groups of molecules that have two different Maxwellian distributions:
f
1
(v)=
m
2πkT
1
3/2
4πv
2
e
− mv
2
2kT
1
(2.19)
f
2
(v)=
m
2πkT
2
3/2
4πv
2
e
− mv
2
2kT
2
(2.20)
where T
1
and T
2
are the temperature of each group respectively.
A mixture of those two groups of molecules is formed by adding two weight factorsω
1
andω
2
which represent the portion of each groups. Once f
3
(v) is calculated, acceptance-rejection method
is used to generate random data that follows the distribution of f
s
(v).
f
s
(v)=ω
1
m
2πkT
1
3/2
4πv
2
e
− mv
2
2kT
1
+ω
2
m
2πkT
2
3/2
4πv
2
e
− mv
2
2kT
2 (2.21)
31
f
1
(v), f
2
(v) and f
s
(v) are plotted in Figure. 2.1
To validate the accuracy of the Maxwellian Mixture model, we generated a set of random data
following f
s
(v), which is a mixture of f
1
(v) and f
2
(v), with w
1
and w
2
serving as the weights
(as defined in Equation 1). Figure 2.1 plots the analytical solutions of f
1
(v), f
2
(v), and f
s
(v), in
addition to the random data following f
s
(v). Meanwhile, Figure 2.2 displays the predicted values
of w
i
and T
i
from the machine learning algorithm.
By comparing the predicted w
i
and T
i
values to the true values of w
1
, w
2
, T
1
, and T
2
, we found
that the Maxwellian Mixture model accurately predicted the weights and temperatures of the two
velocity distributions. These results demonstrate that the machine learning algorithm we used to
predict the weights and temperatures of the Maxwellian Mixture model is reliable and effective.
Figure 2.1: Velocity distribution of two groups of molecules with T
1
(in red) and T
2
(in blue) and
the mixture of the two groups (in purple). Histogram of random data with a distribution of f
s
(v)
obtained by acceptance-rejection method is shown in blue bins
32
Figure 2.2: Red dot: ω
1
andσ
1
, blue dot: ω
2
andσ
2
, green diamonds are two groups ofω andσ
identified by Maxwellian Mixture Model.
33
Chapter 3
Solar Wind Implantation and Its Contribution to Lunar
OH/H
2
O
In this chapter, we carry out reactive molecular dynamics simulations to investigate solar wind
implantation on the lunar surface. This study resolves both the chemical reactions and physical
interactions of implantation, analyzes the effects from hydroxyl saturation, solar wind reflection,
and water molecule sputtering, and quantifies the contribution of solar wind proton implantation
to lunar water formation. The results show that, while solar wind implantation can lead to the
formation of some hydroxyl groups and water molecules, the contribution of the implantation
process itself is not significant enough to account for the observed lunar water content.
3.1 Motivation
The existence of OH/H
2
O has been confirmed by analysis of samples from the Apollo missions
[99] and recent remote sensing data [100, 15, 19, 101, 17]. In particular, the 3µm band by M
3
observation of OH/H
2
O signal [100, 101] and the 6µm band absorption by SOFIA. [19] provided
solid evidence of molecular water. It is well understood that solar wind implantation plays an
important role in the formation of OH/H
2
O. The implanted protons can interact with the oxygen
in lunar regolith to directly form hydroxyl groups [20] and contribute to the formation of water
34
molecules through recombinative desorption (RD) [26]. However, solar wind implantation typi-
cally cannot form a large quantity of water molecules directly because the surface temperature of
the moon is not high enough for RD to occur [102]. Other energetic mechanisms, such as microm-
eteoroid impact [27] or dielectric breakdown[103], are needed to provide the energy required for
water molecule formation.
The overall contribution of solar wind implantation to the formation of OH/H
2
O can be af-
fected by many factors. During solar wind implantation, the formation and loss of− OH occur
simultaneously [21]. The impact of solar wind particles may also release the water molecules
from lunar surface by sputtering. As micrometeoroid impacts and space weather induced dielec-
tric breakdown provide the energy for water formation reaction, the contribution of solar wind
implantation is also affected by the frequency of micrometeoroid impact or dielectric breakdown
events. After a micrometeoroid impact or dielectric breakdown event, most of the hydroxyl groups
are turned into water molecules which are subsequently either gardened to a deeper depth or re-
leased from the surface. Thus, the time it takes for the surface to become re-saturated by− OH is
also a critical factor in lunar water formation. Apart from the chemical reactions, the reflection of
solar wind particles by lunar surface [104, 105] reduces the incidence fluence and thus also plays a
role. Ion irradiation experiments [106, 107] showed that an extremely high reflection coefficient is
expected for small oblique incidence angle. The effects of solar wind reflection may be especially
important at the high latitude region where the oblique incidence angle is small.
Solar wind implantation has been investigated in numerous laboratory experiments. Many
experiments showed that no water molecules were formed after irradiation and concluded that
implantation only contribute to the formation of hydroxyl groups [23, 21, 22, 24] but a few showed
that water molecules were formed after the irradiation [42, 44]. In addition to ion irradiation
experiments, water formed by solar wind irradiation was found from the Apollo samples [43],
and− OH/H
2
O formed by solar wind irradiation was found in a sample returned from Itokawa
[108]. While most laboratory results showed that the solar wind proton at least contributes to
the formation of hydroxyl, Burke et al. [22] didn’t find any significant increase of OH/H
2
O in
35
their experiment and concluded that the implantation process by itself does not contribute to the
formation of either hydroxyl or water molecules. These conflicting conclusions are likely due to
the different experimental conditions. For instance, the amount of the water molecules formed in
an experiment can be sensitively influenced by the proton beam energy and flux used. Laboratory
experiments typically utilize proton beams with an equivalent energy of 1keV or higher and a
beam flux much larger than the actual solar wind flux in order to generate the equivalent fluence
within the experimental time [21]. However, using a high density flux in a short time period
can create a target surface temperature much higher than the actual lunar surface temperature
because the heat transfer rate in a laboratory environment is much smaller than that in a lunar
environment and there is not sufficient time to dissipate the heat generated by beam irradiation.
Anders and Urbassek [49] showed that the beam energy dissipated at the impact location may
lead to significant localized heating of the sample. This can cause any water molecules generated
during implantation to be thermally released. One notes that the significant diurnal change of
water content on the lunar surface also shows that water molecules are thermally unstable [32].
Most laboratory experiments also only considered normal incidence. Such a setup corresponds
to implantation at lower latitudes during local noontime. However, observations have shown that
water content changes significantly with latitude [101, 100, 32], and most of the water found on
the lunar surface are located in cold traps above 80
◦ [18]. The contribution of low incidence angle
implantation to lunar water formation is mostly unknown.
Solar wind implantation has also been investigated by theoretical modeling. Previous studies
have modeled the implantation depth due to physical collisions and the implantation products by
using the chemical reaction rate associated with assumed reaction pathways[109, 110, 111, 112].
For instance, SRIM (Stopping and Range of Ions in Matter) [50] is one of the most frequently used
model which uses binary collision to determine the implantation depth of irradiation. However,
SRIM does not contain a chemical reaction model, and thus cannot resolve the products of solar
wind implantation, such as determining whether the implanted proton exists as single atoms or
becomes− OH or H
2
O. Previous remote sensing observations of lunar water showed the spectral
36
absorption around 2.8− 3.0µm, indicating both− OH and H
2
O. The existence of water molecules
were confirmed only after the 6 µm detection by the Stratospheric Observatory for Infrared Astron-
omy (SOFIA) [19], However, the ratio between− OH and H
2
O is still under debate. Farrell et al.
[110] and Tucker et al. [111] used a Monte Carlo method to investigate the diffusion of implanted
hydrogen based on the activation energy barrier. Morrissey et al. [113] used reactive molecular
dynamics simulation to study the diffusion of hydrogen in silicates. Jones et al. [112] estimated
the production of− OH by implantation by using a kinetic chemical reaction rate. However, no
first-principle based models that resolve the chemical reactions under the realistic solar wind im-
plantation condition have been presented.
This study presents, to our knowledge, the first atomic scale modeling study of the solar wind
implantation process on lunar surface. The focus is on the implantation process in the permanently
shadowed regions (PSRs) where the solar wind flow is almost parallel to the surface. The modeling
study applies molecular dynamics (MD) simulation to resolve both the chemical reactions and
physical interactions of implantation, to dynamically track the time evolution of− OH and H
2
O
in an implantation process, and to quantify the contribution of solar wind implantation to the
formation of− OH/H
2
O triggered by micrometeoroid impacts. This study also investigates several
important aspects that were either missing or not addressed adequately in previous laboratory or
modeling studies, such as the effects from sputtering, reflection of solar wind particles, surface
temperature, and the− OH saturation time.
3.2 Formula and Simulation Setup
In this study, we consider the average solar wind condition with an average solar wind speed of
V
sw
∼ 400km/s, average electron temperature of T
e
∼ 10eV [114], and solar wind density n
p
∼ 0.01− 10 /cm
3
[115]. The solar wind is a mesothermal plasma and flows almost tangentially to
the surface in the lunar polar region. For a mesothermal plasma flowing tangetially to a surface, the
ions enter into the plasma sheath with a normal velocity component of the ion acoustic velocity,
37
C
s
=
p
T
e
/m
i
[116], where m
i
is the ion mass. Thus, the solar wind proton impingement flux at
the lunar polar region is
Γ
p
∼ n
p
C
s
(3.1)
where C
s
≃ 31km/s andΓ
p
∼ 3.1× 10
4
− 3.1× 10
7
/(cm
2
· s) for the solar wind conditions con-
sidered.
Figure 3.1 (a) shows the simulation setup. We model the lunar surface as a substrate of SiO
2
,
the major component of lunar regolith [117]. While the regolith composition also includes other
elements such as Al, Fe, Mg and Ti, the effects of those minor elements are not included in this
study due to the limitation of the force field used in the model. The size of the simulation domain
is 42.9× 42.9× 8000 Angstroms. The dimension of the regolith substrate is 42.9× 42.9× 129.6
Angstroms. The solar wind impinges lunar surface along the z direction. The periodic boundary
condition is applied to the domain boundary in the x and y direction. In the z direction, the domain
boundary is sufficiently far away from the substrate surface so to contain all the sputtered molecules
or reflected atoms generated in the simulation. At the start of the simulation, the temperature of
lunar surface is taken to be 40K, the typical temperature at PSRs.
For an impingement flux of Γ
p
∼ 3.1× 10
4
− 3.1× 10
7
/(cm
2
· s), a surface area of S =
42.9× 42.9
˚
A
2
receives on average about 1 proton per 10
5
− 10
8
s. Here, we shall refer one pro-
ton impingement as one implantation event. The simulation of each implantation event starts by
injecting a hydrogen atom toward the surface along the -z direction with a speed of C
s
≃ 31km/s.
The hydrogen atom is also assigned a tangential velocity component of V
sw
≃ 400km/s . The ini-
tial position of the the hydrogen atom is placed above the surface at a height of 20 Angstroms to
avoid any interactions of the hydrogen atoms and the surface before the implantation. The x and
y coordinates of the hydrogen atoms are randomly distributed to cover the entire x-y plane of the
domain. The time step of the simulation is set as 0.1fs so to resolve the dynamics of each atoms in
the simulation.
38
We find that the interaction between a 1keV H atom and SiO
2
surface is initially dominated
by effects from physical collisions. A high energy incident particle may sputter atoms from the
SiO
2
surface, and either be reflected by the repulsive force or become implanted. For an implanted
particle, as it has lost most of its impact energy, the interaction is dominated by electronic stopping
and chemical bonding. Test runs showed that the physical interaction dominated stage occurs
within the first 4000 steps for the parameters considered in this study. Hence, each implantation
event simulation is first run using ReaxFF, ZBL, and electronic stopping for 4000 time steps so
that both physical and chemical interactions between a 1keV H atom and SiO
2
surface can be well
described. If an incident particle is reflected from the surface, we stop the simulation. Otherwise,
we continue the simulation with the ZBL turned off to focus on chemical interactions caused by an
implanted particle. We note that the ReaxFF potential already contains a repulsive force term for
low energy impact. Thus, including the ZBL term, which is developed to model the reflection and
sputtering for high energy impact, for low energy implanted particles would have led to duplication
of some of the repulsive force effects. Especially in this study, the implanted H atoms are the major
sources of chemical reactions we are simulating. This process is run as a microcanonical ensemble
simulation (NVE simulation).
As the time interval between two solar wind protons hitting the substrate in the simulation
domain is on the order of more than 10
5
s, the temperature increase at the substrate caused by
impingement will have been completely dissipated by heat transfer over the time scale of an im-
plantation event under the lunar environmental condition. Hence, to include the effect of heat
dissipation, we next run the simulation as a canonical ensemble simulation (NVT simulation) to
cool the target surface to the initial temperature of 40K. The NVT simulation is run for 2000 sim-
ulation time steps. This cooling rate is chosen so we can simulate as many implantation events
as allowed by the available computational resources while making sure that any possible chemical
reactions in each cooling process can be well resolved. As shown in [49], during an implantation,
39
only a few atoms around the impact site will be heated. Thus, the cooling rate used won’t signif-
icantly change the overall molecular structure of the implanted sample. Thus, each implantation
event simulation takes 20000 simulation steps.
3.3 Simulation Results
Figure. 3.1 snapshots of the simulation at the start and after 2743 and 8679 implantation events.
The detailed molecular structure of the surface after 8679 implantation events is also shown as
zoomed in panels in Figure 3.1 c. We denote N as the number of implantation events. Figs. 3.1
b and 3.1 c show some implanted hydrogen are found on and under the surface. The implanted
hydrogen atoms react with the oxygen atoms on the substrate and form hydroxyl groups. Figure
3.1 c shows some molecules and clusters, including H
2
O and H
2
, are sputtered off from the surface
At N = 8679, the total number of hydrogen implanted in the surface is 3434, or about 39.6% of the
hydrogen atoms impinged on the surface.
For comparison, we also ran SRIM [50] simulation using the same setup. The SRIM code
resolves only the effects from physical collisions. We find that the reflection rate of the incident
solar wind protons obtained from SRIM is the same as that in our simulation, at around 60% after
N=8679 events. As more than half of the incident particles are reflected,under the condition of
small oblique angle incidence considered in this study. the local implantation saturation time is
longer than that estimated based on regular solar wind flux. The reflected hydrogen atoms are
either lost to space or contribute to secondary implantation events with lower energy. For a high
reflection flux, the effects from secondary implantation could be as important as that from primary
implantation with high reflected flux. However, in this study, we shall focus only on primary
implantation.
To understand the evolution of the substrate during implantation, Figure 3.2 shows the number
of H
2
O , H
2
and OH, the three molecules and chemical groups produced by implantation, as
a function of the implantation event. Here, the total number of H
2
O molecules include water
40
Figure 3.1: Snapshots of molecular structure at N=1 and N= 2743 and 8679 implantation events. N
is the number of implantataion events. Red particles are oxygen atoms, yellow particles are silicon
atoms and black particles are hydrogen atoms.
molecules, the water molecules attached to silica, and H
3
O
+
. Figure 3.2 (a) shows the total column
density of molecules or chemical groups in the system. We find that, while the solar wind protons
can form hydroxyl groups and water molecules at silica surfaces, the number of− OH in the system
becomes stable after about 4500 implantation events. The production rate of H
2
O is relatively low
but the total number of H
2
O increases throughout the implantation process.
Figure 3.2 (b) shows the number of molecules and chemical groups that stay on or underneath
the lunar surface. Initially, the number of− OH grows rapidly until N∼ 4500. This is because
most of the solar wind hydrogen atoms are captured by the dangling bonds of the silica on the
surface in the early phase of the simulation. Hydrogen diffusion during the implantation process
plays a major role in water formation by implantation. The energy dissipated from the implanted
hydrogen enhances the diffusion of hydrogen and thus, facilities more collisions of hydrogen with
hydroxyl groups and oxygen atoms. Nevertheless, the contribution of solar wind implantation to
the formation of hydroxyl or water molecules is minimal. For example, assuming a lunar dust
41
Figure 3.2: Column density of molecules and chemical groups during implantation. Top panel:
the total column density of molecules in the simulation box. Middle panel: The column density of
molecules under the surface. Bottom panel: The column density of molecules above the surface.
42
grain with a diameter of 60µm, the equivalent content of− OH/H
2
O is less than 1ppm. At PSRs,
the solar wind impinges the surface at about the ion acoustic speed, much lower than the solar
wind flow speed. This leads to a small implantation and saturation depth. This suggests that the
− OH/H
2
O content detected by [101] at PSRs cannot be due to solar wind implantation alone but
is likely the combined outcome of implantation and some other processes, such as micrometeoroid
impact.
Figure 3.2 (c) shows the number of molecules above lunar surface, i.e., the molecules sputtered
from the surface during implantation. The sporadic small number of− OHs shown are due to the
sputtering of hydroxylated silica compound. Newly formed water molecules may also be diffused
to the surface or even leave the surface. More interestingly, the sputtered water molecules are
mostly in the form of H
3
O
+
, indicating that water generated by implantation is not stable enough
and can be easily sputtered by H
+
+ H
2
O = H
3
O
+
. This could potentially change the original view
of volatile transport. Current volatile transport models mostly focused on thermal transport ( see
Sch¨ orghofer et al. [118] and reference therein). However, the dynamics of charged particles H
3
O
+
is controlled not only by the temperature but also by the electric and magnetic fields. Thus, lunar
surface charging may have a significant effect on the transport of H
3
O
+
.
In order to quantify the contribution of solar wind implantation to lunar water formation, it is
important to understand whether the implanted hydrogen can combine with all the oxygen atoms
within the implantation depth. Hence, we further analyze the effects of chemical reactions on− OH
and H
2
O distribution on and under the lunar surface from implantation. We define ”implantation
saturation” as the state in which the regolith contains the maximum amount of OH and H solely
from solar wind implantation process (i.e. in the absence of other water formation reactions, such
as micrometeoroid impact or dielectric breakdown). While previous ion irradiation experiments
[21, 23] had found the saturation of− OH in the signal, and previous modeling studies based on
the binary collision approximation had determined the implantation depth, the saturated amount of
− OH had not been determined.
43
From the molecular structure of the substrate shown in Figure 3.1 c, we find that most of
the SiO
2
molecules on the surface are bounded with the H atoms after saturation. The H atoms
mostly exist in the form of hydroxyl and water molecules on the surface (sub-panels (i) and (ii)
in Figure 3.1 c). While the hydroxyl groups are also found underneath the surface (sub-panel (iii)
in Figure 3.1 c), the density of− OH is far less than that on the surface due to chemical reactions
and sputtering. At the early phase of the simulation, the sputtering effect of solar wind protons is
less obvious since the Si atoms and O atoms are strongly bonded. However, once the formation
of water molecule begins, the sputtering becomes very active because water molecules are weakly
bonded with the surface. Thus, some of the collisions by the hydrogen atoms result in sputtering
rather than implantation. As a result, fewer hydrogen atoms can penetrate the surface and become
implanted. We find that the saturation of − OH is a result of the balance between the formation
of− OH (H
+
+− O− =− OH), the formation of water molecules (H
+
+− OH = H
2
O), and the
sputtering of water molecules (H
+
+ H
2
O= H
3
O
+
). The number of the H
2
molecules increases
constantly in all the panels of Figure 3.2. This is because the covalent bond within H
2
is too strong
to be destroyed. The implanted hydrogen atom can pick up a free hydrogen molecule trapped inside
the regolith and form H
2
. After absorbing the kinetic energy from the implanted hydrogen atoms,
the newly formed H
2
molecules have sufficient energy to leave the surface. From the simulation
results, we find that most of the solar wind hydrogen atoms involved in chemical reactions become
H
2
. This is consistent with the observation in some of the ion irradiation experiments [27]. No
reactions from H
2
to− OH/H
2
O is observed in the simulation. This suggests that the formation of
H
2
could negatively affect the formation of− OH/H
2
O. While H
2
is also a valuable resource for
in-situ resource utilization, the collection of H
2
would be a challenging engineering issue because
the H
2
molecules can easily escape to the exosphere [111, 110].
44
3.4 Saturation of Solar Wind Implantation
The combination of solar wind implantation and micrometeoroid impact has been shown to be an
efficient process for lunar water formation by both laboratory experiments[27] and atomic-scale
simulations [3]. In experimental and modeling studies, it was commonly assumed that lunar sur-
face is saturated by solar wind implantation. The simulation results presented also can be applied
to examine this assumption.
The validity of this assumption depends on the time scale of saturation and micrometeoroid
impact. The frequency of micrometeoroid impact is approximately the same for any locations
within PSRs. The time scale of implantation saturation varies at different latitudes because it is
determined by the solar wind impingement flux and surface property such as composition, porosity,
and temperature. We denote the time scale for implantation saturation as t
SoI
and the average time
between micrometeoroid impacts as t
MMI
. If t
SoI
< t
MMI
, the surface is saturated with− OH by
solar wind implantation when a micrometeoroid impact occurs. Figure 3.2 shows that most of
the H atoms after saturation become the H
2
molecules and leave the surface. As a result, not all
implanted solar wind protons will participate in water formation by micrometeoroid impact. On
the other hand, if t
SoI
> t
MMI
, the surface is unsaturated when an impact occurs. In this case, there
will be more hydroxyl formation reactions than the H
2
formation reactions, and thus the efficiency
of utilizing the implanted solar wind proton for water formation is higher.
The saturation time scale can be estimated from t
SoI
=
N
Γ
p
∗ A
, where A is the surface area,Γ the
solar wind ion impingement flux density as given by Eq 3.1, and N the number of implantation
events at saturation. Figure 3.2 shows that− OH is saturated at N∼ 4500. From the typical solar
wind density at PSRs [115] and Eq. 3.1,Γ
p
∼ 10
8
to 10
11
m
− 2
s
− 1
. Thus, the saturation time scale
is t
SoI
∼ O(10
1
) to O(10
4
) yrs.
The frequency of micrometeoroid impacts can be derived by the size-frequency-distribution
(SFD) function [119]. The cumulative flux model from [120] is:
45
F(m,r
0
)=(c
4
m
γ
4
+ c
5
)
γ
5
+ c
6
(m+ c
7
m
γ
6
+ c
8
m
γ
7
)
γ
8
+ c
9
(m+ c
10
m
γ
9
)
γ
10
(r
0
= 1AU) (3.2)
with the constants c
4
= 2.2× 10
3
,c
5
= 15, c
6
= 1.3× 10
− 9
,c
7
= 10
11
,c
8
= 10
27
,c
9
= 1.3× 10
− 16
,c
10
=
10
6
, and the exponentsγ
4
= 0.306,γ
5
=− 4.38,γ
6
= 2,γ
7
= 4,γ
8
=− .36,γ
9
= 2, andγ
10
=− 0.85.
The diameter of the impact crater d
c
can be estimated using the empirical equation from [121]:
d
c
= 1.12· 10
− 4
ρ
− 0.5
t
ρ
0.743
p
d
1.076
p
V
0.727
cos
0.15
θ (3.3)
whereρ
t
is the density of the target,ρ
p
the density of the projectile, d
p
=(6m/ρ
p
π)
1
3
the diameter
of the projectile, V the mean impact velocity, and θ the mean impact angle. The size frequency
function can be derived by the derivative of F(m)
f(m)=− dF(m)
dm
(3.4)
For an order of magnitude estimation of the impact time scale, we choose V = 20 km/s,θ =
45
◦ , and ρ
p
=ρ
t
, and integrate the impact area times the derivative size frequency f(m) for mi-
crometeoroid mass range from 10
− 18
g− 10
2
g. We calculate t
MMI
as the average time for microm-
eteoroid impact events over area A.
t
MMI
Z
m
2
m
1
π((d
c
)/2)
2
f(m
p
)Adm
p
= A (3.5)
which leads to
t
MMI
=
1
R
m
2
m
1
π((d
c
)/2)
2
f(m
p
)dm
p
≃ 3× 10
4
yrs (3.6)
Hence, t
MMI
> t
SoI
unless one considers a surface area much smaller than O(1)m
2
. Thus, the
assumption that the PSR surface is saturated by solar wind implantation when a micrometeoroid
impact occurs is generally valid. Once the surface has reached the saturation state, the simulation
46
shows the rate of H implantation on the substrate is less than 1 for every 100 implantation events
due to reflection and sputtering. Thus, although the solar wind constantly provides H
+
to lunar
surface, few hydrogen atoms will become implanted during the time scale of t
SoI
< t< t
MMI
. This
suggests that the majority of the protons supplied by the solar wind will not be able to participate
in the water formation reaction triggered by micrometeoroid impact. However, we want to point
out that some of the micro-cold traps as described in [18] may have an unsaturated surface due to
the small surface area and very low solar wind incident flux density, and thus could be potentially
efficient water formation sites.
3.5 Conclusion and Discussion
This Chapter investigates the solar wind implantation process at the atomic scale using MD simu-
lations and quantifies the contribution of solar wind implantation to lunar water formation at PSRs.
Simulation results show that, while solar wind implantation can lead to the formation of some
− OH and H
2
O, about 60% of the incident solar wind protons are reflected by the lunar surface at
small oblique incidence angle. Moreover, the formation of− OH and H
2
O at the surface prevents
solar wind protons from penetrating further into the substrate, and many of the H
2
O molecules
formed at the surface are also sputtered by solar wind impact. As a result, the contribution of the
solar wind implantation process itself is not significant enough to account for the observed water
content level. Simulation results also show that, once the lunar surface becomes saturated with
− OH, few subsequent incident solar wind protons will become implanted. We find that the time
scale of saturation t
SoI
is smaller than the average time interval between micrometeoroid impacts
t
MMI
, and thus most of the large PSRs surface will be saturated with− OH when a micrometeoroid
impact event occurs. Hence, although the solar wind constantly impinges lunar surface, the number
of the protons supplied within a time scale of t
SoI
< t< t
MMI
will not be utilized by micrometeoroid
impacts for lunar water formation.
47
Most previous studies of solar wind implantation are based on irradiation experiments. This
study shows that the main outcome from implantation is the formation of− OH, consistent with
most ion irradiation experiments [42, 21, 23, 24, 48]. This study also shows that a low level of water
formation is also possible, while most previous ion irradiation experiments concluded that water
formation by implantation itself is not possible. Managadze et al. [42] is one of the few studies that
found water signal by using secondary ion spectrum instead of the more commonly used infrared
spectrometer. The secondary ion spectrum makes it possible to count sputtered water molecules.
We note that water molecules on the surface are vulnerable and have a very low residence time on
surface. Another reason that water formation was not observed in most experiments may be the use
of a high flux density irradiation in a short time to simulate the equivalent fluence. The use of high
flux density irradiation can easily result in the desorption of water molecules due to overheating
of surface. Thus, even if water molecules were formed in an experiment, it would be difficult to
detect them. A recent study also showed that using high flux ion beam may also cause dielectric
breakdown in the sample[122], which can also lead to water desorption. The possible effects of
surface temperature caused by high density incident in experiments may need to be considered in
future implantation experiments.
The paper considered a simulation setup for solar wind flowing tangentially over a surface with
a temperature of 40K. Parametric simulations will be carried out in a future study to consider higher
surface temperatures and different incident angles so to investigate implantation at high latitude
surface outside the PSRs and low latitude surface. This Chapter used a compact silicate substrate
to model the interactions between solar wind proton and SiO
4
tetrahedral. Future study will need
to adopt a more realistic model that includes defects in lunar surface regolith, and investigate how
the formation of defects may affect the water formation process. The defects on regolith particles
enhance the porosity and create more dangling bonds, and are thus ideal locations to store the
implanted hydrogen from solar wind as well as the diffused hydrogen. Future study will also
need to investigate the contribution of the sputtered volatile and refractory species to the lunar
exosphere.
48
Chapter 4
Deep Dielectric Breakdown: Formation of Water Molecules
In this chapter, Molecular dynamics simulations are carried out to investigate dielectric breakdown
of lunar regolith induced by space weather events and its potential effects on water ice forma-
tion on lunar surface. We find that dielectric breakdown can trigger the water formation process by
breaking the chemical bonds of regolith grains and exposing the oxygen atoms to react with the hy-
drogen implanted by solar wind. In the permanently shadowed region, the water molecules formed
become attached to regolith grains in the molecular structure of ice after the event. Thus, dielectric
breakdown can also enable the preservation of water molecules by changing the hydrophobicity of
regolith grains.
4.1 Motivation
Without a global magnetic field, the lunar surface is directly exposed to space plasma and ra-
diation. The solar wind plasma in aveage condition, due to its relatively low average energy
(10− 10
3
eV ), primarily interacts with the surface, resulting in surface charging. Notably, solar
wind protons typically penetrate the surface to a depth of several dozen nanometers [50]. Yet,
higher energy particles from solar flares or coronal mass ejections (10
6
− 10
10
eV), namely, so-
lar energetic particles (SEPs) and galactic cosmic rays (GCRs) (10
8
− 10
20
eV) have the potential
to penetrate much deeper beneath the surface, to depths of a few millimeters. This deposition
49
of charge by SEPs and GCRs in the subsurface region leads to the phenomenon of deep dielec-
tric charging. Studies show that an uptick in SEP flux during a space weather event can lead
to a significant deposition of charges, consequently creating a potent, localized electric field in
dielectric materials [29]. When this electric field strength surpasses the breakdown threshold of
lunar regolith, primarily composed of SiO
2
[123], dielectric breakdown is the result. Previous es-
timates suggest that a typical SEP event could establish an electric field in the lunar regolith on
the order of 10
6
to 10
7
V/m [29], significantly above the breakdown threshold of silica. Though a
fair amount of literature has been devoted to studying surface and deep dielectric charging on the
Moon [29, 124, 65, 66, 67, 68, 69, 70, 125, 126, 1, 76], the chemical reactions during lunar regolith
dielectric breakdown and their subsequent effects remain largely unexplored.
Observations from spacecraft have confirmed the presence of water molecules and hydroxyl
groups on the Moon [13, 127, 128, 16]. Solar wind-induced hydroxylation has been proposed as
a key process leading to the formation of water and hydroxyl on the lunar surface [129, 42, 110,
130, 112, 111]. There is broad consensus that solar wind proton implantation is a crucial source
of hydrogen for this hydroxylation process. For instance, the Lunar Prospector detected hydrogen
[131], and LCROSS discovered both hydrogen and water in the lunar regolith [17]. However,
some studies argue that solar wind proton implantation alone may not be sufficient to produce
significant quantities of water molecules under typical space weather conditions [22]. The process
of recombinative desorption, a vital step in water formation, necessitates an average temperature
of 450K [132, 26]. Considering that the lunar surface peaks at around 400K and temperatures in
PSRs are typically below 120K, the lunar surface cannot independently provide the requisite energy
to convert hydroxyl into water molecules [26, 133]. Consequently, additional energy sources or
catalysts are required for water formation. Micrometeoroid impact, due to the heat released during
the process, is considered a significant catalyst for this transformation from hydroxyl to water
on the lunar surface [27]. In this Chapter, we introduce a novel triggering mechanism for the
formation of water ice in the context of solar wind proton-induced hydroxylation. Specifically, we
examine the impact of dielectric breakdown, triggered by SEP events, on the regolith grains at the
50
surface of PSRs in the lunar polar region, at a depth ranging from nm to mm. Our study reveals that
the electric field generated by deep dielectric charging holds the potential to disrupt the chemical
bonds of regolith grains. This disruption paves the way for the oxygen in the silica to engage in
a reaction with the solar wind-implanted protons, thereby facilitating the formation of water ice.
This novel finding adds a significant layer of understanding to the complex process of water ice
formation on the lunar surface.
Dielectric breakdown is a bond-breaking process in the atomic scale. During the breakdown
of lunar regolith, a complex set of intermediate reaction steps involving the exposed oxygen, the
implanted protons, and silicon can occur. This results in final products that are heavily influenced
by numerous factors such as charge state, electric field, and temperature, making it challenging
to encapsulate these reactions in a set of straightforward chemical equations. Rising to this chal-
lenge, we utilize molecular dynamics (MD) simulations in this study. This first-principles-based
modeling method provides us the capability to simulate bond-breaking and molecular formation,
a unique approach in our field. Our goal is to delve deep into the chemical reactions that oc-
cur during the dielectric breakdown of lunar regolith, in order to discern the final products that
emerge from such a breakdown event. While kinetic theories, informed by MD simulations, have
previously been applied to study the dielectric breakdown of related materials [134, 135], to our
knowledge, no direct MD simulation has been performed to investigate the dielectric breakdown
of lunar regolith and the subsequent chemical reactions involving the implanted hydrogen. Section
2 presents the formulation and the simulation model. Section 3 discusses the results of the MD
simulation. Section 4 discusses the implications of these results for the distribution of water on the
lunar surface.
51
4.2 Formula and Simulation Setup
Dielectric breakdown can occur during an SEP event if a sufficient number of energetic charged
particles are deposited into the regolith layer, and if the charge deposition rate exceeds the dissi-
pation rate [1]. The charge dissipation rate can be calculated from the discharge time, τ =ε/σ
c
,
whereε andσ
c
are the permittivity and conductivity of lunar regolith, respectively. The dielectric
properties of the lunar regolith are reviewed in [1]. The conductivity and the dielectric constant
of the lunar surface are estimated to be 10
− 17
S/m - 10
− 14
S/m and 2-10, respectively. As the
conductivity is proportional to temperature, one would expect that breakdowns would occur more
frequently in the PSRs due to a longer discharge time. Using the JPL proton fluence model [136]
and lunar temperature measurements from the Lunar Reconnaissance Orbiter’s Diviner instrument
[137], Jordan et al. [1] estimated that SEP-induced electrostatic discharge could occur on average
twice a year in the coldest locations on the Moon.
The solar wind implants protons in the lunar soil. The solar wind is a mesothermal plasma
flow with an average density of n
o
∼ 10cm
− 3
, an average electron temperature of T
e
∼ 10eV , and
an average solar wind flow velocity of v
o
∼ 350km/s. At the lunar terminator region, the flow
of a mesothermal plasma over a rugged terrain at a low sun elevation angle generates localized
plasma wakes [138, 126]. Hence, the proton flux collected by PSRs surface is that from a plasma
wake. As the solar wind plasma expands into the wake, the ion velocity component normal to
each expansion characteristic line equals to the ion acoustic speed [116, 139]. For an order of
magnitude estimation, we take the proton density above the lunar surface to be n∼ 10cm
− 3
and
the proton impingement velocity to be the ion acoustic velocity C
s
=
p
T
e
/m
i
∼ 30km/s. Thus,
the corresponding proton impingement flux is Γ∼ 3× 10
7
/(cm
2
s) under the average solar wind
condition. As SEP events happen sporadically and the charge of implanted protons will dissipate
over time, we consider that the surface regolith layer is implanted with hydrogen atoms in between
SEP events.
We apply MD simulations to study both the bond-breaking process and the chemical inter-
actions after a breakdown occurs in lunar regolith. The MD simulation model considers a lunar
52
regolith grain surrounded by hydrogen atoms. The regolith grain is modeled as a SiO
2
nanopar-
ticle. The simulation setup is shown in Figure 4.1 Here, the yellow and red particles represent
the silicon atoms and oxygen atoms in the SiO
2
nanoparticle, respectively, and the blue particles
represent the hydrogen atoms implanted by the solar wind. The nanoparticle in the simulation has
a diameter of 4 nm. This diameter is much smaller than the average size of a regolith grain because
of computational limitations. However, as the focus of this study is on the chemical reactions, one
may consider that the nanoparticle simulated represents a fraction of the outer layer of the regolith
grain surface.
The simulation domain is 10nm× 10nm× 10nm with periodicy boundary conditions applied to
all boundaries. 454 hydrogen atoms are placed around the nanoparticle as most of the implanted
hydrogen will combine with the oxygen atoms and become hydroxyl groups. Using the estimated
solar wind proton impingement flux of Γ∼ 3× 10
7
/(cm
2
s), the hydrogen atom density in the sim-
ulation domain is equivalent to that from hydrogen implantation over a period of about 6 months,
the average time between breakdown-causing SEP events, under the average solar wind condition.
We assume the regolith particle and the hydrogen atoms have an initial temperature of 40K, a value
similar to that at the shadowed region of lunar craters as detected by the Diviner Lunar Radiometer
Experiment on the Lunar Reconnaissance Orbiter [80].
During deep dielectric charging, the electric field is built up gradually until dielectric break-
down occurs. In this study, the charging process is not modeled. To simulate the effects of SEP
induced deep dielectric charging, an electric field is applied in the simulation domain. In the sim-
ulation presented in this chapter, the applied electric field is taken to be 5 × 10
6
V/m. This electric
field strength is consistent with the estimation of [29, 76].
The simulation time step is based on the force field of the chemical reactions, and is taken to
be dt = 0.25fs. The time step is several orders of magnitude smaller than both the charging and
discharge time scale which are both on the order of days [76, 1]. Hence, the detailed chemical
reactions can be fully resolved in the simulation. During the simulation, the positions and veloci-
ties of each atoms in three dimensions are obtained. The bond orders between each atoms are also
53
calculated. Based on the bond order and the atom positions, a cluster analysis is carried out to
identify each type of molecules, such as H
2
O, SiO
4
tetrahedra, and hydroxyl groups. The interme-
diate chemical reactions in the simulation are tracked by following the evolution of each molecule
groups, the chemical bonds, and the system temperature. An analysis of the chemical bonds can
also reveal the macroscopic state of the system, such as the fragmentation rate of SiO
4
tetrahedra
and the water ice structure. The simulation parameters are summarized in Table 4.1.
Table 4.1: Simulation parameters
SiO
2
particle diameter 4nm
Domain size 10nm× 10nm× 10nm
Initial temperature 40K
Simulation Case 1 2A 2B
Electric field (10
6
V/m) 0 5 0
Simulation duration (10
− 12
s) 175 175 540
Time step (10
− 15
s) 0.25 0.25 0.25
4.3 Results and Discussion
We present results from two simulation studies. Both studies start from the same initial molecular
setup shown in Figure 4.1 a. The first study, Simulation 1, considers that no deep dielectric charg-
ing ever occurs. Hence, no external electric field is applied in the simulation domain. The second
study considers dielectric breakdown due to deep dielectric charging. The second study consists of
two simulations, Simulation 2A and Simulation 2B, running in sequence. Simulation 2A models
the time period during dielectric breakdown. In Simulation 2A, an electric field of E
x
= 5× 10
6
V/m is applied along the x direction in the simulation domain to represent the local electric field
generated by deep dielectric charging. Simulation 2A is stopped once the fragmentation rate of
54
the silica nanoparticle becomes plateaued. Simulation 2B models the time period after dielectric
breakdown. After breakdown, the electric field generated by deep dielectric charging disappears
immediately and the heat generated during breakdown dissipates gradually through heat transfer to
the surrounding area and space. Hence, in Simulation 2B, we switch off the electric field to E
x
= 0,
continue the run from the end results of Simulation 2A until a steady state is reached while gradu-
ally relaxing the temperature from that at the end of Simulation 2A to the original temperature of
40K over the course of the simulation.
Figure 4.1: Snapshots of the molecular structures in the simulation. Figure(a): initial configuration
of Simulations 1 and 2A. Figure (b): the end of Simulation 1. Figure (c): the end of Simulation
2A and beginning of Simulation 2B. Figure (d): the end of Simulation 2B. Red particles represent
oxygen atoms, yellow particles represent silica atoms and blue particle represent hydrogen atoms.
55
Simulation 2A shows that the temperature in the simulation domain during breakdown fluctu-
ates near 1834K, an indication that dielectric breakdown can provide the energy needed for water
formation because this temperature is significantly higher than that needed for recombinative des-
orption [26]. The temperature dissipation after breakdown due to heat transfer is a macroscopic
process and is beyond the scope of the MD simulation model. The time scale of the chemical re-
actions in the MD simulation domain is also orders of magnitude smaller than that of heat transfer.
To include the cooling effect due to heat transfer in Simulation 2B, we slowly decrease the system
temperature from the peak temperature at a rate of 10 degree per 10
4
simulation steps. This cooling
rate was tested to ensure that the system cooling is a near equilibrium process and is sufficiently
slow so to not interfere with the chemical reactions in the simulation. We note this approach does
not affect the products of chemical reactions which depend only on the system state. Simulations
1 and 2A were run for a time period of 175 ps (7× 10
5
simulation steps). Simulation 2B was run
for a time period of 540 ps (2.16× 10
6
simulation steps).
Figures 4.1b, 4.1c, and 4.1d show the snapshots of all the molecules and atoms at the end of
Simulation 1, Simulation 2A, and Simulation 2B, respectively. Figure 4.2 shows the chemical bond
structure at beginning of Simulation 1 and Simulation 2A , and that at the end of Simulation 2B.
Figure 4.3 compares the time history of the number of the water molecules, OH group molecules
and SiO
4
tetrahedra between Simulation 1 and Simulation 2A. Figure 4.4 compares the time history
of the number of H
2
molecules, SiO
4
tetrahedra, free H
2
O molecules, and the total number of H
2
O
molecules between Simulation 2A and Simulation 2B. In Fig 4.4, the free H
2
O molecule refers
to the stand alone molecule of one oxygen atom connecting with two hydrogen atoms. As will
be discussed later, the H
2
O molecules in the simulations can exist either as free molecules or
become attached to silica. The total number of H
2
O molecules accounts for both the free and
the attached H
2
O molecules. Also note that, since the SiO
4
tetrahedra are gathered by the Si-
O bonds, the structure of the silica nanoparticle is composed of SiO
4
tetrahedra (i.e. four oxygen
atoms connecting to one silicon atom with two silicon atoms sharing one oxygen atom) as shown in
56
Figure 4.2 a. The changing in the number of the SiO
4
tetrahedra indicates the breakup or formation
of the silica nanoparticle.
The effects of dielectric charging and breakdown can be seen by comparing the results of
Simulation 1 and Simulation 2A . The most significant difference between the two simulations is
that few H
2
O molecules are formed in Simulation 1 but a significant amount of H
2
O molecules
are formed in Simulation 2A (Figure 4.3 a). The SiO
2
nanoparticle stays intact In Simulation 1
but breaks down almost completely by the electric field in Simulation 2A (Figs 1b and 1c). At
the low temperature of 40K, the oxygen atoms do not have the kinetic energy required to escape
from the silica nanoparticle on their own to recombine with hydrogen atoms. Hence, the reactions
between the SiO
2
nanoparticle and the hydrogen atoms occur only at the nanoparticle surface to
form hydroxyl groups, H + O = -OH (Figure 4.1 b). This is consistent with the observations from
most laboratory experiments on the lunar water formation processes [22]. In Simulation 2A, the
time history of the number of atoms and hydroxyl molecules suggests the following process. As
the strong electric field breaks up the chemical bonds in the SiO
4
tetrahedra, the SiO
2
nanoparticle
breaks down first into smaller fragments of silica and then various types of Si
m
O
n
molecules,
exposing the oxygen atoms inside the silica during the process. At the end of Simulation 2A, the
number of SiO4 tetrahedra nearly approaches zero (Figure 3b). While some of the hydrogen atoms
still interact with the oxygen atoms at the SiO
2
nanoparticle surface to form hydroxyl groups, other
hydrogen atoms react with the open bonds of the exposed oxygen atoms to form water molecules,
H + -O = -OH and -OH + H = H
2
O. The hydroxyl groups formed on the surface can also further
react with the hydrogen atoms and other hydroxyl groups to form water molecules, -OH + -OH =
H
2
O + -O-.
To study the time period after dielectric breakdown, we continue the run with the electric field
turned off in Simulation 2B. As the kinetic energy of the molecules and atoms start to decrease,
various chemical and physical bond formations can occur between the colliding molecules and/or
atoms. Figure 4.4 shows that there are at least two important differences between Simulation 2B
57
and 2A. First, the number of SiO
4
tetrahedra start to increase in Simulation 2B due to the re-
formation of the broken chemical bonds between the Si
m
O
n
molecules. This forms amorphous
silica structure at the end of Simulation 2B (Figure 4.1 d). Second, most of the H
2
O molecules are
free molecules in Simulation 2A but become attached to silica in Simulation 2B. This is because
the H
2
O molecules which are freed by the heat produced during the breakdown process start to
lose their kinetic energy as the temperature goes down in Simulation 2B. Once they are close to the
SiO
4
tetrahedra, physical bonds are formed between the H
2
O molecules and the SiO
4
tetrahedra
as the kinetic energy of the H
2
O molecules is transferred into the potential energy through bond
forming process.
While the H
2
O molecules are mostly attached to silica surface at the end of Simulation 2A (Fig-
ure 4.2 b), hydrogen bonds are also established between the H
2
O molecules on the silica surface at
the end of Simulation 2B (Figure 4.2 c). This process further consumes more kinetic energy from
the free H
2
O molecules into bond formation. We note that the bonds shown are also commonly
found in the molecular structure of water ice. This result is consistent with the detection of the
’frost’ in the shadow region by LRO [140] and the exposed ice by M
3
[101]. At the end of Simu-
lation 2B, the number of each molecule groups are stable, and the total system energy has reached
the minimum state. Hence, the molecular structures shown in Figs. 2b and 2c are stable ones for
the temperatures considered. For this particular simulation, about 15% of the oxygen atoms in the
silica nanoparticles at the start of Simulation 2A become part of the H
2
O molecules attached to
silica at the end of Simulation 2B.
Fully hydroxylated silica surface are found to be hydrophobic [141]. The results at the end of
Simulation 1 show that hydroxyl groups are formed at the silica nanoparticle surface (Figure 4.1
b). Hence, the surface of a typical lunar regolith grain may not be able to hold water. However,
simulation 2B shows that the silica surface become somewhat hydrophilic after dielectric break-
down as H
2
O molecules becomes attached to silica. Free H
2
O molecules are easily lost due to
58
evaporation but the H
2
O molecules attached to silica can be preserved. Hence, we find that dielec-
tric breakdown not only triggers water formation but also helps to preserve the water molecules in
the lunar regolith by changing the hydrophobicity of the regolith grains.
4.4 Conclusion and Summary
This chapter presents, to our knowledge, the first reactive MD simulations of dielectric breakdown
of lunar regolith induced by SEP events. We find that dielectric breakdown is a new triggering
mechanism for the water formation process by breaking the chemical bonds of lunar regolith grains
and releasing the oxygen to react with the hydrogen implanted from the solar wind. Dielectric
breakdown also changes the hydrophobicity of the regolith grains so that the water molecules
generated become attached to silica after a SEP event.
SEP events can affect a broad region on lunar surface [1, 76]. For instance, after an extreme
SEP event, the entire polar region may experience deep dielectric charging and regolith breakdown
because the discharge time scale is about the same across the region. While this chapter focuses
on the PSRs, we note that SEP events may also induce dielectric breakdown at lower latitudes as
long as the surface temperature is sufficiently low [76]. Hence, dielectric breakdown induced by
SEP may be a potentially important mechanism for surface water formation in PSRs as well as, to
a lesser extent, globally on the Moon. Honniball et al. [19] recently reported that the lunar regolith
holds individual water molecules that could be the result of micrometeoroid impact inducing water
formation from hydroxyl. It is interesting to note that the detection in [19] could also be consistent
with this study, which shows water molecules attaching to regolith grains after a breakdown event.
In this study, the regolith grain is modeled as a SiO
2
nanoparticle. The actual lunar regolith
contains other chemical elements, such as Fe, Mg , Al, Ti, Ca, etc. These elements were not
included because a relevant force field is still being developed by the MD community. However,
as metal oxides, the oxides of Fe, Mg, Al, Ti and Ca are more reactive than SiO
2
. Thus, the water
formation reaction would occur even more easily when these elements are included. This study
59
focused on the correlation between water formation and dielectric breakdown. The potential loss
of water molecules during dielectric breakdown was not considered, and will need to be addressed
in future. The breaking/formation of the chemical bounds of the molecules involved in the water
formation process, as well as the quantitative amount of the water that can be formed after an
SEP event are influenced by many factors, such as the electric field strength, the temperature of
the surface, the size, shape, and maturity of the regolith grains, and the density of the implanted
hydrogen atoms in the lunar soil. Parametric MD simulations will be carried out in future to
investigate the effects from these variables. Future studies will also need to evaluate the relative
contribution of dielectric breakdown to water ice formation against other sources and mechanisms,
such as micrometeoroid impact.
60
Figure 4.2: Detailed bond structures at the beginning of Simulation 2A (Figure 4.2 a) and at the
end of Simulation 2B (Figs. (b) and (c)). Figure (a): SiO
4
tetrahedra of the silica nanoparticle.
Figure (b): water molecules attached to silica surface. Figure (c): hydrogen bonds between water
molecules at the silica surface. Red particles represent oxygen atoms, yellow particles represent
silica atoms and blue particle represent hydrogen atoms.
61
Figure 4.3: Comparison of the number of molecules in Simulations 1 and 2A: Number of water
molecules (Figure 4.3 a); Number of SiO
4
tetrahedra (Figure 4.3 b); and Number of OH group
molecules (Figure 4.3 c).
Figure 4.4: Comparison of the number of water molecules, SiO
4
tetrahedra, and hydrogen
molecules in Simulations 2A and 2B.
62
Chapter 5
Micrometeoroid Impact: Lunar Water Retention
In this chapter, we carry out reactive molecular dynamics simulations to study the formation and
retention of water during nanometer-sized micrometeoroid impacts on the lunar surface at the
atomic scale. Results indicate that water molecules are both generated and lost during an impact.
For a hydroxylated surface under average solar wind conditions, the water molecules produced
by a nanometer-sized cosmic dust particle impacting at velocities from 8km/s to 20km/s range
from about 44% to 275% of the pre-existing water molecules. However, due to ejections caused
by the impact, the increase in water content at the impact site is only from 5% to 73%. While
micrometeoroid impacts can generate a substantial amount of new water molecules, the amount of
water lost to space also significantly increases at higher impact velocities. Hence, the increase in
local lunar water content due to micrometeoroid impacts is strongly affected by the impact velocity.
5.1 Motivation
One of the most fundamental questions in planetary science is the origin of water on the Moon.
During the Cassini flyby, the Visual and Infrared Mapping Spectrometer (VIMS) provided the first
evidence of H
2
O/OH on the dayside of the lunar surface [13, 142, 15]. The Deep Impact extended
mission (EPOXI) showed that hydration is distributed globally over the lunar surface [15]. Data
from the Moon Mineralogy Mapper (M
3
) presented direct evidence of exposed surface water ice in
the polar region [101]. The Lunar CRater Observation and Sensing Satellite (LCROSS) provided
63
ground truth data of water in the permanently shadowed regions (PSRs) [17]. The amount of de-
tectable water on the Moon depends on both water formation and retention. Previous studies have
suggested that lunar water may be formed by both internal processes, such as volcanism and other
outgassing events [143, 144], and external processes, such as solar wind and interplanetary dust
implantation, meteoroid impact events (see [14] and references therein), and dielectric breakdown
of the lunar regolith [103]. Studies have also suggested that potential water loss mechanisms may
include photo-dissociation [145], thermal-dissociation [132], and dissociation by energetic parti-
cles [74]. However, there is currently no universally accepted theory or model that can quantify
the amount of water generated and retained by the different mechanisms or processes involved.
Micrometeoroid impact has been considered a major triggering mechanism for lunar water
formation. Solar wind implantation constantly supplies the lunar surface with hydrogen atoms
[110], which are mostly stored as hydroxyl groups rather than water molecules. This is because
the process to convert hydroxyl to water molecules, recombinative desorption (RD), requires a
typical temperature of 450K (Orlando et al. [26]) while the maximum temperature of the lunar
surface is only about 400K. Hence, the lunar surface alone is not able to provide the energy needed
to generate water molecules [27]. It has been shown that the heat released by impact can provide
sufficient energy to start the water formation reaction [146, 27]. However, the detectable amount
of water generated by an impact is influenced by many factors. The heat released during an impact
may generate and liberate water molecules at the same time. Mechanical collisions may also
generate ejecta containing newly formed water molecules which subsequently can be transported
to other locations on lunar surface or the exosphere, or escape the Moon. Impacts are also likely to
form porous or amorphous structures on the lunar surface which can trap more solar wind protons
and water molecules.
Several studies have simulated the micrometeoroid impact process using laboratory experi-
ments [58, 59, 60] and macroscopic simulation models, such as smooth particle hydrodynamic
(SPH) [61, 62]. However, these macroscopic simulation models are not able to resolve chemical
reactions and mechanical collisions simultaneously. Furthermore, precise measurements of water
64
generation and retention due to hypervelocity impact are not yet feasible due to experimental lim-
itations, since the chemical reactions induced occur on a time scale of nano- or sub-nano-seconds.
At the molecular scale, a chemical reaction is a sequence of bond-formation and bond-breaking.
Any changes in surface shape, porosity, and amorphous structure can also be captured by atomic
position displacement. Given this, in this chapter, we apply molecular dynamics (MD) simulations
to study water formation by micrometeoroid impact on the lunar surface.
Previously, Holmstr¨ om et al. [63] used a classical MD model to simulate the deformation of
silica glass by hypervelocity impact. However, their work focused only on the morphology of the
crater after the impact. Building on their work, in this study, we apply the recently developed re-
active force field (ReaxFF) MD model [92] to simultaneously resolve both the chemical reactions
and mechanical collisions involved, and to quantitatively determine the amount of water generated
and lost during an impact. To our knowledge, such a simulation study has never been carried out
before. In Section 2, we present the simulation method and setup. Section 3 discusses simula-
tion results on water generation and loss, as well as crater formation and lunar surface property
changes due to nanometer-size micrometeoroid impacts. Finally, Section 4 contains a summary
and conclusions.
5.2 Formulation and Simulation Setup
Fig. 5.1 (a) shows the locations and the molecular structures of both the micrometeoroid and the
surface at the start of the impact simulation. In the simulation, the lunar surface is a 24nm× 24nm× 30nm volume of hydroxylated silica, representing a fraction of the outer layer of a regolith
grain. The molecule structure of the hydroxylated silica is that of SiO
4
tetrahedra with chemical
bonds connected with the hydroxyl groups, and is determined by a separate MD simulation of
solar wind proton implantation [147]. A closer look of the water molecules and hydroxyl groups
on the substrate, as well as the micrometeoroid is shown in Fig. 5.2. The micrometeoroid is a
6nm diameter silica sphere with a molecule structure of SiO
4
tetrahedra. The simulation domain
65
is 24nm× 24nm× 800nm. Periodic boundary conditions are applied in the x and y directions. In
the z direction, as the height of the box is set at 800 nm, most of the simulation domain in the z
direction represents a vacuum space. The domain size in the z direction is sufficiently large so all
ejecta from the surface are contained within the simulation domain during the simulation.
Figure 5.1: Snapshots of the impact process for Case 1. (a) t = 0 ps. (b) t = 10ps. (c) t = 20ps. (d) t
= 80ps. The upper panels show the micrometeoroid and lunar surface (generated from simulation
results using OVITO [2]). The lower panels show zoomed in molecule structures. Red particles:
O atoms. Yellow particles: Si atoms. Blue particles: H atoms. (In the lower panels, the plots are
sliced through the center of the crater to show the molecule structures.)
Solar wind implantation deposits hydrogen and forms hydroxyl groups around silica. Hence,
we first carry out a separate MD simulation of solar wind proton implantation on lunar surface to
determine the initial condition of the target surface for impact simulation [147]. Under a proton
flux of Γ∼ 3× 10
7
/(cm
2
s), we find that the hydrogen atoms due to implantation is saturated
at a surface density of 2.7× 10
19
/m
2
[147]. Some water molecules are also formed during the
implantation. The number density of− OH and H
2
O formed around the SiO
4
in the regolith are
66
Figure 5.2: Closer look at the molecular setup for micrometeoroid impact simulation.
3.85× 10
17
/m
2
and 4.34× 10
17
/m
2
respectively. These densities correspond to a OH/H
2
O content
of about 1− 2 ppm , a value far less than what has been detected by M
3
[16] and SOFIA [19].
Hence, the implantation process itself is not sufficient to generate water at a detectable level.
The total number of hydrogen atoms in the substrate is 15552, corresponding to the saturated H
surface number density of 2.7× 10
19
/m
2
. The surface also contains 248 water molecules and 220
− OH formed during implantation, corresponding to the aforementioned H
2
O and− OH surface
number density, respectively. The initial temperature of both the micrometeoroid and the surface
is set to be 100K. The micrometeoroid is placed at 5nm above the target surface with an impact
velocity normal to the surface. This distance is larger than the cutoff distance in the reactive force
67
field. Thus, there are no initial interactions between micrometeoroid and target surface. The MD
simulation time step is set to be 0.1fs. This time step is sufficiently small so to allow all the
chemical reactions and molecular interactions fully resolved [103]. The simulations presented in
this chapter will consider 4 different cases, with the impact velocity ranging from 8km/s to 20km/s
in the normal direction . The mass of the silica sphere in the simulation is 2.5× 10
− 18
g. Thus, the
impact kinetic energy is on the order of 10
− 13
J (10
6
eV). The simulation cases are summarized in
Table 5.1.
Table 5.1: Simulation Cases and Statistics of Water Molecules after Impact
Velocity Energy N
H
2
O
new
/N
H
2
O
old
N
H
2
O
total
/N
H
2
O
old
N
H
2
O
local
/N
H
2
O
old
N
H
2
O
e jected
/N
H
2
O
old
N
H
2
O
global
/N
H
2
O
old
N
H
2
O
escape
/N
H
2
O
old
(km/s) 10
− 13
(J)
Case 1 20 8.0 2.75 3.75 1.62 2.13 1.32 0.81
Case 2 16 5.0 2.13 3.13 1.73 1.39 0.92 0.47
Case 3 12 3.2 0.98 1.99 1.11 0.87 0.70 0.17
Case 4 8 1.8 0.44 1.44 1.05 0.38 0.31 0.08
Cluster analysis is applied to identify the neighboring atoms based on the distance and bond
order between atoms. The analysis of MD simulation output will identify the existing molecules
and chemical bonds such as H
2
, H
2
O, and− OH. A smoothing algorithm by OVITO(Open Visu-
alization Tool) [2] is applied to identify the surface deformation during impact. Those molecules
detected above the surface are classified as the ejecta from impact. Those that are below the surface
are considered as buried by the impact. The simulation is stopped once the number of molecules
in the ejecta becomes stable, i.e. when there are no more molecules ejected from the surface due to
either mechanical collision or thermal emission. The simulations presented typically run for more
than 8× 10
5
time steps.
5.3 Retention and Release of Water Molecules
The kinetic energy of micrometeoroid significantly raises the local surface temperature. For in-
stance, in Case 1, the temperature around the crater is raised to 3745K during impact. The heat
generated during impact breaks the chemical bonds in the SiO
4
tetrahedra and liberates the oxygen
68
atoms to recombine with the hydrogen atoms. This triggers the chemical reactions for volatile for-
mation. Some of the water molecules formed during impact remain bounded in the surface while
others, along with those that existed before the impact, subsequently become ejecta.
Let N
H
2
O
old
and N
H
2
O
new
denote the number of the water molecules that existed before the impact
and formed during impact, respectively. Let N
H
2
O
local
and N
H
2
O
e jected
denote the number of the water
molecules bounded to surface and ejected from surface, respectively. The total number of H
2
O
molecules in the system is
N
H
2
O
total
= N
H
2
O
old
+ N
H
2
O
new
= N
H
2
O
local
+ N
H
2
O
e jected
Note that both the old water molecules existed before impact and the new water molecules formed
during impact contribute to N
H
2
O
local
an N
H
2
O
e jected
. Fig. 5.3 shows the time history of N
H
2
O
total
, N
H
2
O
e jected
,
and N
H
2
O
local
during simulation for all the cases considered.
In all the cases, more water molecules are formed than destroyed by micrometeoroid impact.
A higher velocity impact transfers more kinetic energy from micrometeoroid to the surface and
generates more heating. This leads to more H
2
O molecules being formed (Fig. 5.3a). At the same
time, a higher kinetic energy impact generates more ejecta due to mechanical collision and more
thermal emission due to higher surface temperature. This also leads to more H
2
O molecules being
ejected from the surface (Fig. 5.3b). Therefore, the net increase of water molecules at the impact
site is the result of these two competing effects (Fig. 5.3c)
Table 5.1 lists N
H
2
O
total
/N
H
2
O
old
, N
H
2
O
new
/N
H
2
O
old
, N
H
2
O
local
/N
H
2
O
old
, and N
H
2
O
e jected
/N
H
2
O
old
at the end of each
simulation. As mentioned in Section II, in all cases, N
H
2
O
old
= 248 at the start of the impact sim-
ulation due to implantation. N
H
2
O
new
/N
H
2
O
old
represents the new water production rate by impact and
N
H
2
O
local
/N
H
2
O
old
represents the local water content after impact. We find that, while the new water
production rate ranges from 44% (for V=8km/s) to 275% (for V=20km/s), the local water content
in terms of the pre-impact level is increased by 5% (for V=8km/s) to 73% (for V=16km/s). Among
the 4 cases considered, Case 2 (V=16km/s) results in the most local water increase after impact.
69
The ejecta from impact may be either lost to space or captured by the lunar gravity. Hence, we
further analyze the fate of the ejecta based on their ejecting velocities. The orbital velocity around
the Moon, V
1
, and the escape velocity of the Moon, V
2
, are given by
V
1
=
r
µ
m
R
m
= 1.68km/s, V
2
=
r
2µ
m
R
m
= 2.38km/s (5.1)
where µ
m
= 4.9× 10
12
m
3
s
− 2
and R
m
= 1737.1km are the gravitational parameter and the radius
of the Moon, respectively. During an impact, those ejecta with an ejecting velocity larger than V
2
will be lost to space and those with an ejecting velocity smaller than V
1
will fall back to the lunar
surface. Those ejecta with a velocity between V
1
and V
2
will contribute to the water content in the
exosphere at a height of
H
exo
=
µ
V
2
− R
m
(5.2)
The water molecules that fall back to the surface will contribute to the water content at other
locations on lunar surface although those molecules may be only weakly bonded with the surface
and, thus, may become lost again due to space weathering. To determine the redistribution of the
water molecules on lunar surface, we further estimate the transport distance of the ejected water
molecules from the impact site
D
trans
=
V
⊥
V
∥
2g
m
(5.3)
where V
⊥
and V
∥
are the normal and tangential ejection velocity component, respectively.
Fig. 5.4 shows an analysis of the ejected water molecules for Case 1. Fig. 5.4 a shows the
ejection velocity distribution. The lunar orbital velocity V
1
and escape velocity V
2
are also marked.
The shaded area in 0< V < V
1
, V
1
< V < V
2
, and V > V
2
show the amount of water transported
to other parts of lunar surface, deposited to the exosphere, and lost to space, respectively. Figs.
5.4 b and 5.4 c show the probability density function (PDF) of H
exo
and D
trans
, respectively. The
results show that the impact induced water contribution in the exosphere is mostly around a height
70
of H
exo
= 346km, and the impact induced water redistribution concentrates at a distance of about
138km from the impact site, although some water molecules can be transported to a distance
over 500km. Hence, even a nano-meter sized micrometeoroid may generate long-distance water
transport across almost the entire polar region. This suggests that micrometeoroid impact, a local
event, may contribute to surface water distribution over the entire lunar surface.
Let N
H
2
O
escape
denote the number of the water molecules lost to space, and N
H
2
O
global
denote the
number of the water molecules re-distributed to other parts of lunar surface and the lunar exo-
sphere. (Note N
H
2
O
e ject
= N
H
2
O
global
+ N
H
2
O
escape
) Table 5.1 also lists N
H
2
O
global
/N
H
2
O
old
. and N
H
2
O
escape
/N
H
2
O
old
. Not
surprisingly, both the absolute amount and the relative fraction of the water lost to space increases
significantly at higher impact velocities. Hence, while micrometeoroid impact may generate a sub-
stantial amount of new water molecules, its contribution to lunar water content is strongly affected
by the impact velocity (or impact energy).
The impact also ejects some SiO
4
silica tetrahedra from the surface. Let N
SiO
4
total
, N
SiO
4
e jected
, and
N
SiO
4
sur f ace
denote the total number of SiO
4
tetrahedra in the system, the number of SiO
4
that are
ejected above the surface, and the number of SiO
4
that remains on the surface, respectively. Fig.
5.5 shows the time history of N
SiO
4
total
, N
SiO
4
e jected
, and N
SiO
4
sur f ace
. A high impact velocity leads to less
total SiO
4
tetrahedra in the system and relatively more SiO
4
ejecta. This is because the crater
surface area is larger at higher impact velocity, which creates more open bonds and deduces the
total number of SiO
4
tetrahedra in the system. Furthermore, more atoms are displaced due to the
collision and subsequent compression at higher impact velocity. This suggests that micrometeoroid
impact also affects solar wind proton implantation and water retention. The open bonds created
after an impact make it easier for the solar wind protons to become attached to the regolith. Thus,
more hydroxyl groups will form at the crater site. The displacement of the atoms during an impact
also make the top layer of lunar regolith surface amorphous. This enable more solar wind protons
to penetrate deeper under the surface and, thus, more water molecules to be formed under the
surface during subsequent impacts. As water molecules formed underneath the surface are more
71
easily preserved than those exposed at the surface, micrometeoroid impact also changes the surface
property more favorably for water retention.
Farrell et al. [85] used Monte Carlo modeling to study the redistribution of water molecules
on lunar surface after a micrometeoroid impact. Assuming the initial velocity distribution of the
ejected water molecules to be a Maxwell-Boltzmann distribution with a temperature of 4000K[54],
they estimated that about 6% of the ejected water molecules is redistributed to the lunar surface
with a radius of 200km from the impact site. The results presented here are quite similar, showing
that the ejected water molecules follow a similar velocity distribution with a temperature around
3745K, and about 4.6% of the ejected molecules is re-distributed within a radius of 200km.
The Lunar Atmosphere and Dust Environment Explorer (LADEE) and Lunar Dust Experiment
(LDEX) carried out a comprehensive investigation of dust and volatile in the lunar exosphere
[30, 148, 149, 25, 150, 31]. Benna et al. [31] studied water ejection and delivery to the exosphere
by meteorite (mass: O(10
− 12
)− O(10
6
)g) impacts using LADEE data. Their analysis focused
on the water content distribution at 20-100km above lunar surface due to meteorite impacts from
January to April 2014. Since this chapter models a single impact event in PSRs for nanometer sized
cosmic dust particles (mass: O(10
− 18
)g), the simulation results cannot be compared with [31] due
to the very different impact conditions considered. The LDEX measured the ejected regolith grains
(size: 0.1-1µm) from the lunar surface due to micrometeoroid impacts [148]. [148] calculated the
average velocity of the ejected dust grains to be 670m/s, a value much lower than the peak velocity
shown in Figure 5.4(a). This is because the ejecta analysis shown in Figure 5.4(a) is for water
molecules rather than micron-sized dust grains. The water molecules have a much higher velocity
than the dust grains at the same thermal energy because of the much smaller molecular mass.
We note this chapter focuses on water molecule formation/ejection at surface by nanometer sized
micrometeoroid impact. Thus, a direct comparison of the ejected water in the exosphere from
simulations with LADEE is not feasible within the scope of this study but will need to be carried
out in future.
72
5.4 Generation of O
2
and its implication of Hematite on the
lunar surface
Fig. 5.6 displays the time history of the presence of oxygen molecules on the lunar surface. Despite
being a rare specie in the exosphere and on the surface of the moon, molecular dynamics (MD)
simulations have shown that the impact of micrometeoroids generates a significant number of
oxygen molecules. This finding was unexpected since O
2
is a highly reactive molecule. In the
simulation, the generation of O
2
occurs through the collision between oxygen atoms on the target
surface and the oxygen atoms of the micrometeoroid. Unlike water molecules, most of the O
2
generated remains beneath the surface. It is plausible that O
2
molecules are involved in reactions
such as 2H
2
+ O
2
= 2 H
2
O or captured by fragments of silica. The generation of O
2
also provides
a possible mechanism for the recent detection of widespread hematite using M
3
data [151]. The
analysis of lunar samples has revealed the presence of nanophase iron (npFe) created by space
weathering. If O
2
molecules are generated during an impact, the reactions of O
2
and Fe to Fe
2
O
3
are likely to occur, leading to the possibility of various oxides found in lunar soil. This simulation
provides a new perspective on the contribution of micrometeoroid impacts to the lunar surface,
which was not previously considered a factor.
MD simulations demonstrate that oxygen molecules are generated through micrometeoroid im-
pacts on the lunar surface, which was not initially anticipated. These findings do not contradict
observations, given the high reactivity of O
2
. The simulation also provides a possible explanation
for various oxides found in lunar soil, such as hematite, and highlights the importance of consid-
ering micrometeoroid impacts as a contributor to the lunar surface’s evolution. The complexity of
the real lunar soil is also crucial to consider when interpreting these results.
73
5.5 Summary and Discussion
Reactive MD simulations are carried out for the first time to investigate micrometeoroid impact on
lunar surface from the atomic scale. Simulations resolve both the chemical reactions and mechan-
ical collisions, and quantitatively determine the water formation and loss rate. Results show that
water molecules are generated and lost simultaneously during an impact. For a nano-meter sized
micrometeoroid with an impact velocity in the range of 8km/s to 20km/s (impact energy on the
order of 10
− 13
J), the water molecules produced ranges from about 44% to 275% of that existed
before impact. However, the net increase in local water content is only from 5% to 73% due to
ejections caused by impact. Even for nanometer sized micrometeoroids, the impact can deposit
water molecules into the exosphere and transport water molecules across almost the entire polar
region. Thus, micrometeoroid impact contributes to the global water content of the Moon. While
micrometeoroid impact may generate a substantial amount of new water molecules, the amount of
water lost to space also increases significantly at higher impact velocities. Hence, the net increase
of lunar water content is strongly affected by the impact velocity or energy. Results also show
that micrometeoroid impact makes the top layer of lunar regolith surface amorphous and creates
more open bounds in the regolith. This leads to a more favorable surface property for solar wind
proton implantation and enables more water molecules to be formed underneath the surface during
subsequent impacts.
Due to computational constrains, this chapter models micrometeoroids as a nanometer sized
sphere and focused on water molecule formation/ejection at surface. For larger sized microm-
eteoroids at a similar impact velocity, the impact energy/momentum will be significantly larger
than that in the simulations presented. The impact energy and momentum affect the size of impact
crater, surface heating and evaporation, and thus the water formation and retention rate. Parametric
simulations will need to be carried out for different impact energies so to scale the result for im-
pacts by larger micrometeoroids. Parametric simulations will also need to be carried out to study
the effects of the impact angle and expand the impact speed range so to facilitate comparisons with
observations. The results presented here apply to impacts occurring inside PSRs. Future study
74
will also need to consider impacts at different latitudes by including the effects from solar illumi-
nation and considering different solar wind impingement conditions. The relative contribution of
micrometeoroid impact to lunar water formation against other sources and mechanisms will also
need to be evaluated.
75
Figure 5.3: Time history of the H
2
O molecules in simulation. (a) Total molecules in the system
N
H
2
O
total
. (b) The ejected molecules N
H
2
O
e jected
. (c) The molecules that remain locally at the impact
surface N
H
2
O
local
.
76
Figure 5.4: Ejecta Analysis (Case 1). (a) The ejection velocity distribution. The blue dot line is
at V
1
, and the red dot line is at V
2
. (b) PDF of the height in the exosphere H
exo
. (c) PDF of the
transport distance from the impact site D
trans
.
77
Figure 5.5: Time history of the SiO
4
tetrahedra in simulation. (a) Total tetrahedra in the system
N
SiO
4
total
. (b) The ejected tetrahedra N
SiO
4
e jected
. (c) The tetrahedra that remain locally at the impact
surface N
SiO
4
sur f ace
.
78
Figure 5.6: Time history of the O
2
molecules in simulation. (a) Total molecules in the system
N
O
2
total
. (b) The ejected molecules N
O
2
e jected
. (c) The molecules that remain locally at the impact
surface N
O
2
local
.
79
Chapter 6
The Influence of Lunar Surface Hydration Status on the
Exosphere Transport
In the last chapter, we obtained the velocity distribution function (VDF) of ejected water molecules,
which plays a critical role in exosphere modeling. Reactive molecular dynamics simulation offers
a unique opportunity to explore chemical reactions and dynamics simultaneously. In this chapter,
we extended the analysis of the VDF by using a machine learning model to resolve the VDF from
the first principle. Through our investigation, we reveal that various sources of water molecules in
the ejecta contribute to different segments of the VDF. We showed that the VDF of impact released
water molecules strongly depends on the surface hydration status. The model presented in this
chapter can be used to build a better exosphere model together with data from recent ARTEMIS
mission Lunar Trailblazer.
6.1 Motivation
The transport of water molecules on the lunar surface is largely driven by lateral movement, which
is influenced by local temperature, as discussed in Sch ¨ orghofer et al. [118]. This transport even-
tually leads to water molecules accumulating at polar cold traps, or PSRs, which are considered
ideal locations for water storage due to their low temperatures. However, it is important to note
that PSRs are not immune to the effects of space weathering processes, which can result in the
80
release of water molecules through mechanisms such as sputtering or vaporization. The study of
space weathering processes and their effects on celestial bodies has gained significant attention in
recent years. Two of the major processes that contribute to the formation of the surface-bounded
exosphere on the Moon are solar wind sputtering and impact vaporization. Previous studies by
Farrell et al. [85] and Hurley et al. [25], as well as Zimmerman, have focused on modeling the spa-
tial distribution of released molecules using Maxwell-Boltzmann and S-T distributions for impact
vaporization and sputtering velocity distribution functions (VDFs), respectively.
The velocity distribution function (VDF) of impact vaporization has been extensively stud-
ied by Cintala [54], who incorporated the equations of state of regolith under high pressure into
their analysis. In chapter 5, for the first time, we used a first-principle method to simulate the
velocity distribution of ejected water molecules after a micrometeoroid impact event. have taken
a more comprehensive approach with chemical reactions involved to modeling impact vaporiza-
tion by utilizing reactive molecular dynamics (RMD) simulations. These simulations enable a full
physical and chemical description of the impact process, including collisions, chemical reactions,
and thermal expansion, thereby providing a more accurate representation of the VDF. Interest-
ingly, one of the observations from these simulations is that the ejected water molecules, defined
as those that leave the surface after the impact, may have a velocity distribution that deviates from
the Maxwellian distribution traditionally used in impact vaporization models. Instead, a multi-
Maxwellian distribution may be a better fit for the observed VDF. This has prompted us to delve
deeper into the dynamics of these molecules and investigate how the interplay between these vari-
ous processes affects the resulting VDF.
Previous studies, both experimental and numerical, have also reported multi-Maxwellian ve-
locity distributions in situations involving chemical reactions. For example, Tiwari et al. [152]
used a similar model to that of Huang et al. [3] to investigate the dynamics of N
2
in a high-pressure
shock. Their results showed that the resulting velocity distribution of N
2
strongly deviated from
the Maxwellian distribution, largely due to the fact that N
2
can be formed through three different
81
pathways, each of which requires a different activation energy. As a result, the final velocity dis-
tribution of N
2
at the end of the simulation depended on which pathway was dominant. Similarly,
Schaible et al. [153] reported a flux-weighted Maxwellian velocity distribution of photo-stimulated
atomic sulfur, which also deviated from the traditional Maxwellian distribution. The reason for this
deviation was the presence of different binding energies, which can be considered as different ori-
gins of the released molecules. Together, these studies highlight the importance of considering
multiple factors, such as chemical reactions and different formation pathways, when modeling the
velocity distributions of released molecules.
The release of water molecules during micrometeoroid impacts, as discussed in chapter. 5,
can be similarly analyzed using theories that consider the different origins of the ejected water
molecules. In our simulation setup, the substrate contained both− OH and H
2
O on the surface,
and the resulting ejected water molecules included both original water molecules and those formed
through impact. These different origins give rise to distinct dynamics that can complicate our
understanding of water transport and accumulation on the lunar surface. The pre-existing water
molecules might be released at a lower temperature since they only need to overcome the binding
energy between H
2
O and SiO
2
. For the newly formed water molecules, their formation needs
the energy from impact and as a result, they will be released in the later stage where the surface
was already heated up. Scaling up the simulation from atomic scale to the planetary scale, this
feature would provide implications for the impact released process on the lunar surface. 3µm
observations detected OH or H
2
O but was not able to tell the exact composition. Our current
understanding of the hydration status of the lunar surface is a complex mixture of OH and H
2
O,
particularly in high latitude regions where solar wind implantation contributes to the formation of
− OH, and water molecules are transported laterally from low-latitude regions. The dynamics of
water generated from micrometeoroid impact will therefore exhibit a more complex behavior than
previously assumed.
In this chapter, we aim to expand upon the work of Farrell et al. [85] by focusing on the impact
vaporization process and its contribution to the formation of the lunar surface-bounded exosphere.
82
This will also extend the analysis of ejected water molecules presented by Huang et al. [3]. To
better understand the dynamics of water formation during micrometeoroid impacts on the lunar
surface, we will present new theoretical models using machine learning techniques. Specifically,
we will investigate how the local distribution of hydroxyl and water molecules will affect the ve-
locity distribution function of the released water molecules. By taking a comprehensive approach
to modeling these processes and their effects on the lunar surface, we can gain valuable insights
into the potential resources available for future human exploration and utilization of the Moon.
Our work may also have broader implications for the study of water and other volatiles in other
planetary environments.
6.2 Machine Learning Fitting of Velocity Distribution Function
In section 2.3, we discussed the implementation of Mixed-Maxwellian Distribution and how it can
be used to identify different groups of Maxwellian distribution from a mixed distribution. In order
to characterize the velocity distribution function of the ejected water molecules in our simulation,
we fitted the original distribution with a combination of two Maxwellian distributions, namely the
cold group and the high-temperature group. We found that the cold group only accounted for 9.6%
of the total water molecules, and the temperature was calculated to be 529 K. The high-temperature
group, on the other hand, had a much higher temperature of approximately 8014.17 K. The 9.6%
is close to the number of original water molecules in the 20km/s case, which indicates that these
water molecules also behave similarly in terms of the kinetic energy. This corresponds to our
hypothesis that the pre-existing water molecules are released in the early impact stage, while the
newly formed water molecules are released in the post-impact stage. Overall, the fitting of the
velocity distribution captured the low-temperature peak around 0 m/s and the high-temperature
peak near 3000 m/s, which are common features in such simulations. While the fitting was not
ideal due to the limited number of total water molecules (248), the low-temperature group and
high-temperature group were clearly distinguishable.
83
Figure 6.1: Machine Learning Fitting of Velocity Distribution Function from [3]
6.3 Direct Comparison of Si− OH Substrate and SiO
2
− H
2
O
Substrate
We aimed to verify our hypothesis on the release of water from the lunar surface under different
conditions. To achieve this, we set up two different tests of simulation, one with pure SiO
2
− OH
and another one with pure SiO
2
− H
2
O, corresponding to the water-rich and -OH rich regions on
the lunar surface. For the Si-OH case, we randomly added hydrogen atoms throughout the SiO
2
substrate region with a cutoff distance of 1 Angstrom to avoid overlapping. For both cases, we
first ran a NVT simulation for 10000 steps with a timestep of 0.5fs, followed by a 10000 step
NVE simulation with the same timestep to relax the structure and ensure stability and free of
perturbations that could affect our final analysis of the kinetics.
Due to the small number of water molecules that was available to be sampled in Huang et al.
[3], we constructed a new framework that includes stochastic setups. To increase the fidelity of the
statistical analysis, we used 20 stochastic setups for both cases. Also to make sure the substrate was
large enough for the impact, we tracked the kinetic energy of atoms for the largest impact case V =
84
(a) (b)
Figure 6.2: (a) Setup of SiO
2
− OH and (b) Setup of SO
2
− H
2
O
20km/s. Figure 6.3 shows the dissipation of energy as well as ejecta, the boundary was not affected
by the impact which means the substrate is large enough to maintain the energy conservation. After
about 1 ps, when no water molecules were released from the surface, we deleted the surface and
only included the ejecta to run for another 1 ps, this approach significantly reduced the computation
time while maintaining an accurate description of the kinetics of ejecta.
Figure 6.3: 3D snapshots (upper panel) and 2-D Top-views (lower panel) of the temperature con-
tour during micrometeoroid impact with V = 20 km/s at t = 0, 20, 100fs. Color coded by kinetic
energy (10 atoms neighbour average)
85
Our results demonstrated that the velocity distribution of water molecules released in the
SiO
2
− H
2
O case (as shown in Figure 6.4(a)) followed a similar distribution as they were mostly
thermally released. In contrast, the velocity distribution of water molecules released in the Si− OH
case (as shown in Figure 6.4(b)) was largely influenced by the impact velocity. To fit the velocity
distribution, we used a machine learning algorithm, which yielded values of T
V=10km/s
= 742.43K
and T
V=20km/s
= 803.42K for the SiO
2
− H
2
O case, and T
V=10km/s
= 3255.24K and T
V=20km/s
=
8479.91K for the Si− OH case.
The difference of 61 K in temperature between the two impact velocities for the SiO
2
− H
2
O
case can be attributed to statistical error, which is reasonable considering the large difference in
impact energy. However, for the Si− OH case, it was clear that the temperature of the vapor
was a function of the impact velocity, which was consistent with our hypothesis. Specifically, the
temperature increased significantly from 3255.24 K to 8479.91 K as the impact velocity increased
from 10 km/s to 20 km/s. This indicates that the releasing H
2
O can ”feel” the impact energy.
Analysis of Figure 6.4(a) revealed that over 74% of the water molecules ejected in the SiO
2
− H
2
O case were still surface-bounded, while for the Si− OH case, this proportion was only 44%.
This finding challenges previous assumptions that relied on the Maxwellian distribution, which
suggested that a large proportion of ejected water molecules would escape into space. These re-
sults also raise important questions about the transport of water molecules in the surface-bounded
exosphere, which could play a significant role in the overall water budget on the Moon. Despite
the high impact velocity of 20 km/s, our simulation shows that pre-existing water molecules are re-
leased with much lower velocities, although they are still relatively energetic compared to laterally
transported water molecules (T
sur f ace
).
Another notable species in the exosphere is H
2
which has been discussed extensively [111,
118]. Due to its low mass, H
2
is usually considered extremely mobile and is assumed to be lost
into space upon micrometeoroid impact, even at a low velocity of 2 km/s. However, as indicated by
our simulation of water molecules, pre-existing H
2
molecules are released even faster, as they have
a lower binding energy with the regolith. These H
2
molecules would have already left the surface
86
before the temperature rise to the point of vaporization at their original site. Interestingly, our
previous MD simulations [154]) also demonstrated that pre-existing H
2
is a dominant product of
solar wind implantation. Therefore, it is possible that the impact-generated H
2
has a more gravity-
bound portion, which may have implications for the overall distribution of H
2
on the Moon.
6.4 Summary and Conclusions
This study focuses on investigating the dynamics of water molecules during micrometeoroid im-
pact. In order to better understand the impact process, the velocity distribution of water after the
impact is analyzed. The results of the study show that the overall velocity distribution can be fitted
by a mixture of Maxwellian distributions with different temperatures. The different groups of tem-
perature can be attributed to the origin of water molecules, which include both pre-existing water
molecules and newly formed molecules. This approach provides a more comprehensive under-
standing of the dynamics of water molecules during micrometeoroid impact, as it accounts for the
different sources of water molecules and their respective kinetic energies.
In addition, we believe that for the transport of water molecules due to impact is strongly af-
fected by the ratio of− OH and H
2
O. Previous studies were limited in their ability to distinguish
between− OH and H
2
O due to the low resolution of the 3− µm feature [16]. However, recent
measurements by Honniball et al. [19] using the 6− µm band provide direct evidence of the pres-
ence of water molecules on the lunar surface and make it possible to investigate the relative ratio
of− OH and H
2
O. The results of this study demonstrate the need for continued high-resolution
measurements of− OH and H
2
O to better understand the transport of water on the lunar exosphere.
Furthermore, the planned Lunar Trailblazer mission[155] as part of the NASA’s ARTEMIS pro-
gram aims to provide such high-resolution measurements of the lunar exosphere. With the high
resolution data telling the abundance of both− OH and H
2
O, the model in this chapter can be used
to construct a more comprehensive VDF for the exosphere modeling.
87
(a)
(b)
Figure 6.4: (a) Velocity Distribution Function of Ejected H
2
O in SiO
2
− OH case and (b) Velocity
Distribution Function of Ejected H
2
O in SiO
2
− H
2
O
This study provides important insights into the dynamics of water molecules during microm-
eteoroid impact and the transport of H
2
O and possible H
2
on the lunar surface. By refining our
88
understanding of these processes, we can better inform future lunar exploration and habitation,
including the potential use of water resources on the moon. Future studies could further improve
upon these results by using more complex models that consider additional factors that may influ-
ence the transport and distribution of water molecules on the lunar surface. Future work will need
to consider the number of Maxwellian distributions used for the mixture model while in this study
only two were used. While it is possible to increase the number of distributions, a simplified model
was used here by grouping all high-energy water molecules as post-impact released molecules. If
one takes a closer look into the high-energy group of water molecules, these molecules may have
different energy levels due to the temperature changes that occur after the impact. This is due to the
rapid change of temperature for micrometeoroid impact process, these molecules may be released
at different stages of the post-impact process and may therefore experience different temperatures.
However, the low-temperature feature is still observed, and the temperature and weight of this por-
tion are consistent with the two-temperature model, indicating that the two-group assumption is
still valid, and the physical processes explained in this chapter are not violated by the number of
groups assumed for the distribution.
89
Chapter 7
Implications of Water-Surface Interactions to the Measurement
of Icy Grains
The search for liquid water and potential habitable environments in our solar system has led to a
growing interest in the study of ice particles and their impact processes. In this chapter, we inves-
tigate the fragmentation process of water ice grains upon hypervelocity impact. Our investigation
reveals a two-stage fragmentation pattern, with inter-molecular fragmentation occurring at lower
velocities and inter-atomic fragmentation occurring at higher velocities. The impact angle strongly
affects both fragmentation patterns and the yield of H
2
and O
2
. However, we find that the outcome
of the impact remains the same for a given vertical component of the velocity (V× cos(i)).
We show that a power-law distribution fits well with the size distribution of clusters after inter-
molecular fragmentation, especially when the vertical component of the velocity is less than 3.6
km/s. Furthermore, the fitted power law indexes are consistent with previous ice impact experi-
mental results. However, when inter-atomic fragmentation begins, the power index decreases as
large clusters are further fragmented by the free hydrogen produced in this regime. This fragmen-
tation leads to the formation of H
2
and O
2
starting at a velocity of 6 km/s. We propose using the
relative yield of H
2
and O
2
as an alternative method for estimating impact velocities of ice grains
at high velocity ranges. This combination of power-law distribution and chemical yield can offer
a wider range of impact velocity probing for future space missions that involve sampling of ice
grains.
90
7.1 Motivations
Water is one of the most abundant compounds in the solar system. Its presence has been detected
on many planets, moons, and comets besides the earth. The “ocean worlds” objects in the outer
solar system have long been a propriety in planetary sciences, and are targets of both past planetary
missions, such as Cassini and Galileo, and future missions, such as the Europa Clipper [91] and
JUICE [156]. As part of the Europa Clipper mission, a flyby of the plume of Europa is planned
to collect ice particle samples and determine their chemical composition, velocity, and size [157].
The samples will be analyzed using various instruments, including a mass spectrometer and a dust
analyzer, to determine their chemical and physical properties. As the relative velocity between ice
grains and the spacecraft can be as high as 20km/s, it is critical to understand the dynamics and
chemical reactions related to hypervelocity ice grain impact.
Previously, the Cosmic Dust Analyzer (CDA) aboard the Cassini spacecraft provided the mass
spectra data for investigation of the impact process of ice grains around Saturn and its moons [158].
Recently, Klenner et al. [159] conducted a laboratory analogue experiment to reproduce the mass
spectra of water ice grains. The results showed that the ionization conditions varied substantially
depending on the impact speeds of the ice grains onto the metal target of the mass spectrometer.
These variations led to changes in the resulting mass spectra. Similarly, the mass spectra obtained
by Nelson et al. [160] and Ulibarri et al. [88] by hypervelocity of an iron particle on a water ice
layer also showed distinct distributions of water clusters by varying impact velocity. Moreover, the
time of flight mass spectrometer utilized by Surface Dust Analyser (SUDA) exhibits a resolution
of m/∆m= 200 [159], where m is the mass of the particle and δm is the error brought by the
instrument. The resolution is substantially greater than the resolution exhibited by CDA, ranging
from m/∆m= 20− 50 [159]. The precision of SUDA enables the distinguishing of larger clusters
and allows for a more in-depth analysis compared to the mass spectra data acquired through CDA.
It is worth noting that the Enceladus Ice Analyzer, a future conceptual mission, has the potential
to reach a resolution of up to
m
∆m
≈ 1000 [161, 41], which is close to the resolution of laboratory
91
analogue experiments mentioned above. This suggests the possibility of estimating the impact
velocity of ice grains utilizing the mass spectra generated by impact ionization.
The impact velocity of dust particles has been measured in several previous missions by observ-
ing the changes of electric charge of highly polarized polyvinylidene fluoride (PVDF) plastic films
caused by hypervelocity dust penetration. Alternatively, the Wild-2 mission used aerogel to collect
dust grains, and estimated the impact velocity from the trajectory of dust in the gel . However,
water ice grains differ from dust grains in that they are highly volatile. Significant ionization and
fragmentation occur to ice grans during the impact process. Thus, previous measurement methods
designed for dust grains may not be applicable for ice grains.
Recently, atomic-scale molecular dynamics (MD) simulations [90] were applied to investigate
the fragmentation processes of astrobiology-related molecules undergoing hypervelocity impacts
(HVIs). Schulze et al. [162] further investigated the effect of salts on the fragmentation of amino
acids. The protocols and procedures to study molecular HVI were also systematically discussed
in [90, 162]. These studies showed that it is critical to measure the impact velocity of ice grains
accurately because the impact velocity is directly related to the fragmentation of possible probiotic
molecules inside. In this chapter, we apply atomic-scale MD simulations to investigate hyperve-
locity impact of ice grains. We consider a wide range of ice grain sizes and impact velocities,
and focuse on the fragmentation of larger size ice grains. We also present a statistical analysis of
impact-generated water clusters, and explore a possible new method for in situ measurement of ice
impact velocities.
7.2 Simulation Setup
MD simulation is a first-principles-based modeling method used to simulate the interactions be-
tween atoms. In MD simulation, the positions of atoms are resolved through integrating newton’s
equations of motion with an interatomic potential used to define forced between interacting atoms.
In this chapter, we apply the recently developed reactive molecular dynamics (RMD) simulation
92
model [92]. The RMD model utilizes the reactive force field (ReaxFF) to model the bond strength
in chemical reactions, where the inter-atomic potentials explicitly represent the bond energy, and
the bond formation and breaking process can be resolved in a simulation. The use of ReaxFF
reduces the computational costs while accurately describing the energy landscape obtained from
quantum mechanics calculations.
Fragmentation and clustering of water ice is dominated by the hydrogen bonding between
molecules. The bond breaking and forming processes occur during the decomposition of wa-
ter molecules and the formation of new molecules. The RMD model calculates the bond order
explicitly, allowing for quantitative simulation of bond breaking and forming processes. The sim-
ulation considers both chemical reactions and atom dynamics, which are essential for accurately
understanding the impact process comprehensively. By directly defining velocity magnitude and
direction, we can simulate high pressure and temperature conditions and investigate the effects
induced by different impact parameters.
The force field used in the simulations is developed by Fogarty et al. [93] and has been tested
for the silica-water system. The model and force field were also used previously to simulate mi-
crometeoroid impact-generated water molecules on the Moon [3].
Similar to Jaramillo-Botero et al. [90], A Lennard-Jones 12-6 wall is set up to mimic the wall of
detector as none to few reactions occur between the ice particle and the wall. The energy potential
describing the interaction of any molecules with the wall is:
E = 4ε
σ
r
12
−
σ
r
6
r< r
c
(7.1)
Where r is the distance from the particle to the wall, r
c
is the cutoff distance beyond which the in-
teractions between the wall and particles is negligible, andε andσ are Lennard-Jones parameters.
Following the setup of [90], we use r
c
= 2.5
˚
A,ε =1.0 kcal/mol, andσ = 1
˚
A.
The simulation setup is shown in Figure 7.1, showing the impact of a water ice grain onto a
target surface. Computational constrains limit the size of ice grains that can be modeled in an
atomic-scale simulation. Schulze et al. [162] simulated a 3.2 nm diameter water ice nanoparticle
93
with an impact speed in the range of 1-12 km/s and impact angle of i= 0
◦ . In this chapter, we
simulate a 8 nm diameter water ice grain with an impact speed in the range of 1-24 km/s and an im-
pact angle of 0-80 degrees from the normal direction of surface. The water ice grain contains 7453
number H
2
O molecules. As the results in the next section show, a 8nm diameter grain produces
sufficiently different clustering features and fragmentation patterns for the purpose of studying
the fragmentation process. Since the physical nature of fragmentation is the breakup of chemical
bonds between molecules or atoms through collisions between individual water molecules. Both
the impact energy and number of bonds grows linearly with the number of water molecules and
as a result, the division between the different fragmentation regime is independent of the grain
size. To setup the molecular structure for the pre-impact water ice grain, we use an Ice-Ih struc-
ture and ran canonical ensemble (NVT) simulation for 10,000 steps at 130 K (surface temperature
around Europa [163]) with a time step of 0.5 fs in order to relax any overlapping atom setup. for
relaxation. The ice grain is than assigned an impact velocity. For impact simulation, we use a
velocity-dependent time step of dt= 0.12/V fs, where V is the magnitude of the velocity in km/s.
Test runs show that this time step accurately captures the chemical reactions and fragmentation
during the hypervelocity impact.
We perform a cluster analysis to identify the neighboring atoms based on their distances and
bond orders. Here, we utilize a cut-off distance equal to the regular hydrogen bond length between
water molecules to identify multiple water clusters within the system. This cut-off distance is
chosen as 3.3 A based on the largest distance of the hydrogen bond that connects water molecules
in a cluster [164]. Based on the bond order defined by the force field, we identify that the H-H
bond and the O-O bond typically break at a distance of 0.74A and 1.4A, respectively, during the
impact process. These bond distances are used in the group analysis to identify any H
2
and O
2
molecules generated during the impact. An example of the cluster detection is given in the right
side of Figure 7.1 which shows the ejecta after the impact event. The zoomed-in snapshots (a)-(c)
shows the fragments resulting from the impact. Snapshot (a) shows monomers(H
2
O)
1
and dimers
(H
2
O)
2
as the smallest fragments. Snapshot (b) shows the slightly larger fragment (H
2
O)
3
and
94
Figure 7.1: Left: simulation setup and molecular structure of an ice cluster. Right: cluster analysis
of the resulting ejecta (a) monomers and dimers (b) trimmers (c) large clusters.
snapshot (c) shows a large fragment consisting of several water molecules. We also built hydrogen
bonds between water molecules to show the connections.
7.3 Results and Discussions
Previous studies by Kato et al. [165] and Buhl et al. [166] found that the size distribution of ice
fragments follows a power-law distribution. To investigate this distribution at a molecular level, we
sample the fragmentation size and number distribution in our simulation. In this study, we define
the size of fragments as the number of atoms in an individual cluster, denoted as S. We analyze the
number and size of the clusters after impact versus the impact speed and angle.
Figure 7.2 shows the number of clusters (N
clusters
) versus the impact speed for different impact
angles. Figure 7.3 shows the maximum size of the clusters (S
max
). We find that the impact angle has
95
Figure 7.2: Number of clusters after hypervelocity ice impact against the magnitude of velocity
a strong effect on the fragmentation pattern. At an angle of 80
◦ , fragmentation was not significant
until the impact speed exceeded 8 km/s. On the other hand, for normal impact (impact angle of
0
◦ ), fragmentation begins at an impact speed of just 1 km/s, although the majority of the water
molecules remained grouped together. Also at normal impact, with an impact velocity of 6 km/s,
complete breakdown of the clusters occurred, as evidenced by a maximum cluster size approaching
3, the number of atoms in a single water molecule.
Figure 7.4 and Figure 7.5 further show the number of clusters, N
cluster
, and the maximum
size of the clusters, S
max
, versus V
n
, All the curves in Figure 7.3 and Figure 7.2 overlap with the
normal impact (i= 0
◦ ) case, suggesting that the fragmentation pattern is mostly controlled by the
impact velocity component normal to the target surface, V
n
= V cos(i). This can be explained by
the mechanism of the fragmentation, i.e. the collisions between the atoms. For the same V
n
, the
collision frequency between the atoms in the ice grain and that in the target surface is the same.
Thus, the resulting fragmentation patterns are similar.
We next analyze the distribution of the post-impact ice grain size. Figure 7.6 shows the size
distribution for impact angle of 60
◦ , where the x-axis is the number of atoms in each individual
cluster, the y-axis is the impact velocity, ranging from 1 km/s to 12 km/s, and the z-axis is the
96
Figure 7.3: Size of the largest cluster after hypervelocity ice impact against the magnitude of
velocity
Figure 7.4: Number of clusters after hypervelocity ice impact against vertical component of the
velocity
97
Figure 7.5: Size of the largest cluster after hypervelocity ice impact against vertical component of
the velocity
corresponding number of clusters for each size in logarithmic scale. We set the size range as
S
max
= 50, based on the mass range of interest of m= 1− 250 for the SUDA instrument on the
Europa Clipper Mission [91].
We find that the number of small post-impact clusters is relatively small for both the small and
large V
n
(V
n
< 1 km/s and V
n
> 6 km/s) as compared to the middle range of V
n
(1 km/s< V
n
< 6
km/s ) At small V
n
, the impact energy is not high enough to trigger fragmentation, resulting in most
water molecules remaining clustered together as in the initial setup depicted in Figure 1. On the
other hand, at large V
n
, the impact energy is so large that collisions between particles broke apart
the bonds between individual molecules, leaving the ejecta mostly consists of individual water
molecules.
We carry out a power law fitting of the post-impact ice grain size distribution. For S
max
<
100, the number of fragments is too small to provide meaningful results. Hence, the power law
fitting is performed only for impact scenarios with S
max
≥ 100. We include both (H
2
O)
n
H and
(H
2
O)
n− 1
OH as part of the(H
2
O)
n
bin. These clusters, which have an H atom attached or missing,
have a very similar mass to (H
2
O)
n
(δm=± 1 amu). This is particularly important for larger
98
impact velocities where these types of ions were observed. It is worth noting that for most mass
spectrometry experiments, only the positive mode is presented, where H
2
O
n
(OH)
− 1
is usually
missing. However, it can be found in the negative mode from the mass spectrometer [167].
Figure 7.6: Pseudo Mass Spectra of Cluster after Hypervelocity Ice Impact with i= 60
◦ Ice impact experiments measure the cluster size by diameter. To compare with previous exper-
imental results on size distribution [165, 168, 166], we convert the the number of atoms in a cluster
obtained in simulation, S, to the diameter, D.
n(S)∝ S
k
,N(> S)∝ S
k+1
∝ S
n
1
,N(> D)∝ D
3(k+1)
∝ D
n
2
(7.2)
where n(S) is the number density of a cluster with size S, which has the power index of k . Then the
cumulative distribution has the power index of k+ 1, we denote it as n
1
. We also derive the power
index that was usually used in ice impact experiments which is the diameter of the ice fragments
n
2
= 3(k+ 1)
Figure 7.7 shows the power index (n
2
) against V
n
. Kato et al. [165] measured the index n
2
to be
between -1.8 to -3.6, Buhl et al. [166] measured the index to be within -2.9 to -3.7, and Miljkovi´ c
et al. [168] measured the index to be around -2.6. The impact angle was not clearly indicated in
99
Figure 7.7: Power-law index (n
2
which is usueal) fitting against vertical component of the velocity
Buhl et al. [166]. Assuming i= 45
o
, which is usually used in hypervelocity impact experiments,
we find the maximum V
n
in previous experiments is around 3.5 km/s. Our simulation results show
good agreement with the measurements in the range V
n
< 3.5km/s. The power index remains
nearly constant, at -2.4 to -3.6 for V
n
at 1.9 km/s to 3.6 km/s. Our simulation results show that the
power-law distribution with n
1
as the mass distribution index and n
2
as the size distribution index
applies when the size of the post-impact grains are on the order of nanometers or smaller.
For V
n
< 1.8km/s, most of the water molecules remain in the pre-impact ice grain. Thus, there
are not sufficient fragmented ice grains for power law fitting. Hence, the variation is large and the
fitting is not ideal. For V
n
> 3.6km/s , we observed a decrease in the power-index. This indicates
a reduction in the number of large fragments due to ionization and interatomic fragmentation.
At still larger V
n
, the collisions between molecules/atoms can break the covalent bonds between
H and -OH in a water molecule, resulting in the production of a significant amount of free H
atoms or protons. Those free H/OH carries similar energy level as a water molecules thus can also
cause fragmentation similar to reflected water molecules. As a results the total number of reflected
100
particles increases and the power index decreases. This also contributes to a significant feature of
(H
2
O)
n
H and(H
2
O)
n− 1
OH shown in the pseudo mass spectra plot (Figure 7.6). For low-velocity
impact, only S = 3n columns are evident, but with an increasing impact velocity, (H
2
O)
n
H and
(H
2
O)
n− 1
OH become more significant.
Due to the production of high-velocity free H atoms, the interatomic fragmentation domi-
nates at high normal impact velocities. Thus, we can characterize fragmentation into two regimes:
inter-molecular fragmentation, where bond-breaking occurs only at the inter-molecular level, and
interatomic fragmentation, where dissociation within the water molecule occurs. The dissociation
energy for H
2
O= H+ OH is 115.188 kcal/mol (or 4.995 eV) [90]. In our simulation, the col-
lision between the impinging and reflected molecules occurs at relative speed of about twice of
V
n
. Assuming all the impact energy is used to cause dissociation, the impact speed required for
dissociation is 3.658 km/s. This provides an explanation for the decrease in power index observed
beyond V
n
≃ 3.6km/s.
There exist a transition region between inter-molecular fragmentation and inter-atomic frag-
mentation. Although inter-atomic fragmentation starts at V
n
∼ 3.6km/s, not all the water molecules
experience this high energy. This is indicated in Figure. 7.5 where the maximum size of the cluster
in the system is still very high at V
n
≃ 3.6km/s. We notice that , as V
n
increases, inter-molecular
fragmentation stops at V
n
> 6km/s. This is because, at V
n
∼ 6km/s, the largest post-impact cluster
is already single water molecule.
At V
n
> 6km/s, we find new chemical species such as H
2
and O
2
are generated at the end of
the simulation. The increased generation of H
2
and O
2
can be attributed to the fact that the free H
and O atoms have a greater chance to combine without being attached to a H
2
O cluster or break
a hydrogen bonds between water molecules. Figure 7.8 and Figure 7.9 illustrate the generation of
H
2
and O
2
, respectively, with the absolute number of molecules generated on the left axis and the
relative yield with respect to the total water molecules on the right axis. The fact that the yield of
H
2
and O
2
is a function of only V
n
is consistent with our previous fragmentation analysis shown
in Figures 4 and 5. This confirms that the normal velocity component V
n
dominates the chemical
101
reactions during hypervelocity impacts. Notably, we find that the peak yield of H
2
occurrs at
V
n
∼ 14 km/s, which corresponds to the critical threshold for electron impact ionization. Similarly,
the peak yield of O
2
occurrs at V
n
∼ 17 km/s is consistent with the electron impact ionization
threshold for O
2
. Thus, our results suggest that electron impact ionization plays a crucial role in
the formation of H
2
and O
2
during hypervelocity ice impact.
The generation of H
2
and O
2
during hypervelocity impact has also been observed in previous
experiments and CDA mass spectra. For example, Klenner et al. [159] showed a clear signal of O
+
2
and H
+
2
in the baseline-corrected CDA mass spectra with a velocity range of 18-21 km/s. In addi-
tion, Ulibarri [167] and Nelson et al. [160] reported the presence of H
+
2
in high-velocity impact.
One expects that O
2
can also be detected in the negative mode. With a high mass resolution, H
2
should be easily distinguished from H+ or H
+
3
, and O
+
2
can be detected as an independent signal
in the time-of-flight mass spectrometer.
7.4 Implications for Ice Impact Velocity Measurement
The power-law index can be used a useful tool for estimating the impact velocity of ice grains
for inter-molecular fragmentation. However, our results show that for hypervelocity impact of ice
grains at V
n
> 6km/s, significant inter-atomic fragmentation will occur. This leads to the absence
of large clusters, and thus making the power-law fitting an unreliable method for estimating impact
velocities. This issue is evident in [159], where the number of water cluster spectra lines decreases
as the impact velocity increases. Furthermore, at impact speeds of 13-15 km/s, H
3
O
+
accounts
for more than 97.65% of the spectra lines. These findings suggest that additional methods may be
required to accurately estimate the impact velocity for hypervelocity impact.
To address the limitations of power-law fitting for the situation where significant inter-atomic
fragmentation occurs, we suggest an alternative method that may be used to estimate the impact
velocity by analyzing the production of H
2
and O
2
, as shown Figure 7.10. We derive the ratio
between the yields of O
2
and H
2
and plot it as a function of V
n
in Figure 7.11. Figure 7.11 show a
102
strong linear correlation between the H
2
to O
2
ratio and V
n
. This suggests that this ratio can serve
as a reliable parameter for measuring the impact velocity at V
n
> 6 km/s, where power-law fitting
may not provide an accurate estimate. This approach is also supported by Klenner et al. [159],
who observed a strong signal of O
+
2
and H
+
1− 3
in the data from Cassini missions.
Figure 7.8: Number of molecular hydrogen (H
2
) generated and ratio of H atoms in H
2
from H
2
O
Figure 7.9: Number of molecular oxygen (O
2
) generated and ratio of O atoms in O
2
from H
2
O
103
Figure 7.10: Yield of molecular hydrogen (H
2
) and molecular oxygen (O
2
) against vertical com-
ponent of the impact velocity
Figure 7.11: Relative ratio of molecular oxygen(O
2
) yield and molecular hydrogen (H
2
) yield from
H
2
O
7.5 Conclusion
This chapter presents a comprehensive analysis of ice cluster impacts at angles ranging from 0
to 80 degrees and velocities ranging from 1 to 24 km/s. Our investigation revealed that impact
angle strongly affects both fragmentation patterns and the yield of H
2
and O
2
. However, we found
104
that the outcome of the impact remains the same for a given vertical component of the velocity
(V× cos(i)).
Our analysis identified a two-stage fragmentation pattern, namely inter-molecular and inter-
atomic fragmentation. We found that a power-law distribution fits well with the size distribution
of clusters after inter-molecular fragmentation, especially when V
n
< 3.6km/s. Furthermore, the
fitted power law indexes are consistent with previous ice impact experimental results. However,
when inter-atomic fragmentation begins, the power index decreases as large clusters are further
fragmented by the free H produced at this regime. Inter-atomic fragmentation leads to the forma-
tion of H
2
and O
2
starting at V
n
= 6km/s. We propose using the relative yield of H
2
and O
2
as an
alternative method for estimating impact velocities of ice grains at high velocity ranges. This com-
bination of power-law distribution and chemical yield can offer a wider range of impact velocity
probing for future space missions that involve sampling of ice grains.
105
Chapter 8
Unraveling Impact Generated Exosphere of Icy Surfaces: the
Role of Clustering
Velocity distribution is an essential part of the exosphere modeling of planetary bodies as discussed
in chatper. 6. We based on the clustering features found from chapter. 7 and build a more compre-
hensive velocity distribution function (VDF) for the impact generated exosphere on icy surfaces.
In particular, the clustering of water molecules strongly deviates the VDF from a Maxwellian dis-
tribution, which was commonly used for the modeling of impact generated exosphere. We then
constructed a mixed-Maxwellian distribution to incorporate clustering features. The study shows
that for celestial bodies with large escape velocity such as Mercury, the difference of surface-
bounded portion in the ejecta between mixed and single Maxwellian distribution is within 10%.
However, for smaller icy satellites such as the Moon, Europa, the difference ranges from 60% to
100%. For even smaller bodies like Ceres, Tethys, and Enceladus, the error is as high as 300%.
The importance of carefully selecting the power index in modeling water molecules and ice par-
ticles is also emphasized. The findings suggest a different theory for impact generated exosphere
for water ice regions or icy bodies.
106
8.1 Motivation
Water ice is a fundamental compound throughout the solar system and is present in numerous ce-
lestial objects, including planets, moons, and comets. Recent discoveries of water ice on the Moon,
Mercury, Ceres represent significant breakthroughs in our understanding of the solar system’s wa-
ter cycle and have implications for future space exploration. For instance, the detection of water
ice on the Moon [13, 101, 169], particularly in the permanently shadowed regions, is a remarkable
achievement in comprehending the solar system’s water cycle and presents prospects for future
space exploration. LCROSS analyzed the Cabeus crater floor plume and found 4-6% water and
0.1-1% complex volatile molecules, which was reported by Colaprete et al. [17] and Schultz et al.
[170]. Similarly, Mercury Surface, Space Environment, Geochemistry and Ranging (MESSEN-
GER) detected evidence of water ice on Mercury’s surface by identifying bright reflective areas at
the planet’s poles using a neutron spectrometer and a laser altimeter [171]. Additionally, ice was
confirmed on dwarf planets such as Ceres by data from the Dawn mission [172].
Space weathering processes play a critical role in the evolution and understanding of icy bodies
within our solar system. Exposure to solar radiation, cosmic rays, and micrometeorite impacts over
time modify the physical and chemical properties of the icy surfaces, leading to the change of com-
position that can have significant implications for astrobiology and planetary science [173]. These
processes can influence the reflectivity and spectral characteristics of the surface, significantly af-
fecting our remote sensing observations. Moreover, the redistribution of volatiles, formation of
complex organics, and production of exospheres, instigated by space weathering, could potentially
hold clues to the solar system’s early history and the origins of life itself.
Farrell et al. [174] proposed four mechanisms for releasing water molecules from regolith on
the lunar surface, including solar wind ion sputtering, electron stimulated desorption (ESD), pho-
ton stimulated desorption (PSD), and impact vaporization. Impact vaporization has the largest
polar source flux of water molecules, making it essential to understand how water molecules are
transported during impact on the moon. To simulate the transport of water molecules induced by
solar wind sputtering and impact vaporization, Farrell et al. [85] used a Monte Carlo method. This
107
model estimates whether water will be surface bounded or escaped based on the velocity distri-
bution function. Molecules ejected by sputtering follow a Sigmund-Thompson distribution [175],
while those ejected by impact vaporization generally follow a Maxwellian distribution with tem-
perature estimated by [54]. A detailed review of the exosphere transport of water molecules can
be found at [118].
However, experimental studies [165, 166, 176] have shown that clustering of water molecules
are commonly found during hypervelocity ice impact. Such experiments are motivated by mod-
eling secondary craters on planetary surfaces caused by impact ejecta and thus the ejecta counted
are relatively large grains (>0.1 µm). Fragments produced after a hypervelocity impact event are
found to follow a power-law distribution in both size and mass. For a much smaller scale (molecu-
lar level), which are typically considered in exosphere transport modeling, clustering is also found
to be significant. Ulibarri [167] and Nelson [87] used a time of flight mass spectrometer to detect
fragmentation of water ice upon the hypervelocity impact of an iron grain. In particular, Nelson
[87] examined impact velocities ranging up to 25 km/s ([87]) and demonstrated the presence of
large clusters. For instance, large cluster up to(H
2
O)
33
H was found for 16km/s impact case. (Fig.
3.2 from [167]). These findings provide clear evidence of the existence of large water clusters
generated during hypervelocity impact in a wide range of scales.
The mechanism that underlies the fragmentation of ice during hypervelocity impacts is rooted
in the hydrogen bonding that exists between water molecules in an ice structure. Depending on
the energy released by the impact, some of these bonds can survive and link individual molecules,
leading to the creation of water clusters. These clusters can have a much greater mass than indi-
vidual water molecules and, therefore, a lower average velocity. The surface bounded exosphere is
directly determined by the velocity distribution of ejected molecules. As a result, the release of wa-
ter molecules in the form of clusters during hypervelocity impacts can lead to an underestimation
of the proportion of ice captured by gravity if we assume that most water molecules are released as
single molecules. Therefore understanding the formation of water produced during impact would
be necessary to model the surface-bounded exosphere for ice-rich regions of planetary bodies.
108
Previous experiments mostly focused on measuring the size distribution of fragments [165,
166]. However, the dynamics of ejecta remain a significant limitation. One of the primary chal-
lenges in studying ejecta dynamics is the wide range of fragment sizes and velocities that can be
generated during an impact. Smaller fragments tend to have higher velocities, making them more
challenging to track with conventional detectors. Additionally, the angular distribution of frag-
ments can be highly anisotropic, meaning that they are ejected in different directions with different
velocities. This anisotropy can make it difficult to obtain a complete measurement of the ejecta dy-
namics. In chapter 7, we investigated the fragmentation of an ice nanocluster under hypervelocity
extensively using reactive molecular dynamics simulation. The combination of bond order calcu-
lation based on first-principle trained force field and Newtonian equations provide a way to track
both chemical bond breaking and forming as well as the dynamics of molecules. Similar methods
have been used to understand chemical reactions that leads to the formation of water molecules on
the lunar surface including the dynamics of those molecules [3, 154].
In this chapter, we extended previous research by performing an analytical study of the sur-
face bounded exosphere taking into account the clustering of water molecules during impact. We
investigate how clusters of ice affect the portion of water molecules captured by gravity, which is
crucial for understanding the distribution and transport of water molecules on icy bodies. We test
our analytical model on several planetary bodies with ice regions, including the Moon, Mercury,
Ceres, where the presence of water ice has been confirmed by various missions. By considering the
clustering of water molecules, we can improve our understanding of the potential for habitability
on these icy bodies and inform future space exploration efforts.
109
8.2 Method and Formula
8.2.1 Mixed Maxwellian Distribution for Water Clusters
We use the single Maxwellian velocity distribution function (VDF) to model the ejecta that con-
tains only individual water molecules, and the mixed Maxwellian VDF to take into account of the
effect of clustering. The commonly used single Maxwellian VDF is:
f(v)=
m
2πkT
3/2
4πv
2
e
− mv
2
2kT
(8.1)
As introduced before, power-law distribution provides the best fit for the size distribution of
fragments ([165] and reference within). By defining S as the size of the cluster, i.e. (H
2
O)
S
. The
cumulative distribution of water clusters is:
N(> S)∝ S
− a
(8.2)
One can then derive the size distribution based on the cumulative distribution function as:
n(S)∝ S
− a− 1
(8.3)
The proportion of each cluster from cluster size 1 to n is then:
ω
cluster
(S)=
S
− a− 1
∑
S
cuto f f
S=1
S
− a− 1
(8.4)
As a cluster contains S water molecules, the probability of finding a water molecules in a cluster
with size of S is then:
ω
H
2
O
(S)= S× S
− a− 1
∑
S
cuto f f
S=1
S× S
− a− 1
=
S
− a
∑
S
cuto f f
S=1
S
− a
(8.5)
110
For different size distributions, the resulting velocity distribution would also be different as
they have different mass. The VDF assuming equilibrium for each clusters with their size equals
to S is:
f
S
(v)=
Sm
2πkT
3/2
4πv
2
e
− Smv
2
2kT
(8.6)
Taking the proportion of size as the weight for each specific distribution, the overall VDF is in
the form of:
f
all
(v)=
S
cuto f f
∑
S=1
S
− a
∑
S
cuto f f
S=1
S
− a
Sm
2πkT
3/2
4πv
2
e
− Smv
2
2kT
(8.7)
By setting an escape velocity of a celestial body, one can estimate how much water can be
captured by gravity. S
cuto f f
is taken as 33 based on the largest cluster detected in hypervelocity ice
impact experiment by Nelson [87].
8.2.2 Validation of multiple Maxwellian Distribution
In a companion paper, we conducted a thorough examination of the ice cluster fragmentation pro-
cess resulting from hypervelocity impact, where we found that the power-law distribution observed
from our simulations aligned with experimental results. While previous experiments have primar-
ily focused on investigating the characteristics of the fragmentation process itself, few have ex-
plored the dynamics of the resulting ejecta. Utilizing molecular dynamics (MD) simulations, we
were able to track the position and velocity of every atom, thereby enabling us to take a closer
look into the kinetic energy of ejecta. Specifically, by performing cluster analysis, we can identify
individual clusters and sample the velocity distribution function of each clusters. This provide an
unique opportunity to compare the dynamics of single water molecules and clusters.
The simulation is performed with V = 12km/s with impact angle i= 45
◦ . The beginning ice
cluster is consist of 7453 water molecules which makes the diameter around 12 nm. After the
impact, we found 1304 H
2
O molecules and 495(H
2
O)
2
clusters in the ejecta.
111
Figure 8.1: Validation of Mixed Maxwellian Distribution by Reactive Molecular Dynamics Simu-
lation
By sampling the velocity distribution of each particle type individually, we obtained a clear
two-temperature Maxwellian distribution. Making use of the machine learning algorithm ”Maxwellian
Mixture Model” described in Sec. 2.3. Two histograms were generated to display the statistics of
the velocity distribution for both the individual molecules and clusters, respectively in Figure.8.1 .
We found that a Maxwellian distribution with a temperature of 4591.34 K fit well with the (H
2
O)
2
velocity distribution, while a temperature of 7893.45 K fit well with the H
2
O velocity distribution.
These findings align with Eq. 8.6, which suggests that an equivalent temperature of T/S would be
appropriate for each cluster with size S. Although we were able to detect the presence of(H
2
O)
3
and up to (H
2
O)
10
, statistics of those large clusters were not significant enough due to limited
sample size. Nonetheless, the kinetic of (H
2
O)
2
and H
2
O is able to validates Eq. (6), indicating
that our overall distribution analysis considering clusters holds true.
112
8.3 Results and Discussions
8.3.1 Dependence on the Escape Velocity
Figure 8.2 compares the velocity distribution functions (VDFs) of a single Maxwellian distribu-
tion (described by Eq.8.1) and a mixed Maxwellian distribution (Eq.8.6) for different vaporization
temperatures. The range of impact velocities tested in this study covers temperatures from T =
1000 K to T = 10000 K, which is consistent with previous research on impact velocity distribution
[54] and temperature of water vapor under the compression of shock [177]. The solid curves in
Figure 8.2 represent the VDFs for the mixed Maxwellian distribution, while the dashed curves
represent the VDFs for the single Maxwellian distribution. Each curve is color-coded by the va-
porization temperature. The mixed Maxwellian distributions exhibit a lower average velocity and
a narrower velocity distribution compared to the single Maxwellian distributions. This difference
can be attributed to the presence of larger particles, or clusters, in the mixed distribution, which
have a higher equivalent mass than smaller particles. The thick black curves indicate the escape
velocity for several celestial bodies, including Europa, the Moon, and Mercury. Integrating the
VDF in Figure 8.2, one can obtain the culmulative distribution function (CDF) in Figure 8.3. The
intersection points between each CDF curves and the escape velocity dashed curves shows the
probability of finding an ejected particle with a velocity lower than the escape velocity, denoted
by P(V < V
escape
). This value is an important metric for understanding the likelihood of ejecta
deposition and whether it can escape the gravity or not. The mixed Maxwellian distribution tends
to exhibit a higher probability of finding ejected particles with velocities below the escape velocity,
whereas the single Maxwellian distribution yields a lower probability.
We define ω =
N
bounded
N
all
as the ratio of the molecules bounded by gravity to the total water
molecules ejected, where the subscript “single” denotes the single Maxwellian VDF and the sub-
script “mixed” denotes the mixed Maxwellian VDF. Figure. 8.4(a) shows ω
mixed
− ω
single
for the
three cases. The figure provides a clear illustration of the variation in the difference between
ω
mixed
and ω
single
across the three celestial bodies with different escape velocities. This variation
113
Figure 8.2: Velocity distribution function for Single Maxwellian (dashed curves) and Mixed
Maxwellian (solid curves). Black dashed line indicates the escape velocity of Europa, the Moon
and Mercury
Figure 8.3: Cumulative distribution function for Single Maxwellian (dashed curves) and Mixed
Maxwellian (solid curves). Black dashed line indicates the escape velocity of Europa, the Moon
and Mercury
114
Figure 8.4: (a) Difference of surface bounded portion between single Maxwellian distribution and
mixed Maxwellian distribution (b) Relative difference assuming single Maxwellian distribution
indicates the importance of escape velocity in determining whether a single or mixed Maxwellian
distribution should be used to model the velocity distribution of water molecules. As the impact
vaporization temperature becomes higher, the difference also becomes more significant, however
depending on the escape velocity, the difference for the case of Europa declines starting from
6000K as when the temperature is higher, large clusters also gain enough velocity to escape the
gravity.
We further calculate the relative difference,ε, between the results using the mixed Maxwellian
VDF and the single Maxwellian VDF:
ε =
ω
mixed
− ω
single
ω
single
(8.8)
The results are shown in Figure 8.4(b). The relative difference reveals a strong dependence
on the escape velocity of planetary bodies. As shown in Figure 8.4(b), for Mercury, where the
escape velocity is V
escape
= 4300m/s, the largest difference is within 10%, suggesting that a single
Maxwellian VDF may be sufficient to accurately model the velocity distribution of water molecules
115
in this scenario. However, as the escape velocity decreases, the relative difference increases signif-
icantly. On the Moon, the largest difference is 76%, which is considered significant and highlights
the limitations of a single Maxwellian distribution in accurately modeling the velocity distribu-
tion of water molecules in low escape velocity environments. Similarly, for Europa, the relative
difference is as high as 100%, indicating that using a single Maxwellian distribution may not be
sufficient to accurately model the velocity distribution of water molecules in this scenario. In fact,
the actual portion of surface-bounded water assuming a mixed Maxwellian distribution is almost
double that assuming a single Maxwellian distribution. In these cases, the effect of clusters domi-
nates the analysis of the surface-bounded exosphere, further highlighting the limitations of a single
Maxwellian distribution in accurately modeling the velocity distribution of water molecules in low
escape velocity environments. At an extremely high vaporization temperatures, neither the mixed
Maxwellian VDF nor the single Maxwellian VDF will have more energetic water molecules. As a
result, fewer water molecules fall within the range of escape velocities and the difference between
the two distributions decreases. This effect is due to the high energy of the impact event, which
leads to a wider range of velocities and a greater proportion of particles with velocities above the
escape velocity.
8.3.2 Sensitivity Test of Power Index
The significant difference observed in the case of Europa highlights the necessity of considering
cluster distributions, especially for icy moons. Many icy moons are believed to harbor organic
molecules, which could have important astrobiological implications. In this section, we investi-
gated the sensitivity of the selection of the power index, a, in Eq. 8.3 . The power index determines
the distribution of clusters, which is an essential component of the analysis presented in this chap-
ter. By varying the value of a, we were able to test the robustness of our results to changes in
the cluster distribution. Our analysis reveals that the choice of power index can have a significant
116
impact on the relative difference defined in Eq. 8.8, particularly in scenarios with low escape ve-
locities. Specifically, we find that when the power index is increased, the relative abundance of
surface bounded water molecules decreases as there are fewer clusters.
Based on previous studies, such as Kato et al. [165], the power index in Eq.8.3 is expected
to fall within the range of 0.67 to 0.72. To test the sensitivity of our results to changes in the
power index, we selected the upper bound of 0.72 and the lower bound of 0.67 as the extreme
values for our analysis. Our analysis, as shown in Figure. 8.5, reveals that even for Europa and
the moon, where the error is the largest, the deviation is controlled within 20%. This suggests that
the selection of the power index is valid and that our results are robust to changes in the cluster
distribution.
However, for smaller planetary bodies, such as Ceres, Tethys, and Enceladus, the relative error
varies a lot. Our analysis reveals that, for Enceladus, the error between the assumptions of mixed
and single Maxwellian distributions is as high as 300%, underscoring the importance of consid-
ering more complex distributions in this scenario. At the same time, we also observed the range
of the error is as high as 50%. This indicates a more accurate power-law index is needed to limit
the large deviation. In addition, the change power-index due to molecular structure and possible
chemical reactions are also necessary to be considered.
8.3.3 A General Model for All Exosphere Species
The model presented in this chapter has broad applicability beyond the study of water molecules
in hypervelocity impact. It is reasonable to assume that our findings could be extended to other
molecules or atoms commonly found in the exosphere that has the form of clusters. For instance,
calcium in the exosphere of Mercury, which has been studied by [178], is comprised of both Ca
atoms and Ca-Ca dimers. The Ca-Ca dimers are thought to be produced by the vaporization of
larger Ca clusters. This could also indicate that larger Ca clusters is also possible to exist in
Mercury’s exosphere with a lower altitude as the scale height of those larger cluster would be
smaller:
117
Figure 8.5: Relative Ratio of Mixed Maxwellian distribution compared with single Maxwellian
distribution for Mercury, Moon, Europa and Triton
Figure 8.6: Relative Ratio of Mixed Maxwellian distribution compared with single Maxwellian
distribution for Ceres, Tethys and Enceladus
118
H
S
=
k× T
m
S
g
=
k× T
S× m
1
g
(8.9)
where m
S
is the mass of(Ca)
S
. S =1 corresponds to the single Ca atom case. From a global point
of view, the overall exosphere is composed of multiple layers with scale height of(Ca)
S
equals to
H
S
.
In general, whether it’s necessary to use the mixed Maxwellian distribution rather than single
Maxwellian distribution depends on the species interested. If there is none or very weak binding
energy between the atoms or molecules then the ejecta would mostly consist of individual atoms
or molecules. For volatile species like water ice discussed in this chapter, Nelson [87] tested the
impact of iron to thick water substrate for the velocity from 0 - 25+ km/s. The range covers
average impact velocity of most celestial bodies which provides a good reference for the validation
studies here. While the mechanisms underlying fragmentation can be complex and multifaceted,
the findings of these experiments suggest that clustering and fragmentation are likely to occur
under certain conditions, particularly at higher impact velocities.
For mineral species, there have been extensive studies regarding the vaporization process, in
particular, complete vaporization and incomplete vaporization was discussed in Killen et al. [178] .
Depending on the impact velocity, when the pressure and temperature created by the impact leads
to incomplete vaporization, it’s necessary to consider mixed Maxwellian distribution discussed in
this chapter.
8.4 Conclusions
This chapter proposed a framework to analyze the transport of molecules in exospheres, partic-
ularly those composed of clustered molecules or atoms. In this study, we constructed a mixed
Maxwellian VDF by taking the power-law distribution as the size distribution of impact ejecta
and calculated the weighted distribution. The resulting VDF behaves differently from the single
Maxwellian VDF. Depending on the escape velocity, the amount of water captured by gravity
119
can be significantly underestimated. We quantitatively compared the relative difference of surface
bounded proportion between the two assumptions. For planets with large escape velocity like Mer-
cury, the relative difference is as low as 10%, however, for smaller icy bodies such as Europa , the
relative difference is as high as 100%. Future mission by Europa Clipper ([161]) can provide a
more accurate in-situ measurement of the power index by its mass spectrometer measurement of
ice grains hypervelocity impact.
The results presented highlight the need to accurately model the VDF of the ejected water
molecules in order to fully understand the physical processes that govern the transport of water
molecules in the exosphere. The results also show the importance of carefully selecting the power
index in order to accurately model the behavior of water molecules and ice particles in different
space environments, and to understand the formation and evolution of planetary systems, as well
as the behavior of water molecules and ice particles in other space environments. For instance,
with a small 8% of the variation of power index, resulting relative difference bar is as high as 50%
for the relative difference. Hence, it is necessary to further investigate the power index and provide
a more accurate model for it. Future research should involve a comprehensive analysis of the
power index by combining theoretical modeling, experimental studies and in-situ measurement.
While the analysis presented focuses on water ice ejecta, the model is applicable to the molecules
and atoms of a wide range of other volatiles and refractory materials in the exosphere, such as
the calcium exosphere discussed in [178]. This model can be used to establish a new exosphere
model with the clustering taken in to account. Future studies will also need to extend the model
to other species detected in the exosphere and compare with in-situ measurement of the exosphere
structure.
120
Chapter 9
Summary and Recommendation for Future Studies
In this chapter, the main findings and implications of the research conducted in this dissertation
are summarized and discussed. The research question of this dissertation aimed to develop a
physical-chemical understanding of the chemistry and dynamics of volatiles on the lunar surface
and icy moons. The study’s conclusions are presented, and recommendations for future research
are provided. These findings offer valuable insights into the formation and transport of volatiles on
planetary surfaces and exospheres. Moreover, this study sheds light on future human explorations
of the moon and icy moons by identifying the formation mechanisms of water molecules, which
are crucial for in-situ resource utilization.
9.1 Summary of Lunar Water Cycle Modeling
Three key space weathering processes that contribute to the formation of water were thoroughly in-
vestigated in Chapter 3-6. One of these processes entails chemical reactions resulting from dielec-
tric breakdown under extreme space weather conditions, which were identified through reactive
molecular dynamics simulation.
Additionally, the processes of solar wind and micrometeoroid impacts have been extensively
discussed in previous studies. However, the integration of chemistry and dynamics in these pro-
cesses has not been fully explored. While binary collision models utilize collision databases and
121
employ Monte Carlo methods to investigate the transport, they do not consider the chemical reac-
tions. Similarly, hydrodynamics codes employ equations of state to simulate the impact process
but do not capture the occurring reactions. In this study, reactive molecular dynamics simulation
offers a more accurate estimation of these two processes. By combining atomic-scale data with
the planetary-scale conditions described by the lunar space environment, these simulations have
implications for the water cycle in the permanently shadowed regions of the moon.
9.2 Discussion: Contribution of Dielectric Breakdown to the
Water Formation in a Grain Scale
Solar wind implantation contributes mostly to the− OH on the lunar surface instead of H
2
O. Mi-
crometeoroid impacts are believed to convert those implanted H into H
2
O. In this study, we in-
vestigate whether dielectric breakdown similarly contributes to the formation of water molecules.
From a planetary science perspective, the energy flux from solar energetic particle (SEP) events on
the lunar surface has been estimated to be comparable to that brought by micrometeoroid impacts
[75]. It is possible that dielectric breakdown, which has not yet been experimentally quantified,
could also contribute to water formation on a similar scale. To address this knowledge gap, we
provide an analytical estimation based on the results of our previous study (see Chapter 4). Ac-
cording to Garrett and Whittlesey [179], strong electric fields can accumulate up to a few hundred
microns, making it reasonable to assume that the entire implantation layer of a typical lunar dust
grain (diameter of 60 µm) experiences a strong electric field. We estimate the final water weight
ratio in the dust by assuming that the implantation layers containing H-rich regions have a similar
weight ratio as calculated in Chapter 4.
The scaling take the following equation:
ω
dust
=ω
nm
(R
3
dust
− (R
dust
− d
imp
)
3
)
R
3
dust
(9.1)
122
Whereω
dust
is the weight ratio at the lunar dust scale andω
nm
is the weight ratio at the implan-
tation layer. R
dust
represents the radius of the dust grain, and d
imp
denotes the implantation depth.
Figure 9.1 illustrates the variation of water content depending on the radius of a lunar dust grain,
assuming an implantation depth of 10 nm (considering an average implantation angle). For typical
lunar regolith with radii ranging from 10 to 100 µm, the water content varies between 10 and 325
ppm. Similarly, with an average radius of 30 µm and an implantation depth varying from 0 to 14
nm, the water content ranges from 0 to 144 ppm (Figure 9.2). These ranges align with the detected
water content at high latitudes, which is approximately between 0 and 500 ppm [16]. These results
suggest that dielectric breakdown alone can convert implanted hydrogen from the solar wind into
water and account for the observed content.
Figure 9.1: Water weight ratio when scaling up to the radius of lunar dust grain from 0-100 µ m
123
Figure 9.2: Water weight ratio when scaling up to implantation depth of 0-20 nm
9.3 Discussion: Timescale and Spatial Scale of Dielectric Breakdown
and Micrometeoroid Impact
The timescale and spatial scale of the three space weathering processes differ due to their respec-
tive origins. Implantation or proton events originate from the solar wind, which has an average
velocity of 400 km/s and a number density of n
sw
= 10/cm
3
. In permanently shadowed regions
(PSRs), the flux toward the surface is influenced by the plasma sheath formed inside the crater.
The perpendicular velocity (V
⊥
) is then determined by the ion acoustic velocity, which is approx-
imately 30 km/s. The number density can be orders of magnitude lower due to the expansion of
plasma flow to the wake region [116]. Therefore, the solar wind number density at PSRs can vary
124
between 0.01− 10/cm
3
. The saturation timescale for implantation ranges from O(10
1
) to O(10
4
)
years.
Micrometeoroid impacts are caused by interplanetary dust grains [120]. By utilizing the size
distribution of interplanetary dust and flux, we derived a timescale between two micrometeoroid
impact events (t
MMI
) using Equation 3.6 to be approximately 30,000 years. As discussed in Chap-
ter 4, dielectric breakdown is primarily influenced by the frequency of solar energetic particle
(SEP) events that induce breakdown. The timescale of dielectric breakdown is estimated by com-
paring the flux of SEP events and the energy level of the SEPs. In order to achieve the electric
field used in Chapter 4, the average timescale is on the order of O(10
3
) years at a temperature of
40 K. However, the timescale increases significantly as the temperature rises. Since the discharge
timescale decreases rapidly with temperature increase, at a temperature of 100 K, the timescale be-
comes two orders of magnitude higher, surpassing the timescale of t
MMI
. Consequently, dielectric
breakdown primarily dominates in extremely cold PSRs, while micrometeoroid impacts dominate
a wider range of areas.
As discussed in Section 3.4, if the timescale for converting hydrogen (H) to water molecules is
longer than the saturation timescale (t
SoI
), then H atoms from the solar wind will predominantly be
lost as H
2
molecules due to saturation. Micrometeoroid impacts, for example, have a timescale that
is longer than t
SoI
. Interestingly, the minimum timescale for dielectric breakdown falls within the
range of O(10
1
) to O(10
4
), which suggests that in extremely cold regions, dielectric breakdown
can convert H atoms from an unsaturated surface to H
2
O before the next dielectric breakdown
event occurs. This implies that the water cycle in these regions is dominated by a combination
of solar wind implantation and dielectric breakdown, rather than solar wind implantation and mi-
crometeoroid impact. The interval for the new cycle has a much lower timescale thus facilitate
the formation and accumulation of water. This supports the general idea that cold planetary solid
regions (PSRs) are more likely to retain H from the solar wind, resulting in a higher water content.
Here we use the timescales for different processes and estimate the water formation cycle
timescale in a crater. We took the kinetic particle in cell simulation from Zimmerman et al. [115]
125
to estimate the relative timescale of those three different process. The typical solar wind condition
is used with n
0
=5 /cm
3
, v
SW
= 450 km/s and T
e
= 9.98 eV . The crater has the height of 250
m. The solar wind proton influx varies from 10
8
m
− 2
s
− 1
to 10
11
m
− 2
s
− 1
. We used the saturation
timescale discovered in Chapter 3 and the flux of protons to estimate the saturation of solar wind
implantation as a function of distance from the bottom corner of the wall.
Figure 9.3: Comparison between timescales of solar wind implantation saturation, micrometeoroid
impact and dielectric breakdown in a crater.
Figure. 9.3 shows the resulting timescale comparisons. The blue curve is the timescale of
solar wind implantation saturation as a function of impinging flux. We used the same conversion
in Chapter 3 to calculate the timescale. The Red dashed line shows the micrometeoroid impact
timescale and the blue dashed line show the dielectric breakdown timescale. In particular, for x
< 750 m, the timescale of dielectric breakdown is smaller than that of saturation, indicating that
the water formation cycle is in the form of dielectric breakdown on an unsaturated surface. This
126
is believed to have a higher efficiency of converting hydrogen from solar wind to water molecules
based on the analysis. For x> 750 m, the overall timescale is then dominated by dielectric break-
down. Micrometeoroid impact would have a timescale that is about one order of magnitude higher
that of saturation and dielectric breakdown. This indicates that for extreme cold traps within PSRs,
dielectric breakdown is the dominated energy providing processes that contribute to the formation
of water and due to the ion void region created by plasma expansion, the near crater wall region
tends to have a higher efficiency of utilizing solar wind protons.
9.4 Recommendation for Future Studies on Lunar Volatile Modeling
The study presented in this study is closely related to future space missions towards the moon
and icy moons such as numerous ARTEMIS missions. For instance, the LunaH-Map [180] which
is currently observing the flow of neutrons emitted from the Moon’s surface to determine the
hydrogen distribution. Lunar Trailblazer Mission [155] will be launch in the upcoming ARTEMIS
missions to provide a higher resolution of IR spectra to determine the detailed form of water on
the lunar surface. V olatiles Investigating Polar Exploration Rover(VIPER) [181] and Lunar Vertex
[182] missions will sent rovers to the moon and provide in-situ analysis of the volatiles on the lunar
surface.
The four missions mentioned above are directly related to Chapter 3-6 where we discussed the
impact of space environment to the formation and loss of lunar water. In particular, the VIPER
mission is planning to visit the polar region and the data can be compared to previous collected
samples by Apollo missions from lower latitude regions. Polar regions generally experienced
more extreme space weather events and we hypothesis the solar wind implantation and dielectric
breakdown to be dominate water formation mechanisms as oppose to micrometeoroid impact. The
sample collected from VIPER missions will reveal how dielectric breakdown contribute to both
the space weathering process and water formation process.
127
Previous mission such as M
3
[13] and SOFIA [19] measured 3− µm and 6− µm individually
and the 3− µm data is not able to distinguish− OH and H
2
O.With a much higher resolution, Lunar
Trailblazer Mission will reveal the abundance of both hydroxyl(− OH) and water(H
2
O). This will
enable a critical analysis that was not possible before which is the relative ratio of− OH and H
2
O.
As discussed in Chapter 6. From the atomic scale, we discovered that the transport of water in the
exosphere and re-distribution of water on the surface strongly depends on the relative abundance of
− OH and H
2
O. With a detailed mapping of− OH and H
2
O, we are able to re-visit the exosphere
modeling of water on the lunar surface.
Some detailed future research plans are listed below:
• Determine the− OH and H
2
O abundance from in-situ measurement and investigate the exo-
sphere generated by micrometeoroid impact.
• Compare the samples collected by VIPER mission with previous Apollo samples and analyze
the timescale of dielectric breakdown as oppose to micrometeoroid impact.
• With the global mapping of hydrogen distribution from Luna-H mission, construct a diffu-
sion model which will enable us to extend the model in Chapter 3-6 from PSRs to lower
latitude regions.
9.5 Summary of Hypervelocity Ice Impact Modeling
Using reactive molecular dynamics simulations, we have identified a two-stage fragmentation pat-
tern for hypervelocity water ice impacts in Chapter 7, involving both intermolecular and inter-
atomic fragmentation. The fragmentation process begins when the velocity is high enough to
break the hydrogen bonds between water molecules. Once the velocity reaches a level where
covalent bonds between hydrogen (H) and oxygen (O) within a water molecule can be broken,
interatomic fragmentation begins. As the interatomic fragmentation range is reached, new prod-
ucts are observed on the ”pseudo-mass spectrometer” in our simulations (as well as on actual mass
128
spectrometers in experimental studies [167]). The velocity threshold identified in our simulations
is in good agreement with experimental results. Based on the two-stage fragmentation pattern ob-
served, we propose that power-law distribution fitting would be applicable until inter-molecular
fragmentation occurs. After interatomic fragmentation, the relative ratio of O
2
and H
2
produced
by the impact would be a useful parameter for determining the velocity of the impact.
Inspired by the correlation between cluster size and dynamics, Chapter 8 presented a use-
ful framework for understanding molecule transport in exospheres, particularly for clusters of
molecules or atoms. Complex velocity distributions are crucial for accurately modeling water
molecule behavior following high-speed ice impacts. A mixed Maxwellian distribution, incorpo-
rating a power-law distribution for impact ejecta size, is constructed and yields a different veloc-
ity distribution function compared to a single Maxwellian distribution. Gravity capture of water
molecules can be significantly underestimated depending on the escape velocity. Accurate model-
ing of water molecule velocity distribution is essential for comprehending the physical processes
governing their transport in exospheres. Comparative analysis reveals a relative difference of 10%
for high escape velocity planets like Mercury, while smaller icy bodies like Europa and Pluto
exhibit a relative difference as high as 160%.
Another important discussion is the difference between dust-impact-on-ice and ice-impact-on-
dust. Laboratory experiments conducted by Nelson [87], Ulibarri et al. [88] have deduced that
fragmentation patterns are primarily governed by the interaction between water molecules in ice,
resulting in similar general patterns. Our model aligns with this assertion, as the kinetic energy
utilized to break hydrogen and covalent bonds is the primary controlling factor. This phenomenon
has been analyzed by O’Keefe and Ahrens [183, 184] in the context of comet impacts and mi-
crometeoroid impacts on ice surfaces. The differences between these scenarios can be attributed
to variations in energy partitioning. In our simulation where ice serves as a projectile, the energy
partition is nearly 1, as all water molecules are subjected to intense pressure caused by hyperve-
locity impacts and the kinetic energy they release. Conversely, when ice acts as a substrate with
the same impact energy, the volume of water molecules sharing the energy is significantly larger.
129
Consequently, the average energy for each molecules or bonds for ejecting molecules and breaking
bonds is considerably reduced. An estimation of the equivalent velocity for ice as an impact can be
obtained by using a coefficient that takes the ratio of N
e jected
and N
pro jectile
for the projectile case.
This approach offers a first-order approximation of the relationship between the two scenarios. We
recommend that future research further explore the connections between dust-impact-on-ice and
ice-impact-on-dust cases.
9.6 Recommendation for Future Studies on Hypervelocity Ice
Impact Modeling
Europa Clipper mission[40] is scheduled to be launched in 2024 and the surface dust analyzer
(SUDA) [91] will sample the ice grains in the plume of Europa as well as those in the exosphere.
The hypervelocity impact of those ice particles will be a critical process to determine the physical
properties of the grains. Compared to the Cosmic Dust Analyzer (CDA) which has a resolution of
m
∆m
= 20− 50 for the mass spectrometer, SUDA will provide a much accurate measurement with
a resolution of
m
∆m
= 200. This will enable us to analyze the data using the hypervelocity impact
modeling described in chapter 7 and chapter 8. Some detailed future research plans related to
hypervelocity ice impact are listed below:
• Recent lab experiments has clear signals of H
+
1− 3
and O
2
from time of flight mass spec-
trometer. In-situ data from SUDA can provide more evidence regarding the dependence of
velocity and angle.
• Postberg et al. [35] categorized the ice grains sampled from CDA in Cassini Missions to
three different types based on the mass spectra. In particular, type II grain contains organic
molecules that could contains bio-signatures from the internal oceans. Future reactive molec-
ular dynamics simulation with specific force field is able to investigate whether the organic
130
molecules are originally from the internal ocean or a product upon hypervelocity impact to
the instrument.
• Previous detection of calcium exosphere has provided some evidence of the emission of
clusters instead of single atoms or single molecules. A more detailed detection of Mercury
exosphere will be made by BepiColombo mission [185]. Exospheres of icy moons will
also be visited by Europa Clipper missions and future missions towards Enceladus. With a
better detection of the vertical distribution of volatiles or refractory materials. The exosphere
model in Chapter 7 will be tested.
131
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Abstract (if available)
Abstract
The origin of lunar volatiles is a long-standing problem. As the moon does not have a global magnetic field and a sustainable atmosphere, solar wind particles, micrometeoroids, and energetic particles can interact directly with the lunar regolith surface. Such interactions have been proposed to play a critical role in the formation of lunar water. This dissertation presents the first atomic scale simulation study of the dynamics and chemical reactions of lunar surface-environmental interactions and their contributions to lunar water formation and the lunar exosphere.
Reactive molecular dynamics simulations are carried out to model solar wind implantation on the lunar surface, micrometeoroid impact on the lunar surface, and dielectric breakdown of lunar regolith due to space weather effects, and to understand how these processes affect the lunar wa- ter formation cycle. The solar wind implantation simulation study closely replicates the energy and flux conditions of solar wind particles. The results show an efficient formation of hydroxyl groups (-OH) and molecular hydrogen (H) but relatively weaker water synthesis. Additionally, a saturation feature of hydroxyl due to solar wind implantation is identified for a timescale of 1 to 1000 years. The micrometeoroid impact simulation study resolves both the chemical reactions and physical collisions during impact on the hydroxylated regolith surface, as well as the dynamics of the released water molecules. The results reveal that water molecules are both generated and lost during micrometeoroid impacts and that water retention is significantly affected by the impact ve- locity significantly affects water retention, with higher velocities resulting in greater water loss to space. The dielectric breakdown simulation study resolves the effect of the electric field from deep dielectric charging in regolith grain due to space weather events. The results show that such deep dielectric charging can break the Si-O bonds in regolith grain and facilitate the formation of water molecules, which are subsequently preserved as water ice attached to the regolith. The combined results from these simulation studies show that, while solar wind implantation can lead to the for- mation of some hydroxyl groups and water molecules, the contribution by the implantation process itself is not significant enough to account for the observed lunar water content. Micrometeoroid impacts and dielectric breakdown provide the required energy or catalyst for water formation reac- tions. For all the cases considered, micrometeoroid impacts always produce more water molecules. However, a comparison of the time scale of implantation saturation against that of micrometeoroid impacts (104 years) and dielectric breakdown (103 years) indicates that dielectric breakdown ex- hibits a higher efficiency in converting the hydrogen from solar wind into water molecules. This provides further evidence that the permanently shadowed regions are ideal locations for both water formation and water preservation.
The results of chemical bond calculations are further combined with transport simulation to study the dynamics of released water molecules from the lunar surface. Machine learning is applied to identify the different sources of water molecules in the ejected water molecules. The results show that the original water molecules and the newly formed water molecules have very different velocity distributions, and thus have a distinct contribution to the exosphere. This suggests the need for a clear identification of the form of water on the lunar surface in exosphere studies.
While the focus of this dissertation is on lunar water formation, the simulation methodology is also extended to study hypervelocity ice impact to support future exploration of icy moons. The results reveal a two-stage fragmentation pattern as we increase the impact velocity, the inter- molecular fragmentation and inter-atomic fragmentation. The inter-molecular fragmentation stage shows a consistent power-law size distribution while the inter-atomic fragmentation stage shows a correlation between the generation of molecular hydrogen and molecular oxygen. We proposed that the chemical reactions products in the inter-atomic fragmentation stage could be used as a velocity probing method for icy moon exploration missions. An examination of the dynamics of the water molecules generated by hypervelocity impact also shows that, when there are significant clusters of water molecules, the overall velocity distribution function of the ejected water should be modeled by mixed Maxwellian distributions rather than a single Maxwellian distribution for impact generated surface bonded exosphere. Thus, future exosphere modeling should include the effect of clustering and need to integrate surface chemistry with transport dynamics.
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Asset Metadata
Creator
Huang, Ziyu
(author)
Core Title
Interactions of planetary surfaces with space environments and their effects on volatile formation and transport: atomic scale simulations
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Astronautical Engineering
Degree Conferral Date
2023-08
Publication Date
08/08/2023
Defense Date
08/08/2023
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English
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Wang, Joseph (
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), Gruntman, Mike (
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), Nakano, Aiichiro (
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), Nomura, Ken-ichi (
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)
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ziyuhuan@usc.edu;dylan18usc@outlook.com
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(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA
Repository Email
cisadmin@lib.usc.edu
Tags
molecular dynamics
planetary science
space physics