Etterbeek, Belgium Prof. Dr. Karl-Heinz Glassmeier Technische Universität
Braunschweig, Braunschweig, Germany Dr. Norbert Krupp Max-Planck-Institut für
Sonnensystemforschung, Göttingen, Germany Dr. Elias Roussos Max-Planck-
Institut für Sonnensystemforschung, Göttingen, Germany Dr. Yoshifumi Futaana
Swedish Institute of Space Physics, Kiruna, Sweden Prof. Dr. Karl-Heinz
Glassmeier Technische Universität Braunschweig, Braunschweig, Germany Assoc.
Prof. Dr. Yoshifumi Futaana Swedish Institute of Space Physics, Kiruna, Sweden
8.10.2018 2018 5.12.2018 2018

# A search for signatures of Europa’s atmosphere and plumes in Galileo charged
particle data

Hans L.F. Huybrighs

## Publications

Partial results of this work were published in advance in the following
contributions:

### Peer-reviewed publications

Huybrighs, H.L.F., Futaana, Y., Barabash, S., Wieser, M., Wurz, P., Krupp, N.,
Glassmeier, K.H., Vermeersen. B., 2017, On the in-situ detectability of
Europa’s water vapour plumes from a flyby mission. Icarus 289, 270-280.
https://doi.org/10.1016/j.icarus.2016.10.026

Carnielli, G., Galand, M., Leblanc, F., Modolo, R., Beth, A., Huybrighs,
H.L.F., Jia, X., First 3D test particle model of Ganymede’s ionosphere.
Submitted to Icarus.

### Poster and oral presentations

Carnielli, G., Galand, M., Modolo, R., Leblanc, F., Beth, A., Huybrighs,
H.L.F., Jia, X., 2018, Constraining Ganymede’s exosphere through numerical
simulations of its ionosphere and Galileo observations. European Planetary
Science Congress 2018, Berlin.

Carnielli, G., Galand, M., Modolo, R., Leblanc, F., Leclerq, L., Beth, A.,
Huybrighs, H.L.F., 2018, Constraining Ganymede’s neutral and plasma
environment through numerical simulations of its ionosphere. Magnetospheres of
Outer Planets 2018, Boulder. Poster presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Fraenz, M., Futaana, Y., Barabash,
S. Glassmeier, K.-H., 2018, Signatures of Europa’s atmosphere in Galileo EPD
data during the E12 flyby. Magnetospheres of Outer Planets 2018, Boulder.
Poster presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Fraenz, M., Futaana, Y., Barabash,
S. Glassmeier, K.-H., 2017, The search for active Europa plumes in Galileo
plasma particle detector data: the E12 flyby. AGU fall meeting 2017, New
Orleans. Poster presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Fraenz, M., Futaana, Y., Barabash,
S. Glassmeier, K.-H., 2017, Are there signatures of active Europa plumes in
Galileo in-situ data? European Planetary Science Congress 2017, Riga. Oral
presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Fraenz, M., Futaana, Y., Barabash,
S. Glassmeier, K.-H., 2017, The search for Europa plume signatures in Galileo
plasma particle data. Magnetospheres of Outer Planets 2017, Uppsala. Poster
presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Fraenz, M., Futaana, Y., Barabash,
S. Glassmeier, K.-H., 2017, The search for Europa plume signatures in Galileo
in-situ data. DPG Frühjahrstagung 2017 (German Physical Society Spring
Meeting), Bremen, March 14, 2017. Poster presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Futaana, Y., Barabash, S.
Glassmeier, K.-H., 2016, Feasibility study of the in-situ detectability of
Europa’s neutral and plasma plumes from a flyby mission. Europa-Enceladus
Plumes Workshop, Caltech, October 15, 2016. Oral presentation.

Huybrighs, H.L.F., Roussos, E., Krupp, N., Futaana, Y., Barabash, S.
Glassmeier, K.-H., 2016, Feasibility study of in-situ measurements of Europa’s
neutral and plasma plumes with JUICE/PEP. In: Geophysical Research Abstracts
Vol. 18, EGU2016-13425, 2016 EGU General Assembly 2016, Vienna. Oral
presentation.

###### Contents

  1. Publications
    1. Summary
    2. Zusammenfassung
  2. 1 Introduction and motivation
    1. 1.1 Europa as a planetary object
      1. 1.1.1 Subsurface ocean and interior
      2. 1.1.2 Tenuous atmosphere
      3. 1.1.3 Water vapour plumes
    2. 1.2 Magnetospheric interaction
      1. 1.2.1 Basic types of magnetosphere interaction with planetary bodies
      2. 1.2.2 Jupiter’s magnetosphere
      3. 1.2.3 Jupiter’s magnetosphere at Europa’s orbit
      4. 1.2.4 Interaction of Europa with its magnetospheric environment
    3. 1.3 Plasma & energetic charged particle measurements at Europa by the Galileo mission
      1. 1.3.1 Low energy plasma particles
      2. 1.3.2 Energetic charged particles
    4. 1.4 Main research question of the thesis
  3. 2 Research methodology
    1. 2.1 Galileo and instrumentation
      1. 2.1.1 Plasma instrumentation (PLS)
      2. 2.1.2 Energetic Particle Detector (EPD)
      3. 2.1.3 Magnetometer (MAG)
    2. 2.2 Charged particle motion
      1. 2.2.1 The Lorentz force and gyration
      2. 2.2.2 ExB drift
      3. 2.2.3 Magnetic gradient drift
      4. 2.2.4 Magnetic curvature drift
      5. 2.2.5 Magnetic mirror
      6. 2.2.6 Trapped particle motion
    3. 2.3 Charged particle tracing simulation
      1. 2.3.1 Simulation approach
      2. 2.3.2 Model inputs
    4. 2.4 Selected instrumentation and simulation method
  4. 3 Comparison of the Galileo Europa flybys using charged particle data
    1. 3.1 Geometric overview of the Galileo flybys of Europa
    2. 3.2 Data analysis
    3. 3.3 General comparison of the flyby data
      1. 3.3.1 Magnetic field measurements
      2. 3.3.2 Plasma observations
      3. 3.3.3 Energetic particle observations
    4. 3.4 Candidate orbit selection
    5. 3.5 Selected candidate: E12
    6. 3.6 Main findings and implications for the simulation
  5. 4 Characterisation of Europa’s tenuous atmosphere during the E12 flyby
    1. 4.1 Energetic particle simulation setup
      1. 4.1.1 Charge exchange cross sections
      2. 4.1.2 Boundary conditions
      3. 4.1.3 Overview of the input models and parameters
    2. 4.2 Simulations of energetic particle depletions
    3. 4.3 Comparison with data
      1. 4.3.1 Proton channels (TP1, TP2 and TP3)
      2. 4.3.2 Oxygen channels (TO2 and TO3)
    4. 4.4 Possible plume signatures during the E12 flyby
    5. 4.5 Main results and recommendations for future work
  6. 5 Predictions for future missions
    1. 5.1 Future missions to Europa
      1. 5.1.1 JUpiter ICy moons Explorer (JUICE)
      2. 5.1.2 Europa Clipper
    2. 5.2 Overview of Europa plume models
    3. 5.3 Europa plume simulation setup and assumptions
    4. 5.4 Simulations of detecting Europa plume particles
    5. 5.5 Main results and recommendations for future work
  7. 6 Conclusions and outlook
  8. A Appendix: Galileo data analysis
    1. A.1 Processing of EPD data
    2. A.2 Processing of the PLS data
      1. A.2.1 Energy spectrum
      2. A.2.2 Other data products
      3. A.2.3 PLS instrument pointing
    3. A.3 Overview of the data
  9. Acknowledgements
  10. Curriculum Vitae

### Summary

Europa, the fourth largest moon of Jupiter, is thought to harbour a
potentially habitable ocean of water under its icy surface. Remote sensing
observations indicate that Europa is surrounded by a tenuous atmosphere.
Furthermore, recent observations and historic data from Galileo hint at the
occurrence of water vapour eruptions originating from the interior that create
200 km high plumes. Taking samples of the atmosphere, and more directly, the
plumes, could offer a "window" into Europa’s interior, without even having to
land. Due to the lack of adequate measurements large uncertainties exist in
the properties of Europa’s atmosphere (e.g. loss rate and structure) and
plumes (e.g. structure, source location, duration), of the latter one the
existence is not even confirmed. Unexploited opportunities to constrain
properties of the atmosphere or plumes remain in the in-situ data collected by
the Galileo mission, the only mission that has surveyed Europa from close by.
As it was not equipped with a neutral particle detector, no direct detections
of the particles of the atmosphere or the plumes could have been made.
However, it carried two charged particle detectors, the energetic particle
detector (EPD) and the plasma instrumentation (PLS), and a magnetometer (MAG)
that can be used to investigate if charged particles interact with the tenuous
atmosphere or possible plumes.

In this thesis, I investigate how to constrain the properties (density, scale
height) of Europa’s tenuous atmosphere and plumes, using data from the Galileo
in-situ particle detector instruments (PLS, EPD). First, I analyse and compare
the flybys, with a focus on the E12 flyby as it demonstrates the strongest
signs of interaction of the atmosphere and the magnetospheric environment.
Next, I simulate the depletion of energetic protons and oxygen ions measured
during the E12 flyby. A Monte Carlo particle tracing method is used to
simulate the particle trajectories and determine where they are depleted: at
the surface or in the atmosphere. The simulations show that the depletions of
energetic ions observed in the range 80 to 540 keV can be explained by charge
exchange with neutral atmospheric particles, but not by impact on the surface
alone. This suggests that an atmosphere must have been present during the E12
flyby. The simulations best represent the sublimated component of the
atmosphere and favour higher surface densities than the literature, but are
not sensitive to the scale height. Furthermore, an additional depletion is
visible very briefly in the energetic protons with energies from 540 to 1040
keV. This feature could be consistent with localized losses from a Europa
plume, although such a solution is not unique. Finally, I simulate the
detection of plume and atmosphere originating H2O and H2O+ by the neutral
particles sensor and the ion sensor part of the upcoming JUpiter ICy moon
Explorer. By comparing the signature of atmospheric H2O and H2O+ and plume
originating H2O and H2O+ particles, I show that the signature of the plume
can, in principle, be recognized in the combined atmosphere-plume signal.

Though the most direct measurements of Europa’s tenuous atmosphere and plumes
will come from optical imaging or the in-situ detection of neutral particles,
this work shows that the atmosphere and the plumes can influence energetic
particle and plasma properties near the moon. The synergy between the optical
measurement and the in-situ measurements of neutral and charged particles will
allow a detailed characterization of the atmosphere-plume system, a capability
that is available both in the upcoming JUICE and Europa Clipper missions, and
can be extended to other moons of Jupiter.

### Zusammenfassung

Europa ist der viertgrößte Mond des Jupiter und es wird angenommen, dass
dieser einen eventuell bewohnbaren Ozean aus Wasser unter seiner eisigen
Oberfläche beherbergt. Beobachtungen mittels Satelliten-Fernerkundung (’Remote
sensing’) deuten darauf hin, dass Europa von einer dünnen Atmosphäre umgeben
ist. Darüber hinaus zeigen jüngste Beobachtungen sowie historische Daten von
der Galileo Satellitenmission, dass Wasserdampferuptionen auftreten, die im
Inneren von Europa entstehen und 200 km hohe Dampffahnen (’Plumes’) erzeugen
können. Die Entnahme von Proben aus der Atmosphäre, insbesondere aus den
auftretenden Dampffahnen, können daher einen Einblick in Europas Inneres
bieten, ohne dass es einer Landung bedarf. Aufgrund unzureichender Messungen
gibt es allerdings nicht nur große Unsicherheiten in den Eigenschaften der
Atmosphäre Europas (z.B. Verlustrate und Struktur), sondern auch der
Dampffahnen (z.B. Struktur, Herkunft, Lage, Dauer), deren Existenz nicht
einmal bestätigt ist. In den von der Galileo Mission gesammelten ’in-situ’
Daten befinden sich ungenutzte Möglichkeiten um die Eigenschaften der
Atmosphäre oder der Dampffahnen zu erkunden. Dies war die einzigen Mission,
die Europa aus nächster Nähe erkundet hat. Da Galileo nicht mit einem
neutralen Teilchendetektor ausgestattet war, konnten die Teilchen der
Atmosphäre oder der Dampffahnen nicht direkt nachgewiesen werden. An Bord
waren jedoch zwei geladene Teilchendetektoren, der energetische
Teilchendetektor (EPD) und das Plasmainstrument (PLS), und ein Magnetometer
(MAG), mit denen untersucht werden konnte ob die geladenen Teilchen mit der
dünnen Atmosphäre oder den möglichen Dampffahnen interagieren.

In dieser Arbeit untersuche ich, wie man die Eigenschaften (Dichte,
Skalenhöhe) der dünnen Atmosphäre und der Dampffahnen von Europa mithilfe von
Daten aus dem Galileo ’in-situ’ Teilchendetektorinstrumenten (PLS, EPD)
erforschen kann. Zuerst analysiere und vergleiche ich die Vorbeiflüge, wobei
ich mich auf den E12-Vorbeiflug konzentriere, da dieser die stärkste
Wechselwirkung zwischen Atmosphäre und Magnetosphäre aufzeigte. Als Nächstes
simuliere ich den Abbau von energetischen Protonen und Sauerstoffionen, die
während des E12-Vorbeifluges gemessen wurden. Ein Monte-Carlo Verfahren zur
Teilchenverfolgung wird angewendet, um die Flugbahnen der Teilchen zu
simulieren und um festzustellen, wo diese abgebaut werden - entweder an der
Oberfläche oder in der Atmosphäre. Die Simulationen zeigen, dass der Abbau von
energetischen Teilchen, die im Bereich von 80 bis 540 keV beobachtete werden,
durch Ladungsaustausch mit neutralen Teilchen in der Atmosphäre erklärt werden
können, und nicht durch den Aufprall auf die Oberfläche allein. Dies deutet
darauf hin, dass während des E12-Vorbeifluges eine Atmosphäre vorhanden sein
musste. Die Simulationen stellen vor allem die sublimierte Komponente der
Atmosphäre dar und begünstigen höhere Oberflächendichten als die in der
Literatur vorkommenden, und sind zudem unempfindlich gegenüber der Skalenhöhe.
Darüber hinaus ist ein sehr kurz beobachtbarer zusätzlicher Abbau von
energetischen Protonen mit Energien von 540 bis 1040 keV sichtbar. Diese
Eigenschaft könnte mit örtlich begrenzten Verlusten aus einer Dampffahne
übereinstimmen, obwohl diese Lösung nicht eindeutig ist. Schlussendlich
simuliere ich die Detektion von der aus der Atmosphäre und Dampffahne
stammenden H2O und H2O+ Signatur mit dem neutralen Teilchen- sowie
Ionensensor, die beide Bestandteile der kommenden ’JUpiter ICy moon Explorer’
Mission sind. Durch den Vergleich zwischen der atmosphärischen und der von
Dampffahnen stammenden H2O und H2O+ Teilchen-Signatur, zeige ich, dass die
Signatur der Dampffahne im gemeinsamen Signal der Atmosphäre und Dampffahnen
erkannt werden kann.

Obwohl die direktesten Messungen von Europas dünner Atmosphäre und Dampffahnen
mithilfe von optischer Bildgebung (’Optical imaging’) oder ’in-situ’ Detektion
von neutralen Teilchen gewonnen werden, zeigt meine Arbeit, dass die
Atmosphäre und Dampffahnen die energetischen Teilchen- und Plasmaeigenschaften
in der Nähe des Mondes beeinflussen können. Die Synergie zwischen optischer
Messung und ’in-situ’ Messungen von neutralen und geladenen Teilchen
ermöglicht eine sehr genaue Bestimmung des Atmosphären-Dampffahnen Systems.
Beide Methoden werden in den kommenden JUICE und Europa Clipper Missionen
verfügbar sein, und können auch auf andere Monde des Jupiter angewendet
werden.

##  Chapter 1 Introduction and motivation

The goal of this thesis is to constrain the properties of Europa’s tenuous
atmosphere or any water vapour plumes, using data from the Galileo mission’s
in-situ particle detector instruments. Galileo studied the Jupiter system
between 1995 and 2003 and made several flybys of Europa. In this chapter the
context of the thesis and the motivation are provided, and, based on this, the
main research question will be formulated.

First, Europa, its tenuous atmosphere and its plumes, will be introduced
(Section 1.1). Next, since plasma and energetic charged particles are key to
this thesis, Europa’s magnetosopheric environment and the interaction will be
discussed (Section 1.2). Special emphasis is put on the interaction of plasma
and energetic charged particles with Europa (Section 1.3). Finally the main
research question of this thesis will be formulated (Section 1.4).

Figure 1.1: Europa in front of Jupiter, photographed by Voyager 1 on March 3rd
1979. [NASA/JPL-Caltech/Kevin M. Gill, CC BY 2.0].

###  1.1 Europa as a planetary object

Europa is Jupiter’s fourth largest moon. It was discovered in 1610 by Galileo
Galilei, together with the other Galilean moons Ganymede, Callisto and Io. Its
orbit is located between those of Io and Ganymede. Europa in particular has
captured the attention of the scientific community because it is thought to
harbour a subsurface ocean of liquid water, which could be habitable. Europa
possesses a tenuous atmosphere and a torus of neutral particles collocated
with its orbit. Furthermore plumes of water vapour are thought to erupt on the
surface.

This section provides a description of Europa as a planetary object. First
Europa’s interior, surface and habitability are discussed before moving
outwards to Europa’s atmosphere and the plumes therein. Table 1.1 provides an
overview of general properties of Europa that are relevant to this work.

Property | Value and units
---|---
Mean radius | 1562.09 km
Mass |  $4.79982\times 10^{22}$ kg
Escape velocity | 2.025 km/s. From Singer et al. (2013).
Orbital eccentricity | 0.0101
Semi-major axis | 670900 km or $\leavevmode\nobreak\ 9.38$ Jupiter radii ($R_{j}$)
| 1 $R_{j}$ = Jupiter’s equatorial radius = 71492 km
Orbital period | 3.551810 days
Rotation period | Approximately synchronous,
| so the same as the orbital period.
Table 1.1: General properties of Europa relevant to this chapter. From
Schubert et al. (2009), unless specified otherwise.

####  1.1.1 Subsurface ocean and interior

Europa is thought to have a differentiated interior, made out of a water ice-
liquid outer layer, covering a rocky interior and a metal core. An overview of
the interior is shown in Figure 1.2. Evidence for a differentiated interior
has been obtained from gravity field measurements from Doppler shifts in
Galileo’s radio signals (Anderson et al. 1997, 1998). The ice-liquid layer is
thought to exist out of an ice shell covering a liquid water ocean. There are
multiple signs that indicate that there is a liquid (or at least a warm,
ductile, partially melted "slushy" layer) beneath the icy shell, some of these
are:

  * •

Young surface age: Europa’s surface is devoid of impact features, compared to
objects of similar age, such as the other Galilean moon Callisto (see Figure
1.3). Crater densities on the surface of Europa suggest a young surface of age
of 40 to 90 million years (Bierhaus et al. 2009). Such a young age suggest
that resurfacing processes are taking place that remove craters over time.

  * •

Chaos terrain: a terrain type characterized by broken apart pieces of surface
ice that have moved with respect to each other, formation of such structures
might require ductile layers underneath (Greeley and Chyba 2004).

  * •

The occurrence of hydrated materials close to surface features thought to be
signs of disruption in the surface: such as ridges or chaos terrain (Greeley
and Chyba 2004).

  * •

Unusual crater morphology: various unusual properties of Europa’s craters such
as a relative shallowness and concentric rings around the craters have been
interpreted as signatures of a ductile or liquid layer underlying the ice
layer (Greeley and Chyba 2004).

Figure 1.2: Overview of Europa’s interior
[https://photojournal.jpl.nasa.gov/catalog/PIA01669]. Figure 1.3: Europa’s
surface is relatively crater-free. Image obtained by the Galileo mission.
[https://www.nasa.gov/jpl/europas-stunning-surface].

Strong evidence for a liquid layer underneath the outer ice shell has been
obtained from Galileo magnetometer data. These data suggest that Jupiter’s
magnetic field induces a magnetic field in Europa. Jupiter’s magnetic moment
is tilted by about 10 degrees with respect to the orbital plane of Europa.
Because of this, Europa experiences a magnetic field that varies in time. The
varying component is responsible for the induction of a magnetic field in a
conductive layer in Europa’s interior. This conductive layer is thought to be
a salty liquid water ocean (Khurana et al. 1998; Kivelson et al. 1999; Zimmer
et al. 2000; Schubert et al. 2009).

Gravity field measurements suggest that the total thickness of the combined
ice-ocean layer ranges from 80 to 170 km (Anderson et al. 1998). Galileo
magnetometer data constrain the thickness of the ice-only layer to less than
7-15 km, depending on the assumed composition of the ice layer (Schubert et
al. 2009). The total volume of water in Europa’s ocean ($3\times 10^{9}$km3)
is thought to exceed the total volume of water on Earth’s surface (Greeley and
Chyba 2004).

Europa’s ocean is likely kept in a liquid state by tidal heating (Schubert et
al. 2004). Europa’s orbit is eccentric (see Table 1.1), which causes the tidal
forces it experiences during one orbit around Jupiter to vary. This results in
friction that is released in the form of heat and also deforms the surface.
The eccentricity of Europa’s orbit is maintained by the gravitational
interaction between Io, Europa and Ganymede.

Europa’s subsurface ocean is considered as a potential habitat. The JUICE
Yellow Book (Titov et al. 2012), which defines the science case for the future
JUpiter ICy moons Explorer (JUICE) mission, defines four criteria required for
(earth-like) life and states why these are met at Europa: the presence of
liquid water for an extended period time, essential elements (S, P, O, N, C,
H) and a source of (chemical) energy. The presence of liquid water was
discussed previously. It is thought the ocean has been liquid continuously for
at least a large part of Europa’s history. The required elements have either
been observed or their presence is inferred based on detections on other moons
or on Jupiter (Carlson et al. 2009; Hand et al. 2009). Hydrothermal vents on
the bottom of Europa’s ocean are thought to be a possible source of chemical
energy (Kargel et al. 2000; Vance and Goodman 2009).

The potential habitability of Europa justifies the special interest in this
moon. Assessing the habitability of Europa’s ocean is complicated by the ice-
layer which seals it off completely and prevents any direct study. One
possibility to study the contents of the ocean is by sampling Europa’s
atmosphere. Organic molecules could be transported to the surface and
sputtered away from it by impacting heavy energetic ions (Johnson and
Sundqvist 2018). Europa’s plumes could provide a more direct way of accessing
the ocean, assuming the water of the plumes originates from it. This
emphasizes the importance of studying Europa’s atmosphere and plumes in the
context of assessing Europa’s habitability.

####  1.1.2 Tenuous atmosphere

Europa possesses a tenuous atmosphere, which is the product of interaction
between its surface and charged particles from Jupiter’s magnetosphere . It is
thought that sputtering by energetic ions (On+, Sn+ and H+) is the main
process responsible for the formation of the atmosphere (Plainaki et al.
2018). Sputtering mostly releases water molecules. The water subsequently
disassociates in OH, H, H2 and O, through processes such as electron impact
dissociation. These products react chemically to produce mostly O2 and H2.
Molecular oxygen is thought to be the most abundant species in the atmosphere,
because it doesn’t stick to the surface as much as other species (such as H2O)
or escapes Europa’s gravity easily (such as H2) (Plainaki et al. 2018). While
sputtering is responsible for the extended, large scale height atmosphere,
sublimation could also cause an additional low altitude confined atmospheric
component with a much smaller scale height (Smyth and Marconi 2006).

Published results about the atmosphere are restricted to remote sensing
observations with the Hubble telescope, Earth-based telescopes and results
obtained during the Jupiter flyby of the Cassini mission (Plainaki et al.
2018). No direct in-situ detections of the atmosphere have ever been
published. Electrons from Jupiter’s magnetosphere impact neutral atmospheric
particles and dissociate and excite them, which leads to Auroral glows that
are observable in UV. This allowed for the first detection of the atmosphere
(Hall et al. 1995). Hubble UV observations support the hypothesis that the
extended atmosphere is mostly composed out of O2 (Hall et al. 1995; Roth et
al. 2016). The presence of H2 , H2O, SO2 , and Cl has been inferred indirectly
(Plainaki et al. 2018).

The spatial distribution of O2 as modelled by Plainaki et al. (2013) is shown
in Figure 1.4. This model takes into account the release of O2 by sputtering
and sublimation. Various models have provided density profiles of the
atmospheric constituents, in Figure 1.5 the profile of O2, O, H2O and OH
provided by Shematovich et al. (2005) is shown.

Figure 1.4: Spatial distribution of O2 released by S+, O+ and H+, including
the sublimation component. [Reprinted from Plainaki et al. (2012) with
permission from Elsevier]. Figure 1.5: Altitude profile of Europa’s
atmosphere. This model includes sublimation and sputtering. [Reprinted from
Shematovich et al. (2005) with permission from Elsevier].

Large uncertainties exist in properties of the atmosphere, such as the loss
rate and structure, due to a lack of adequate measurements (Plainaki et al.
2018). Hubble observations reported by Hall et al. (1995) suggest an average
scale height of 145 km. Various analytical models approximate the density of
the O2 atmosphere as a single component atmosphere, exponentially decaying as
a function of altitude. In these models the profile is entirely determined by
a scale height and a surface density (Saur et al. 1998; Liu and Schultz 2000;
Schilling et al. 2007, 2008; Dols et al. 2016). The O2 scale height
assumptions in these models range from 145 km (Saur et al. 1998; Schilling et
al. 2007, 2008), 150 km (Dols et al. 2016), to 175 km (Liu and Schultz 2000).
Surface density estimates in these models are around $\sim 10^{7}$ particles
per cm3 (Saur et al. 1998; Liu and Schultz 2000; Schilling et al. 2007, 2008).
Other analytical models approximate the O2 atmosphere as a two component
exponentially decaying atmosphere, the two components being a sputtered and
sublimated component, each entirely determined by a scale height and surface
density (Rubin et al. 2015; Jia et al. 2018). The sputtered O2 scale height
assumptions range from 145 km (Rubin et al. 2015) to 500 km (Jia et al. 2018).
Surface densities of the sputtered component vary from $5\times 10^{4}$
particles per cm3 (Rubin et al. 2015) to 106 particles per cm3 (Jia et al.
2018). Scale heights for the sublimated components vary from 20 (Rubin et al.
2015) to 100 km (Jia et al. 2018). Densities for the sublimated component vary
from $5\times\sim 10^{7}$ (Jia et al. 2018) to $5\times 10^{8}$ (Rubin et al.
2015). Other models employ a Monte Carlo method to determine the distribution
of the atmospheric components (Shematovich et al. 2005; Smyth and Marconi
2006; Plainaki et al. 2012, 2013; Vorburger and Wurz 2018). These models
consider both sublimation and sputtered components, Vorburger and Wurz (2018)
shows separate results for sputtering and sublimation. In this model, the
atmospheric density for altitudes > $300$ km is dominated by the sublimated
component. The sublimated O2 surface density near the surface is $5\times
10^{7}$ particles per cm3 while the sputtered component is below $10^{4}$
particles per cm3. The scale height of the sublimated component is around 20
km, while the scale height for the sputtered component is around 600 km.
Shematovich et al. (2005); Smyth and Marconi (2006) report surface densities
of $10^{8}$ particles per cm3, while Plainaki et al. (2013) predicts densities
of up to $10^{8}$ per cm3 under sunlit conditions. The scale heights near the
surface in these models are near 20 km. The range of atmospheric parameters is
summarized in Table 1.2. By comparing the different previous studies it is
clear that the surface density of the sublimated component is expected to
exceed that of the sputtered component, while the scale height of the
sputtered component is larger than the sublimated component.

Property | Value | Sources
---|---|---
Surface density (single component) [cm-3] | $\sim 10^{7}$ | [1-5]
Scale height density (single component) [km] | 145-175 | [1-5]
Scale height (sputtered) [km] | 145-600 | [6-8]
Surface density (sputtered) [cm-3] |  $\sim 10^{4}$ to $\sim 10^{6}$ | [6-8]
Scale height (sublimated) [km] | 20-100 | [6-10]
Surface density (sublimated) [cm-3] |  $\sim 10^{7}$ to $\sim 10^{8}$ | [6-8,10-12]
Table 1.2: Overview of the range of surface densities and scale heights of
Europa’s O2 atmosphere reported in previous studies. Sources: [1] Saur et al.
(1998), [2] Liu and Schultz (2000), [3] Schilling et al. (2007), [4] Schilling
et al. (2008), [5] Dols2016, [6] Rubin et al. (2015), [7] Jia et al. (2018),
[8] Vorburger and Wurz (2018), [9] Plainaki et al. (2012), [10] Plainaki et
al. (2013), [11] Shematovich et al. (2005) and [12] Smyth and Marconi (2006).

As the model by Plainaki et al. (2012) shows (Figure 1.4), the atmosphere of
Europa is not spherically symmetric. Plainaki et al. (2013) states that the
peak density occurs when the sub-solar point and the leading edge towards the
flow of plasma at Europa’s orbit fall together. This is because the flux of
energetic ions, which is responsible for the extended atmosphere, is largest
on the leading edge and because the incidence of solar radiation is what
determines sublimation. The structure of the atmosphere can be expected to
vary in time, since the incidence of solar

The upper part of Europa’s atmosphere is referred to as the exosphere. The
lower boundary of the exosphere, the exobase, is defined as the altitude at
which the average distance travelled by a particle between collisions (mean
free path) becomes larger than the scale height. The exobase is species
dependant, for the O2 profile in Shematovich et al. (2005) the exobase is
estimated to be $\sim 80$ km (Plainaki et al. 2018). In the rest of the thesis
I will refer to the entirety of atmosphere and exosphere as Europa’s tenuous
atmosphere.

It has been argued that eruptions of water vapour originating from Europa’s
interior (’plumes’) contribute to the formation of its atmosphere (see also
Section 1.1.3). Another topic related to Europa’s atmosphere is the Europa
torus, a torus of neutral particles located along the moon’s orbit, see
Section 1.3.2. Interaction between Europa, its atmosphere and its
magnetospheric environment are described in more detail in Section 1.2 and
1.2.4.

####  1.1.3 Water vapour plumes

Recent Hubble observations indicate that recurring plumes of water vapour
occur on Europa. In the absence of published reviews of the plume related
papers, this section provides an overview of the existing literature on this
topic. First, early arguments for the existence of the plumes and previous
observation attempts are discussed. Next, the main findings of the
observations by Hubble and Galileo are summarized.

#### Early arguments for activity and remote sensing observation attempts

The occurrence of multiple processes on the surface of Europa that result in
the release of vapour and the formation of plumes have been hypothesized by
several authors, such as the boiling of water exposed to vacuum when a surface
crack is opened by tidal forces (Hoppa et al. 1999), the production of vapour
by shear heating when two sides of a crack move with respect to each other
(Nimmo et al. 2007) or the release of water by exploding bubbles formed when
volatiles exsolve under vacuum conditions (Fagents et al. 2000; Quick et al.
2013).

No plumes or changes in surface features were observed with optical
instruments during the flybys of Galileo, the Voyagers or New Horizons (Hoppa
et al. 1999; Pappalardo et al. 1999; Phillips et al. 2000; Fagents 2003;
Hurford et al. 2007; Roth et al. 2014b). De La Fuente Marcos and Nissar (2000)
suggested that a transient bright feature on Europa, observed in 1999 with an
Earth-based telescope, could be the result of explosive venting. Saur et al.
(2011) discusses observations of UV auroral emissions ($O_{I}$ 130.4 nm and
135.6 nm emissions) of Europa with the Hubble Space Telescope in 1999. In
these observation a surplus of emission near 90∘ west longitude is noticed.
The authors argue that this could point to a radially asymmetrical atmosphere
and state that active plumes could be one mechanism to explain this feature.

#### Remote sensing observations by Roth et al. (2014b)

Figure 1.6: Graphic interpretation showing the position and extent of the
emission surplus reported in Roth et al. (2014b)
[https://www.nasa.gov/content/goddard/hubble-europa-water-vapor]

The first clear measurement of active plumes on Europa came from Roth et al.
(2014b). They discussed UV auroral emissions observed with the Hubble Space
Telescope at Europa, a similar method to Saur et al. (2011). The authors
report the observation of an emission surplus observed near Europa’s south
pole. The surplus is observed in the oxygen OI line (130.4 nm). What is
different from Saur et al. (2011) is that a surplus is also visible in the
Lyman-$\alpha$ line, while no enhancement is noticed in the oxygen OI line
(135.6 nm). The authors argue that this is indicative of electron impact
ionization of H2O. Furthermore the surplus is observed off the limb of Europa,
so without Europa in the background (see Figure 1.6). The surplus was observed
for $\sim$7 hours, the duration of the observation window. The observed plume
reached altitudes of 200 km, with an uncertainty of 100 km due to the low
resolution of the observation. Supersonic velocities of 700 m/s are needed for
plume particles to attain this height. The mass flux is estimated to be 7000
kg/s. The observations of Roth et al. (2014b) and Roth et al. (2014a) showed
no correlation with Europa’s orbital location. Further repeat observations
using the same method did not result in additional plume detections (Roth et
al. 2016, 2017). In total only one out of twenty measurements have resulted in
a plume detection. Several reasons for this low detection rate can be thought
of. It could be that the event reported in Roth et al. (2014b) was an
exceptionally strong event, meaning that the typical plume eruption doesn’t
generate enough vapour to make detection possible. Another possibility is that
the magnetospheric conditions during the successful detection were very
different, resulting in a much higher electron flux than usual.

#### Remote sensing observations by Sparks et al. (2016) and Sparks et al.
(2017)

Figure 1.7: Limb darkening feature (bottom left) observed on January 26, 2014.
[NASA/ESA/W. Sparks (STScI)/USGS Astrogeology Science Center]

Sparks et al. (2016) and Sparks et al. (2017) observed transits of Europa in
front of Jupiter. They identify darkening features at the limb of Europa, and
argue that these could be caused by plumes (Figure 1.7). The detection rate is
higher than the work by Roth et al. (2014b), the presence of the limb
darkening is reported in four out of twelve observations (each last about one
hour). No information on the composition of the darkening features can be
obtained from these observations. The authors estimate the column density from
the observation and combine this with an estimate of the dimensions of the
plume to obtain a total mass estimate. The total mass is of the order of
$\leavevmode\nobreak\ 10^{6}$kg, which is the same as the mass estimated by
Roth et al. (2014b). The reported plume heights are up to 220 km. The limb
darkening featured discussed by Sparks et al. (2017) occurs at the same
location on Europa’s surface as one of the observations from Sparks et al.
(2016), a location in the vicinity of the crater Pwyll. Sparks et al. (2017)
points out that this observation coincides with a thermal anomaly measured by
the Galileo Photopolarimeter-Radiometer. Trumbo et al. (2017) reports ALMA
observations of Europa’s thermal emissions obtained in 2015, prior to the
observation reported in Sparks et al. (2017). The observation suggests that
the thermal anomaly might have cooled down since the Galileo observations.
McGrath and Sparks (2017) state that the strongest ionospheric signature found
in Galileo radio occultation data nearly coincides with a location 50 km above
the Pwyll crater. They report a peak electron density of $\sim 1.3\times
10^{4}$ particles per cm3 at an altitude of $\sim 50$ km. The repeated
detection of the plume near Pwyll, with Hubble and the coinciding detection of
the strongest ionosphere profile and the thermal anomaly lead the authors to
suggest that this plume source has been active since the Galileo period.

#### Arguments from in-situ data by Jia et al. (2018)

From the point of in-situ data the argument for plume activity has been made
previously, in particular for the E12 flyby of Galileo.

  * •

A significantly raised electron density (Kurth et al. 2001) and anomalously
strong magnetic fields (Kivelson et al. 2009) were measured during the E12
Galileo flyby. Kivelson et al. (2009) states that the observed increase in
magnetic field could be related to a local source of pickup ions.

  * •

Bagenal et al. (2015) states that atypical conditions during E12 could be
related to active processes on Europa’s surface, but also considers the
passing of a small, cold, dense blob of plasma originating from Io as another
hypothesis.

Figure 1.8: Magnetic field components during the E12 flyby, indicated are the
Galileo MAG data and the model by Jia et al. (2018) with and without a plume.
[Reprinted by permission from Springer: Nature Astronomy, Jia et al. (2018),
$\copyright$ (2018)]

Jia et al. (2018) implemented a MHD model of Europa’s interaction with the
corotating plasma to investigate the hypothesis of Kivelson et al. (2009).
Additionally Jia et al. (2018) presents an electron density enhancement not
previously reported in Kurth et al. (2001). Jia et al. (2018) simulates the
changes in plasma density and magnetic field components observed during the
E12 flyby from 12:00 to 12:03 for two cases: one case where Europa has just a
tenuous atmosphere and a second case where a plume is superposed on the
atmosphere. The results of the magnetic field simulations are shown in Figure
1.8. The authors conclude that the features observed in the data cannot be
explained by a globally distributed atmosphere, but that the effect of a plume
corresponds to what is seen in the data. The structure causing the disturbance
is about 1000 km in size along Galileo’s trajectory. The plume in their model
is located at 245 West longitude and 5 South latitude. The plume is modelled
analytically, as an exponentially decaying atmosphere with a surface density
of $2\cdot 10^{9}$cm-3 a scale height of 150 km and an angular width of 15∘.
Furthermore the plume is tilted 15∘ from the radial direction.

Additionally the authors investigate a magnetic perturbation seen during the
E26 flyby. Without showing the data or the simulation results they state that
this feature cannot be explained by the same plume model as used for the E12
flyby. Blöcker et al. (2016) studies the interaction of the plumes with
Europa’s magnetospheric environment with an MHD model. They state that an
exospheric inhomogeneity could have been present during Galileo’s E26 flyby.

#### Overview of plume observations

The recent observations by Roth et al. (2014b); Sparks et al. (2016, 2017);
Jia et al. (2018) suggest that plumes are erupting from Europa’s surface, at
least in once case from the same location. Current observations can only give
approximate constraints on properties such as the column density, height of
the plumes and the minimal eruption time. In Figure 1.9 the locations of the
observations of Roth et al. (2014b); Sparks et al. (2016, 2017); Jia et al.
(2018) are indicated on a map of Europa. The observations are represented by
vertical lines of which the size indicates the latitudinal extent spanned by
each observation along the limb of Europa at the time of the observation.
Table 1.3 presents an overview of the plume properties derived from the
observations by Roth et al. (2014b); Sparks et al. (2016, 2017); Jia et al.
(2018).

Figure 1.9: Locations of the plume observations on the surface. The vertical lines represent the latitudinal extent of the observed plumes as reported in Roth et al. (2014b); Sparks et al. (2016, 2017). The location of the plume reported in Jia et al. (2018) is represented by a purple dot. [Map of Europa obtained from: USGS] Property | Roth et al | Sparks et al | Jia et al
---|---|---|---
Height |  $\sim 200$ km |  $\sim 50$ to $\sim 220$ km |
Column density | $1.5\times 10^{20}m^{-2}$ | $0.7\times 10^{21}m^{-2}$ |
|  | to $3.3\times 10^{21}m^{-2}$ |
Surface density |  $1.3\times 10^{9}$ cm-3 cm-3 |  |  $2\times 10^{9}$cm-3
| to $2.2\times 10^{9}$ cm-3 |  |
Scale height | 200 km |  | 150 km
Total H2O molecules | $1.3\times 10^{32}$ |  $0.5\times 10^{32}$ to $1.8\times 10^{32}$ |
Persistence | > 7 hours | > 1 hour | > 3 mins
Mass flux |  $\sim 1000$ kg/s |  |
Table 1.3: Overview of Europa plume properties, based on Roth et al. (2014b);
Sparks et al. (2016, 2017); Jia et al. (2018).

###  1.2 Magnetospheric interaction

Key to this thesis are charged particles, both plasma and energetic particles,
that interact with Europa. To understand the populations of charged particles
near Europa, it is necessary to introduce Europa’s magnetospheric environment,
which is done in this section. First, the basic types of magnetospheric
interaction with planetary bodies are discussed. Next, Jupiter’s magnetosphere
as a whole is presented, before focusing on the environment Europa is exposed
to directly.

####  1.2.1 Basic types of magnetosphere interaction with planetary bodies

An overview of the different types of magnetospheric interaction can be made
based on properties of the body and the magnetospheric environment. A first
way to categorize the types of interaction is according to the relative
velocity of the plasma flowing past the object (Kivelson and Bagenal 2007; De
Pater and Lissauer 2010):

  * •

Supersonic: An example of this interaction is the Earth and the solar wind.
Analogous to the formation of a bow wave in front of a boat in water, a bow
shock is formed in the solar wind upstream of Earth’s magnetosphere. In the
case of the bow wave the spreading of the information of the presence of the
boat upstream is limited, because the flow moves faster than the waves that
can spread the information. This is analogous to the formation of the bow
shock, where the relevant waves are waves in a magnetized plasma. However, a
super-magnetosonic environment does not necessarily imply the formation of a
bow shock, as that also depends on the electromagnetic properties of the
object which interacts with the magnetized flow, this will be discussed in the
following paragraphs.

  * •

Subsonic: In this case the waves propagating the disturbance caused by the
object in the plasma flow are not limited in their propagation, no bow shock
is formed upstream of the object. Examples of this kind of interaction are
moons embedded in planetary magnetospheres, like Titan, Io or Europa. The
relevant plasma population is not the solar wind plasma for these objects, but
the plasma corotating with the magnetic field of the central planets.

The interaction can also be categorized according to the electromagnetic
properties of the object (Kivelson and Bagenal 2007; De Pater and Lissauer
2010):

  * •

Unmagnetized body:

    * –

Insulating: An example of this case is Earth’s moon, which does not possess an
intrinsic magnetic field. Without conductivity of the body and the absence of
a conducting ionosphere the Moon cannot influence the flow of the solar wind,
the solar wind particles hit the surface of the object and are absorbed by it.
A wake is formed behind the moon that lacks particles.

    * –

Conducting: in the case of a conducting body the plasma will move around the
conducting layer, rather than impacting it. The magnetic field lines will
drape around the body as a consequence of the diversion of the plasma. What
drives this interaction are electric currents imposed by the upstream plasma
flow on a conducting layer of the planetary body. In turn, these currents will
drive magnetic fields that will react to the upstream disturbance. Examples of
this type of interaction are Mars, Venus or Europa, neither of these have a
(significant) intrinsic magnetic field, but they do possess a conducting
ionosphere. In case of Mars and Venus the relevant plasma population is the
solar wind, but in Europa’s case it is the plasma from Jupiter’s magnetosphere
that is corotating with its magnetic field. The conducting layer can also
react to the changes in the magnetospheric environment, driving the formation
of an induced magnetic field. Europa’s subsurface ocean and Callisto’s
ionosphere are two cases where reaction to periodic changes in the
environmental magnetic field induce magnetic fields.

  * •

Magnetized body: Bodies with a sufficiently strong intrinsic magnetic field
can form a magnetic cavity in which the magnetic field of the body dominates
the structure and dynamics of the charged particle populations, referred to as
a magnetosphere. Examples of this type are Mercury, Earth, Jupiter, Saturn,
Uranus and Neptune but also Jupiter’s moon Ganymede.

Jupiter is characterized as a magnetized body who’s magnetosphere interacts
with the supersonic solar wind. Jupiter’s magnetosphere is discussed in
Section 1.2.2 and 1.2.3. Europa is embedded in this magnetosphere and its
interaction is characterized as that of an unmagnetized conducting body that
is embedded in a sub-sonic flow. The interaction of Europa and its
magnetospheric environment will be discussed in more detail in Section 1.2.4.

####  1.2.2 Jupiter’s magnetosphere

Jupiter is a magnetized planet that interacts with the super-magnetosonic
solar wind. The region where Jupiter’s magnetic field dominates the dynamics
and structure of the space environment defines its magnetosphere. A sketch of
Jupiter’s magnetosphere is shown in Figure 1.10. Jupiter’s magnetosphere is
the largest in the solar system, besides the Sun’s. Its magnetopause, the
boundary between the interplanetary magnetic field and Jupiter’s magnetic
field, extends from up to 45 $R_{J}$ to 100 $R_{J}$ (1 $R_{J}$ = 71492 km) in
the direction of the Sun (Khurana et al. 2004). Jupiter possesses a strong
magnetic field, with equatorial strengths up to $400000$ nT at the surface
(Khurana et al. 2004). It is generated by an internal dynamo. The polarity of
the field is opposite to that of Earth’s magnetic field, meaning that the
field lines flow from the north pole to the south pole. Jupiter’s rotation
axis is not perfectly aligned with the axis of the magnetic field, the angle
between them is approximately 10∘, meaning that the magnetosphere wobbles as
Jupiter rotates with respect to an observer or a moon in a Keplerian orbit
within the magnetosphere.

Figure 1.10: A schematic overview of Jupiter’s magnetosphere. Also indicated
is Europa’s approximate location in the inner magnetosphere. [Schematic: Fran
Bagenal and Steve Bartlett
http://lasp.colorado.edu/home/mop/files/2012/04/JupMag-8W.jpg Europa: NASA]

Most of the plasma in Jupiter’s magnetosphere is derived from Io and not from
the solar wind (Khurana et al. 2004). Io is located in the inner
magnetosphere, at $\sim 5.9R_{J}$. Neutral particles released from Io become
ionized and this results in the formation of Io’s plasma torus which is
corotating with Jupiter’s magnetic field (see also Figure 1.11). Collisions
between the plasma and Io’s atmosphere cause the release of 0.6-2.6 ton/s of
neutral, atmospheric particles, which form an extended cloud of neutral
particles in Io’s orbit (Bagenal et al. 2015). This neutral cloud exists
mostly out of S and O, with an O/S ratio of 2-4. The neutrals in this cloud
are ionized, resulting in the production of heavy ions (various charge states
of S and O). The newly formed ions are accelerated to the speed of the bulk
plasma flow, which is corotating with Jupiter’s magnetic field (Kivelson et
al. 2004). The production rate of plasma is about 0.3-1.4 ton/s (Bagenal et
al. 2015).

Figure 1.11: Schematic of the particle environment between Jupiter and Europa.
Indicated are Io’s neutral torus and the plasma resulting from the ionization
of these neutrals. The arrows pointing towards Jupiter indicate that energetic
particles are diffusing towards Jupiter. At Europa the flow direction of the
plasma is indicated as well as the torus of neutrals associated with Europa’s
orbit (see Section 1.1.2). [Reproduced from Bagenal et al. (2015) with
permission from Elsevier.]

Initially the plasma forms a torus around Io’s orbit, rotating together with
Jupiter’s magnetic field. After which the plasma will flow radially outward
because of centrifugal forces, confined to Jupiter’s magnetic equator. This
plasma is referred to as the plasma sheet. Within the inner magnetosphere the
plasma will keep corotating with Jupiter’s magnetic field (Khurana et al.
2004; Bagenal et al. 2014). This heavy plasma inflates the magnetosphere
through the centrifugal force and thermal pressure. The outward motion is a
major driver of Jupiter’s global dynamics, as it provides the means to
transport large quantities of plasma towards the outer magnetosphere, where it
can be shed towards the magnetotail.

Charged particles are not limited in the thermal, corotating energy range, but
extend to much higher, suprathermal energies (Paranicas et al. 2000). After
having been transported radially outwards from Io’s orbit, charged particles
from the magnetosphere are accelerated to these high energies while they
diffuse radially inward (Khurana et al. 2004). Energetic charged particles
have been detected all the way to the magnetopause, and high fluxes of these
particles interact with the moons. Detected species include protons, sulphur
and oxygen, with energies > 10 MeV. The intensity of energetic ions in
Jupiter’s magnetosphere is shown in Figure 1.12. The number density of
energetic particles (energy > 10 keV) is significantly lower than the plasma
sheet density (Kivelson et al. 2004). For example, the number of protons
between 50-200 keV is approximately a thousand times lower than the total
plasma density (Paterson et al. 1999; Paranicas et al. 2002). Though the
density of energetic particles is significantly lower than that of the plasma,
they still play a significant role in the magnetospheric interaction because
of their high energy which translates also into high partial particle
pressure. Pressure gradients can be especially important for driving current
and modifying the local magnetospheric environment, e.g. Sergis et al. (2007).

Figure 1.12: Ion intensity in ions per cm2s sr keV for several energies for
protons, sulphur and oxygen, from Galileo Energetic Particle Detector (EPD)
data. The x-axis is in units of "L". This is the radial distance of the
magnetic field line at the magnetic equator, divided by Jupiter’s radius (see
Section 2.2.6), Europa is located at 9.38 L. [Adapted by Paranicas et al.
(2009) from Mauk et al. (2004)]

####  1.2.3 Jupiter’s magnetosphere at Europa’s orbit

Europa is continuously embedded inside Jupiter’s magnetosphere, since it
orbits Jupiter at 9.38 $R_{J}$. This region of the magnetosphere is referred
to as the inner magnetosphere, a region that extends up to 10 $R_{J}$ in which
the plasma is corotating rigidly with Jupiter (Khurana et al. 2004). At
distances >10 $R_{J}$ corotation breaks down gradually.

The dominant population of plasma at Europa’s orbit is the plasma from the Io
torus that has moved radially outward, as illustrated in Figure 1.11. It takes
the plasma 10-50 days to move radially outward from Io’s plasma torus to
Europa (Bagenal et al. 2015). The plasma is corotating with the magnetic
field, so the rotation period is about 10 hours. This is much faster than
Europa’s orbital period (3.55 Earth days). This means that the corotating
plasma is overtaking Europa, moving from Europa’s leading edge to its trailing
edge, with an average velocity of 76 km/s (Kivelson et al. 2009).

In the time period it takes the plasma to move from Io to Europa, collisions
occur, which can alter the composition of the plasma; by for example
increasing its charge state (Bagenal et al. 2015). Near Europa, the dominant
ions are oxygen and sulphur. Oxygen ions include O+ and O${}_{2}^{+}$, of
which the ratio is not well determined. The dominating sulphur ion is S2+
(Bagenal et al. 2015). Ion densities near Europa vary between 12-170
particles/cm3 (McNutt et al. 1981; Bagenal 1994; Crary et al. 1998; Paterson
et al. 1999; Frank and Paterson 2001). Typical electron densities obtained by
the plasma wave instrument of the Galileo spacecraft, near Europa’s orbit but
not closer than 2.5 $R_{E}$ to Europa, are shown in Figure 1.13. The electron
density varies between 50-400 particles/cm3 (Bagenal et al. 2015). It is clear
that the E12 flyby is an exceptional case with an extreme density of 600
particles/cm3. Figure 1.14 shows the electron density during the close flybys
of Europa, as measured by the plasma wave instrument. The typical densities
near Europa vary 35-300 particles/cm3. Similarly as for the data collected
further away, shown in Figure 1.13, E12 represents an extreme case with
densities up to 600 particles/cm3. No ion densities have been derived for the
E12 flyby.

Figure 1.13: Electron density based on Galileo’s plasma wave instrument data
(PWS) as a function of longitude. The values were obtained between 8.9 and 9.9
$R_{J}$ but farther than 2.5 $R_{E}$ from Europa. E4 to E26 indicate the
Galileo flybys of Europa. Longitude is expressed here in the SIII frame, this
is a Jupiter centred reference frame that has its z-axis aligned with
Jupiter’s rotation axis and rotates with the planet. [Reproduced from Bagenal
et al. (2015) with permission from Elsevier.] Figure 1.14: Electron density
based on Galileo’s plasma wave instrument data (PWS) during the close Europa
flybys. [Reproduced from Kurth et al. (2001) with permission from Elsevier.]

Europa orbits around Jupiter in Jupiter’s rotational equator. Because of the
tilt of the magnetic field, Europa experiences a varying magnetospheric
environment. The position of the center of the plasma sheet will move above
and below Europa. When Europa is located in the center of the plasma sheet the
plasma density will be higher than when it is located above or below it
(Khurana et al. 2004). Additionally, the components of the magnetic field will
change from Europa’s perspective. In a reference frame with the z-axis aligned
to Europa’s rotation axis the z-component of the field remains mostly
constant, while the x-component (along the corotation) and y-component
(towards Jupiter) will vary. It is these varying components that are
responsible for the creation of Europa’s induced magnetosphere, mentioned
previously in Section 1.1.1 (Khurana et al. 1998; Zimmer et al. 2000).
Europa’s induced magnetic field will influence the trajectories of charged
particles in its vicinity.

At Europa’s orbit in Jupiter’s magnetosphere energetic charged particles are
present. Detected species include protons, sulphur and oxygen, with energies >
10 MeV (Paranicas et al. 2009). Clark et al. (2016) shows that energetic
sulphur ions are predominantly multiply charged and energetic oxygen is a mix
between singly and doubly charged. In Figure 1.15 the energy spectra of
energetic ions at Europa’s orbit are shown. Below $\sim$0.1 MeV the conditions
can differ more than one order of magnitude between flybys, however, above
$\sim$0.1 MeV the conditions are stable. Even though the density of the
energetic charged particles is low, compared to the plasma, they dominate the
energy density (Johnson et al. 2009).

Figure 1.15: Energy spectra for protons, oxygen ions and sulphur ions at
Europa’s orbit, from Galileo Energetic Particle Detector (EPD) data.
[Paranicas et al. (2009)]

Finally, in Table 1.4 properties of Europa’s magnetospheric environment
relevant to this work are summarized.

Property | Value and units | Source
---|---|---
Magnetic field magnitude |  $\sim 400$ nT | [1]
Electron density range | 50-400 [$\\#$/cm${}^{-}3$] | [2]
Electron temperature | 10-30 [eV] | [2]
Ion density range | 12-170 [$\\#$/cm${}^{-}3$] | [3]
Ion charge | single and multiple | [2]
Ion mass | 18.5 amu | [3]
Ion temperature | 30-500 [eV] | [2]
Plasmasheet rel. vel. to Europa (range) | 76 (56-86) km/s | [3]
Table 1.4: General properties of Europa’s magnetospheric environment relevant
to this work. Sources: [1]: Khurana (1997), [2]: Bagenal et al. (2015), [3]:
McNutt et al. (1981); Bagenal (1994); Crary et al. (1998); Paterson et al.
(1999); Frank and Paterson (2001)

####  1.2.4 Interaction of Europa with its magnetospheric environment

This section discusses how Europa interacts with its magnetospheric
environment. Europa is characterized as a unmagnetized conducting body that is
embedded in a sub-magnetosonic flow. This implies that no bow shock is present
in front of Europa, but that Europa’s conducting layers divert the corotating
plasma flowing past it. There are two conducting layers, as explained below:
its inferred subsurface, salty water ocean and its ionosphere.

The ionosphere is derived from Europa’s tenuous atmosphere that is partly
ionized by charge exchange with magnetospheric plasma, electron impact
ionization and photo-ionization (Lucchetti et al. 2016). The ionosphere has
been detected with radio occultation measurements by Galileo (Kliore et al.
1997). Other indications that Europa is a source of plasma have been obtained
with the plasma particle detector PLS on the Galileo mission (Paterson et al.
1999). This dataset will be discussed in more detail in Section 1.3.
Additionally, waves in the magnetic field detected downstream of Europa during
the E11 and E15 flybys have been identified as signatures of positively and
negatively charged pickup ions (Volwerk et al. 2001). Pickup ions are
atmospheric neutral particles that become ionized and are transported in the
direction of the corotational flow. More pick-up ions seem to be present
during the E15 flyby than during the E11 flyby (Volwerk et al. 2001).
Furthermore, Intriligator and Miller (1982), Russell et al. (1998) and Eviatar
and Paranicas (2005) suggest that Europa is trailed in the direction of the
corotational flow by a plume of plasma, based on Pioneer 10 and Voyager 2
plasma analyser data and on Galileo magnetometer and plasma wave data.

The deflection of the corotating plasma by the conducting ionosphere prevents
most of the cold plasma flow from hitting the surface (Saur et al. 1998). This
deflected flow has been modelled as a fluid passing by a cylindrical object
(Ip 1996; Dols et al. 2016). The diversion of the flow causes the velocity
magnitude of the corotational plasma to vary. Just in front of and behind
Europa (from the point of view of the plasma flow) this results in a slow down
of the corotating plasma (Kivelson et al. 2009). The diversion of the
corotational plasma by Europa’s ionsosphere has been observed directly by the
plasma particle detector PLS (Paterson et al. 1999), more about this in
Section 1.3. The region directly downstream of Europa (from the point of view
of the corotational plasma) which is within the cross section of Europa, is
referred to as the geometric wake (Figure 1.16).

Figure 1.16: Schematic of Europa’s geometric wake with respect to the
corotational plasma flow.

When the flow is slowed down the magnetic field is affected too, because the
field is frozen-in to the corotating plasma. So when the plasma slows down in
front of Europa, magnetic field lines start piling up. This results in a local
increase of the magnetic field strength, a phenomenon referred to as magnetic
pile-up. Increases in the magnitude of the magnetic field in the vicinity of
Europa have been reported for the E12, E14 and E19 flybys that all passed
upstream of Europa. The conditions during the E12 flyby are exceptional: one
minute before the closest approach the field strength reaches $\sim 800$ nT,
almost double the upstream value (Kivelson et al. 2009). The occurrence of
both this extreme magnetic field increase and the extreme plasma density
mentioned earlier, suggest an increased production of ions. Which might
indicate a high density of neutral particles (Kivelson et al. 2009).

An additional aspect of the slow down is the formation of so called Alfvén
wings. As already mentioned the magnetic field lines are frozen in the plasma,
hence they move together (Kivelson et al. 2009). The plasma closer to Europa
will be slowed down more than the plasma further away, this results in a
bending of the magnetic fields lines. This is shown in Figure 1.17. In three
dimensional space these Alfvén wings can be thought of as cylinders extending
along the magnetic field lines. These are called Alfvén wings because the
perturbation induced near Europa propagates along the magnetic field with the
Alfvén speed, which is the fundamental speed at which magnetic perturbations
are transported.

Figure 1.17: Schematic of Alfvén wings. Corotation velocity is to the right
($V_{cr}$). [Reproduced from Southwood et al. (1980)]

Europa has a wake with respect to the corotating plasma flow (Figure 1.16).
Galileo flybys E4, E11, E15 and E17 passed through the geometric wake of
Europa. Perturbations in the magnetic field related to these wake passes have
been identified for all these flybys (Kivelson et al. 2009). Another important
aspect of Europa’s interaction with its magnetospheric environment is the
induction of a magnetic field in Europa. This phenomenon was studied with
Galileo’s magnetometer and was previously discussed in Section 1.1.1.

The interaction of Europa with its magnetospheric environment influences not
only the motion of plasma particles around it, as has just been shown, but
also the motion of energetic charged particles trapped in Jupiter’s
magnetosphere. The diversion of the corotational flow affects the electric
fields near Europa, which affects the motion of the energetic charged
particles. The magnetic field pile-up will on its turn affect the trajectories
of charged particles. Furthermore, energetic charged particles are depleted in
the vicinity of Europa (Paranicas et al. 2000). Energetic particles do not
carry enough energy density to cause any detectable response in the magnetic
or electric field, when their distribution is perturbed. As a result of this,
energetic particles in particle simulations can be treated as test particles
of which the trajectories are sensitive to the perturbations introduced by
cold plasma processes and the magnetic field induced by the conductive ocean
layer.

###  1.3 Plasma & energetic charged particle measurements at Europa by the
Galileo mission

In this section measurements of lower energy plasma and energetic charged
particles that show the interaction with Europa and its particle environment
are discussed in more detail. Focus is in particular on the data gathered by
two Galileo instruments, the plasma particle detector PLS and the energetic
particle detector EPD. Technical details of these instruments will be
discussed in more detail in Section 2.1.1 and 2.1.2. Overview plots of the
data collected by these instruments are included in Appendix A.3.

####  1.3.1 Low energy plasma particles

Plasma particles at Europa have been studied by the PLS instrument. Paterson
et al. (1999) presents PLS data collected during the E4 and E6 flybys. In
preparation of the PLS analysis presented in this thesis, the main findings of
Paterson et al. (1999) relevant for this thesis are discussed. Data collected
during these flybys are shown in Figure A.4 and Figure A.5 in Appendix A.3.
The E4 and E6 flybys were the first two Europa flybys. Studies of the PLS data
of none of the subsequent Europa flybys has been published.

Fits to the spectra measured two radii upstream, during the E4 flyby, indicate
that multiple heavy ion species are present in the corotating plasma. The
species that are fitted are: H+, O${}_{2}^{+}$, O+, S${}_{2}^{+}$ and S+. The
authors argue that pick-up ions originating from Europa are also present, in
the downstream region during both E4 and E6, and upstream during E6. The
assumed pick-up ion species are H+, H${}_{2}^{+}$ and H2O+. Europa’s wake was
shown to contain enhanced ion densities, possibly caused by pick-up ions from
Europa. The presence of pick-up ions provide an indirect indication that
Europa possesses an atmosphere.

The bulk velocity vectors of the plasma were determined from the PLS data. A
flow deflection (see Section 1.2.4) was measured during flybys E4 and E6. This
verifies that Europa is a weakly mass loading object, hosting a tenuous
exosphere. The deflection during the E4 flyby is shown in Figure 1.18. The
temporal extent of the flow deflection is also indicated in the overview
plots, Figures A.4 and A.5.

Figure 1.18: Bulk flow-vectors during Galileo’s E4 flyby on December 19, 1996.
[Reproduced from Paterson et al. (1999) with permission from John Wiley and
Sons. Copyright 1999 by the American Geophysical Union.]

####  1.3.2 Energetic charged particles

Energetic charged particles at Europa have been studied by the EPD instrument.
Paranicas et al. (2000) presents energetic ion and electron data collected by
the EPD instrument during the E4, E12, E14 and E15 flybys of Europa and
physically interprets the data. A variety of features is identified that are
linked to interaction of energetic particles with Europa. Here an overview is
presented of the most relevant aspects, in preparation for the EPD analysis
later in this thesis.

Figure 1.19: Energetic particle data collected during the E12 flyby. E1 (29-42
keV) and F3 (527-884 keV) are electron channels, A1 (42-180 keV) and A6
(825-2050 keV) are ion channels that do not discriminate between species and
TP3 (540-1040 keV) is a proton channel. The two red dots indicate two examples
of depletions that occur because the detector has moved behind the radiation
shield. The grey vertical lines indicate the extent of the depletion features
discussed in the text. [Reproduced from Paranicas et al. (2000) with
permission from John Wiley and Sons. Copyright 2000 by the American
Geophysical Union.]

During the E12 upstream flyby, deep decreases in the energetic ion rate are
reported, from 12:01 to 12:07, this period is marked by vertical grey lines in
Figure 1.19. Note that there are two types of depletion visible in this
figure: depletions when the detector moves behind the radiation shield (see
Section 2.1.2) and depletions that occur without the shield. The two red dots
indicate examples of radiation shield depletions. These measurements allow to
determine the noise level in the specific channel of the instrument. Of
importance here are the measurements without the shield. An overview of all
the E12 particle data can be seen in Figure A.7 in Appendix A.3. It is argued
by Paranicas et al. (2000) that the depletions of the more energetic ions
during this flyby is a consequence of the size of these particles’ gyroradius.
This is the radius of the circular orbit that these energetic particles
perform about the magnetic field lines (the motion of charged particles will
be discussed in more detail in Section 2.2). Their gyroradius is larger than
the altitude of Galileo, hence these particles are lost by collisions with the
surface. As an example Paranicas et al. (2000) states that the gyroradius of
protons with energies of 750 keV is around 200 km at the closest approach,
which is the same as the altitude of Galileo. These particles are measured in
the TP3 channel shown in Figure 1.19. The "bite-out" feature in lower energy
ions, visible in the A1 channel in Figure 1.19 just before the closest
approach at 12:02, cannot be explained by this effect. Instead it is proposed
that this is a consequence of a drift motion that lets electrons drift towards
Jupiter and ions away from Jupiter. This drift motion is referred to as the
grad-B drift (see Section 2.2.3). Due to magnetic field pile-up upstream of
Europa charged particles approaching Europa experience a gradient in the
magnetic field perpendicular to the field lines, which causes the grad-B drift
motion. The drift makes particles drift perpendicular to the gradient in the
magnetic field and the field lines. The strongest gradient coincides in time
with the "bite-out", the particles would thus be drifting away from this
region. Furthermore the bite-out in higher electrons is larger than in the
lower energy ones, which is to be expected for the grad-B drift, since its
effects scales linearly with the particle energy. The hypotheses of Paranicas
et al. (2000) have not been verified by modelling.

During the E4 flyby, prior to entering the wake, a depletion of ions is
observed of which the gyroradius is not large enough to reach the surface. The
E14 flyby is another upstream flyby. During this flyby no signs of interaction
with Europa are reported. Finally it should be noted that the other upstream
flybys E19 and E26 are not discussed in Paranicas et al. (2000).

Depletions of energetic electrons and ions are observed in the wake of Europa,
during flybys E4, E11 and E15. Paranicas et al. (2000) propose that the main
mechanism responsible for the depletions observed is the depletion of trapped
energetic particles bouncing up and down along magnetic field lines that come
in contact with Europa and impact the trailing side. The authors note that the
center of the wake is shifted towards Jupiter (during the E4, E11 and E15
flybys).

Paranicas et al. (2001) discusses EPD electron data from E12, E14 and E26. It
is argued that energetic electrons (10 keV-10 MeV) primarily impact Europa’s
trailing hemisphere, explaining the observed difference in albedo between
Europa’s trailing and leading hemispheres (Figure 1.20).

Figure 1.20: Albedo dichotomy between Europa’s leading (top) and trailing
(bottom) hemispheres. Left: natural color, right: enhanced color. [NASA
https://photojournal.jpl.nasa.gov/target/Europa].

Electrons primarily impact the trailing side because their bounce period is
small compared to the contact time of the magnetic field line their are
travelling along with Europa (the ratio of the half bounce time and the
contact time is less than one). This is unlike ions whose bounce period is
larger than the contact time (ratio exceeds one). Bombardment of electrons is
highest at low latitudes. E26 data for the ions and electrons are discussed in
Paranicas et al. (2007). A reduction of particle flux in both channels is seen
corresponding to the direction of Europa, suggesting that these particles have
been depleted after direct interaction with the surface. E26 is a high
latitude pass at low altitudes. Paranicas et al. (2007) argues that what is
seen in the EPD data is the ongoing process of Europa moving with respect to
the magnetic field and the particles travelling along the field being
depleted.

Part of the neutral particles of Europa’s tenuous atmosphere escape Europa’s
gravity and form a torus of (neutral) particles located along Europa’s orbit
around Jupiter (Johnson et al. 2009). The torus provides evidence of the
release of material from Europa’s surface from the atmosphere, the plumes or a
combination of both. Evidence for this torus has been provided by the Ion and
Neutral Camera (INCA) instrument on the Cassini mission, that observed the
Jovian system when it flew by Jupiter on its way to Saturn (Mauk et al. 2003).
INCA detected energetic neutral atoms (ENAs) originating from Europa’s orbit
around Jupiter (see Figure 1.21).

Figure 1.21: Jupiter and the Europa torus are identified as major sources of
Energetic Neutral Atom (ENA) emission by Mauk et al. (2003) using data from
Cassini’s ENA detector. The red hue indicates the trapped energetic protons
thought to be responsible for the ENA generation. The trapped particles
responsible for the ENA’s are depleted to such an extent that Io’s neutral
torus does not appear as a signficant source of ENA’s. [NASA
https://photojournal.jpl.nasa.gov/catalog/PIA04433].

These ENAs are formed when neutral atoms charge exchange with energetic ions
trapped in Jupiter’s magnetosphere, this is similar to the ENAs predicted at
the Io torus (Futaana et al. 2015). Without being influenced by the Lorentz
force, the neutralized energetic ions continue as ENA’s along a path
determined by gravity and their velocity vector at the point of the charge
exchange. Independent evidence for the existence of the neutral torus has been
obtained from Galileo EPD data (Lagg et al. 2003; Kollmann et al. 2016). A
depletion of protons at energies between 80 and 220 keV was observed by Lagg
et al. (2003) and Kollmann et al. (2016), they argue that this depletion is
caused by the charge exchange of the energetic protons with neutral particles
in the torus. Mauk et al. (2004) constrains the total number of neutral atoms
and molecules in the torus to $0.6(\pm 0.25)\times 10^{34}$, while the
vertical thickness of the torus is constrained to 1 $R_{J}$ and its density to
1.6-410 particles/cm3 (Kollmann et al. 2016). The large density range is
indicative of systematic uncertainties in the method to invert EPD data rather
than a large scale variability. Modelling of atmospheric losses of O and H2 by
Smyth and Marconi (2006) predict densities for Europa’s torus that are within
the range determined by these observations. In their model the loss is
dominated by H2. Recently Dols et al. (2016) has suggested that the
atmospheric loss is dominated by O2 losses instead. These measurements
discussed by Lagg et al. (2003) and Kollmann et al. (2016) reveal the
depletions of energetic ions detected in-situ due to charge exchange with
neutrals of the torus. This method could in principle be used to detect
Europa’s atmosphere, but has never been applied to the close vicinity of
Europa.

###  1.4 Main research question of the thesis

Remote sensing observations indicate that Europa is surrounded by a tenuous
atmosphere. Large uncertainties exist in properties of this atmosphere, such
as the loss rate and structure, due to the lack of adequate measurements
(Plainaki et al. 2018). Recent observations by the Hubble telescope and past
data from Galileo in-situ instruments hint at the existence of eruptions of
water vapour originating from the interior of Europa at six different
occasions (Roth et al. 2014b; Sparks et al. 2016, 2017; Jia et al. 2018). The
cloud of material created by these eruptions is referred to as "plumes". Large
uncertainties remain in the properties these plumes, as the observations can
only approximately constrain properties such as their gas column density,
scale height, source location and the minimal eruption time. Even their
existence has not been confirmed by direct measurements. The plumes could
offer an opportunity to directly study Europa’s interior, by flying a
spacecraft through the plumes and taking samples. Therefore, the plumes could
offer a "window" to Europa’s interior without even having to land on the
surface. As the atmosphere contains material originating from the surface, it
also offers an opportunity to assess properties of Europa’s interior, though
the information derived from the atmosphere is less direct than from the
plumes.

The only missions that has studied Europa from close by is the Galileo
mission, which was active in the Jupiter system from 1995 to 2003. In this
time period it made 12 flybys of Europa (Alexander et al. 2009). As it was not
equipped with a neutral particle detector, no direct detections of the
particles of the atmosphere or the plumes could have been made. Amongst its
in-situ instruments Galileo carried two charged particle detectors, the
energetic particle detector (EPD) and the plasma instrumentation (PLS)
(Williams et al. 1992; Frank et al. 1992). Data from in-situ instruments on
Galileo have been used to show that:

  * •

the plasma corotating together with Jupiter is diverted near Europa, based on
PLS data from the first two flybys (Paterson et al. 1999). This confirms that
an ionosphere is present, which is the result of the ionization of atmospheric
particles. Furthermore direct signatures of newly formed pick-up ions
originating from Europa’s atmosphere have been seen in PLS data during the
same flybys. PLS data collected during the other flybys have not been
published in literature.

  * •

an extreme plasma density derived from the plasma wave data and changes in the
magnetic field measured during the E12 flyby could be caused by a local
enhancement of the neutral particle density (Jia et al. 2018), such as a
plume.

  * •

energetic charged particles are depleted in the vicinity of Europa (Paranicas
et al. 2000). A torus of neutral gas associated with Europa’s orbit depletes
energetic ions by charge exchange. This is based on data from the energetic
particle detector (EPD) collected inside Europa’s orbit, but not in the
vicinity of the moon (Lagg et al. 2003; Kollmann et al. 2016). The depletions
detected close to the moon have not been analysed previously in the context of
an atmosphere or plume.

This implies that even though the atmosphere and the plumes could not have
been detected directly by Galileo instruments, the in-situ data can contain
signatures of the interaction of the charged particle environment with the
atmosphere, plumes and torus. Furthermore, possible unexploited opportunities
might remain in the Galileo in-situ data to detect signatures of the
atmosphere or plumes and constrain their physical properties. Thus, I
formulate the following research question:

"Can the properties (density, scale height) of Europa’s tenuous atmosphere or
any water vapour plumes be constrained using data from the Galileo in-situ
particle detector instruments (PLS, EPD)?"

In addition to this main topic, I will exploit the opportunity to make
predictions for future observations of Europa’s atmosphere and plumes with in-
situ particle detector instruments. The upcoming Europa missions are NASA’s
Europa Clipper mission and ESA’s Jupiter ICy moons Explorer (JUICE) (Grasset
et al. 2013), which are scheduled to make 45 and 2 flybys of Europa in the
early 2030’s, respectively. In this thesis I will focus on JUICE in
particular.

The structure of this thesis is as follows. First the methodology chosen to
address the research question is discussed in Chapter 2. The approach chosen
is to combine the interpretation of spacecraft observations and simulations.
Then, in Chapter 3, the Galileo charged particle dataset is analysed. Next, in
Chapter 4, simulations are used to reproduce the data to characterize the
atmosphere and possible plumes. Subsequently, Chapter 5, is dedicated to
predictions of future measurements. Final conclusions and recommendations for
future work are discussed in Chapter 6.

##  Chapter 2 Research methodology

A combination of the interpretation of spacecraft observations and simulations
is chosen as the approach to identify signatures of Europa’s tenuous
atmosphere and plumes in the Galileo charged particle data. The first step is
to analyze the data to identify signatures of the interaction between Europa’s
atmosphere or plumes, and the magnetosphere in plasma and energetic particles
(Goal 1). Then, simulations will be used to reproduce the identified
signatures and characterize the atmosphere and possible plumes (Goal 2).

Goal 1 will be addressed by characterizing and comparing the charged particle
data collected by Galileo during the Europa flybys to select the best time
period(s) to search for signatures of the atmosphere or any plumes. Goal 2
involves simulating the data, specifically the depletion of energetic charged
ions near Europa. These particles are depleted near Europa when they hit the
surface or charge exchange with the tenuous atmopshere. Therefore, to
determine the cause of the depletion it is necessary to simulate the
trajectories of the particles. Different scenarios that involve an atmosphere
and no atmosphere will be simulated, to characterize the contribution of the
atmosphere to the depletions. Then, the simulation results will be compared to
the data to determine the contributions of surface impacts or any atmospheric
losses, in the measured depletion of the energetic particles. The comparison
will allow to constrain atmospheric properties such as density and scale
height.

In this Chapter the methodology is explained in more detail. First, in Section
2.1, the Galileo mission and the charged particle detector instruments onboard
this mission (EPD and PLS) will be introduced. Then, in Section 2.2 the motion
of the charged particles that can be detected by the instruments will be
described and the appropriate method to simulate them. Finally, in Section
2.3, the computer code is discussed that will be used to simulate the
trajectories of neutral and charged particles.

###  2.1 Galileo and instrumentation

In this section NASA’s past Galileo mission, a mission of particular interest
to this thesis, is discussed in more detail, including its most relevant
instrumentation.

The Galileo mission (Figure 2.1) was launched in 1989 with Space Shuttle
Atlantis that was active in the Jupiter system between 1995 and 2003. During
this period the Galileo mission studied Jupiter and several of its moons. The
primary part of the mission ran from December 1995 to December 1997, after
which it was extended two times. An object of special interest for the Galileo
mission was Europa, to which the first extension of the mission was dedicated:
it was named the ’Galileo Europa Mission". A detailed overview of all the
Galileo Europa flybys will be presented in Section 3.1. Galileo carried
several in-situ and remote sensing instruments. Of particular interest for
this work are the following in-situ instruments: the plasma instrumentation
(PLS), the Energetic Particle Detector (EPD) and the magnetometer (MAG) (Frank
et al. (1992); Williams et al. (1992); Kivelson et al. (1992)). PLS and EPD
are discussed in more detail in the next section. A particular challenge
facing the scientists working on the Galileo mission is the failure of the
main antenna to unfold. This severally limited the data rate during the whole
Galileo mission. After the final mission extension, the spacecraft descended
into Jupiter’s atmosphere in 2003 (NASA (2018)).

Figure 2.1: Artist impression of the Galileo mission [NASA
https://photojournal.jpl.nasa.gov/catalog/PIA18176]

####  2.1.1 Plasma instrumentation (PLS)

For the purpose of studying the plasma environment in-situ, Galileo was
equipped with the plasma instrumentation PLS (Frank et al. 1992). PLS was a
charged particle detector designed to detect both (positive) ions and
electrons. A photo of the instrument is shown in Figure 2.2. Figure 2.3 shows
a diagram of the main components of PLS.

Figure 2.2: Photo of PLS. [NASA PDS] Figure 2.3: Diagram of PLS [NASA]

Since this thesis only considers the PLS ion data, only the ion detection
aspect of PLS is explained in more detail. Charged particles entered PLS
through either of the two apertures that are indicated in the diagram in
Figure 2.3 and are also clearly visible in the photo shown in Figure 2.2.
After entering the detector through the aperture the particles passed through
the electrostatic analyser (ESA). The electrostatic analyser was made out of
two curved plates with a spacing in between. Over the spacing a voltage was
applied. Only those particles with the desired energy per charge (E/q) could
pass through the spacing between the plates and reach the detectors, without
hitting the plates. By varying the field over the space between the plates,
PLS could scan over energy per charge. The energy-per-unit charge (E/q) ranges
from from 0.9eV to 52 keV. PLS had 7 ion detectors (1P to 7P in Figure 2.3)
that each detected ions coming from a different direction of the sky. PLS was
located on the magnetometer boom of Galileo, as is shown in Figure 2.4.
Therefore the PLS instrument was rotating about Galileo’s rotation axis.

Figure 2.4: Location of the PLS instrument on the magnetometer boom. Shown is
the Galileo model at the Jet Propulsion Laboratory, Pasadena. The main body of
the spacecraft is on the right side, the main antenna can be recognized in the
top right corner. [N. Krupp]

The detectors were oriented in such a way that during one spin (around 20
seconds) of the Galileo spacecraft (approximately) the whole sky was scanned.
The detectors were channel electron multipliers (CEM), also referred to as
Spiraltrons. CEMs consist out of a tube with a coating that has a high
probability of giving secondary electron emissions upon impact by a particle
(Eklund 2002). When a particle entered the tube and hits the wall of the tube,
secondary electron emission would occur. These secondary electrons were
accelerated by the electric field inside the tube, so that they would produce
even more secondary electrons when they hit the wall, this is referred to as
an ’avalanche’ effect. It is the current generated by these secondary
electrons that was measured and not the original ion. PLS data was transmitted
in the units of counts per duty time, per energy bin and per direction bin
(referred to as sector). Using the calibration data (’chi-factor’), obtained
from laboratory experiments, the recorded counts can be converted to
differential flux in units of cm-2s-1sr-1eV-1. Due to the malfunction of the
deployment of Galileo’s main antenna, mentioned before, the PLS data rate was
very limited during the entire mission. Hence, for each spin only a limited
part of the collected data was transmitted to Earth, resulting in an
incomplete coverage of the sky in both energy and direction.

PLS was also equipped with three miniature mass spectrometers, each of these
mass spectrometers was equipped with one "Integral" sensor (1MI to 3MI) and
one "Differential" sensor (1MD to 3MD), these are indicated in Figure 2.3
(Frank et al. 1992). Each mass spectrometer was equipped with an electromagnet
that deflects incoming ions. Only particles with the desired mass per charge
ratio (M/Q) could enter the MD detectors, allowing to determine the flux of
particles per M/Q. The MI detectors were positioned such that they accepted
ions that are not deflected by the electromagnet. The mass spectrometer data
is not considered further in this thesis due to various technical difficulties
associated with this data. Finally, in Table 2.1 the main properties of PLS
relevant to this work are summarized.

Property | Value
---|---
Detectors | 7
Coverage | $\sim 4\pi$
Full scan time |  $\sim 20$ s
Energy range | 0.9eV to 52 keV
Table 2.1: Overview of PLS properties.

####  2.1.2 Energetic Particle Detector (EPD)

The Energetic Particle Detector (EPD), was the Galileo instrumentation tasked
to characterize the energetic charged particle environment in Jupiter’s
magnetosphere (Williams et al. 1992). A photo of EPD is shown in Figure 2.5.

Figure 2.5: Photo of EPD. [NASA]

EPD could detect charged particles (ions and electrons) with energies much
higher than PLS. For ions with atomic number Z > 1 the energy is range is from
20 keV to 55 MeV, while for electrons the energy range is from 15keV to > 11
MeV. For elemental species Helium to Iron the energy range is from 10 keV per
nucleus to 15 MeV per nucleus.

The particle detectors of EPD were mounted on a rotating platform. This is
shown in Figure 2.6.

Figure 2.6: Diagram of EPD. [NASA]

The axis of the rotating platform was perpendicular to the spin axis of the
Galileo spacecraft. During one spin (20 seconds) only one segment of the sky
(perpendicular to the spin axis) was scanned. After every spin of Galileo, the
motor position of the rotating platform was changed. There were seven motor
steps, so in around 140 seconds a spatial coverage of $4\pi$ could be
achieved. A consequence of this canning procedure is that one particular
direction of the sky was only scanned every 140 seconds. In this sense EPD
differs from PLS, as PLS had seven detectors that operate simultaneously and
that could therefore scan the entire sky in one spin.

Also shown in Figure 2.6 is the source holder or foreground shield, behind
which the 0 degree ends of the detector could be positioned to estimate the
noise level. When the detector passed behind this shield, the particle species
of interest could not enter the detector any more. Only the noise signal would
remain. The source of noise were particles with extremely high energies that
penetrated the instrument shielding and the foreground shield and reached the
detectors without passing through the filtering systems that allowed only the
particles of interest to pass. EPD was composed out of two particle detecting
telescopes that were mounted on the rotating platform (Figure 2.6). The two
telescopes are the Low Energy Magnetospheric Measurement System (LEMMS) and
the Composition Measurement System (CMS). Solid State Detectors (SSD) were
used to detect the charged particles in both telescopes. A solid state
detector is made of a semi-conducting material. When a charged particles
passed through the detector, electric charge was released that was used to
detect the particle. The amount of charge depends on the particle species and
energy. Both telescopes were bi-directional telescopes, particles could enter
the detectors from both sides. The properties of the two entrances of LEMMS
are:

  * •

0 degree end: Used magnetic deflection to separate ions and electrons. Ion
detectors A and B (E > $\sim 20$ keV), and electron detectors E1, E2, F1 and
F2 ($\sim 0.52$ MeV > E > $\sim 15$ keV) were on this side.

  * •

180 degree end: this end detected the higher energy electrons and ions.
Absorbers were located on this side to filter out particles with a lower
energy than the ones of interest. Detector C and D were on this side. Both
ions (E > $\sim 16$ MeV) and electrons (E > $\sim 11$ MeV) were detected.

The two sides of CMS were configured as follows:

  * •

0 degree end: a time of flight mass spectrometer was located on this side. The
mass spectrometer allowed for the separation of ions in different species. CMS
provided energy spectra above around 10 keV per nucleus for elements from
helium to iron. Stop and start signals in the TOF system were generated by,
respectively, a foil and a detector (named KT). When charged particles passed
through this foil and hit the detector electrons were generated that were
detected by Multi Channel Plates (MCP). These are plates of electron
multiplier tubes stacked together. Detector KT also gave the total energy of
the particle, combining this information with the time of flight (thus the
velocity of the particle) allows for the determination of the mass per charge
(m/q). A valid detection of a particle in the CMS TOF required a triple
coincidence: a start signal, a stop signal and a KT energy pulse. This made
CMS TOF less sensitive to penetrating background radiation since penetrating
particles would not generate these three coincidences. The channels of CMS
that detected protons (TP) and oxygen (TO) are the most important ones for
this work. In particular the data from the TP1, TP2, TP3, TO2 and TO3
channels, which differ in energy (Table 2.2), will be used in this work. The
definition of these channels is explained in more detail in Appendix A.1.

  * •

180 degree end: this end was not used due to data transmission issues,
therefore it will not be discussed here further.

Unlike PLS, EPD operated at full resolution, but only during the close moon
flybys. The data of this type is referred to as "record mode", which is the
only data product that will be considered in this thesis. Finally, in Table
2.2 the main properties of EPD relevant to this work are summarized.

Property | Value
---|---
Coverage | $\sim 4\pi$
Motor positions | 7
Full scan time |  $\sim 20$s $\times 7$ = $\sim 140$ s
Energy range ions | 20 keV to 55 MeV
Energy range electrons | 15keV to > 11 MeV
Mass separation | Helium to Iron
Proton channels | TP1 (80-220 keV), TP2 (220-540 keV)
| TP3 (540-1040.0 keV)
Oxygen channels | TO2 (416-816 keV), TO3 (816-1792 keV)
Table 2.2: Overview of EPD properties (in the high resolution mode used during
close moon flybys). Also indicated are the TP and TO channels, which are most
relevant to this work.

####  2.1.3 Magnetometer (MAG)

Though not the main focus of this project, the magnetometer data is referred
to frequently in this work, therefore Galileo’s magnetometer instrument is
introduced here briefly. Galileo’s magnetometer (MAG) consisted of two
triaxaial fluxgate magnetometers (Kivelson et al. 1992), that could take up to
30 samples per second. The two magnetometers were located on the boom of the
Galileo spacecraft, one at 11.03 meter and the other at 6.87 meter from the
spin axis, this is shown in Figure 2.7. The reason for having two
magnetometers was to acquire information about the spacecraft generated
magnetic field and also to provide redundancy.

Figure 2.7: Configuration of the two magnetometers. [NASA]

Magnetic fields generated by the spacecraft decrease in magnitude with
increasing distance from the spacecraft. These fields were characterized by
comparing the fields measured by the first and second detector, which were
located at different distances from the spacecraft. By assuming the sources
are dipoles, their contribution could be removed from the measured magnetic
field. Calibration of the magnetometer was done by measuring the field
generated by a known source at the end of the boom. The magnetometer data was
processed onboard. The data was calibrated and converted into a reference
frame that is not spinning with the spacecraft, it can therefore be
interpreted directly. The final data product are the three components of the
magnetic field in the non-spinning fame. The details of the processing and
further technical aspects of MAG are described in Kivelson et al. (1992). In
this thesis only the processed data product from PDS is used.

###  2.2 Charged particle motion

Understanding the motion of charged particles (ions, electrons) under the
influence of electric and magnetic fields is important for this thesis. Here
the main aspects of this motion are described. The equations provided express
particle motion in the non-relativistic limit, which is appropriate for this
thesis as only non-relativistic ions are studied.

####  2.2.1 The Lorentz force and gyration

The basic equation expressing the force experienced by a charged particle
under the influence of electric and magnetic fields is that of the Lorentz
force (Equation 2.1). In this equation $m$ is the mass of the particle,
$\bm{v}$ is its velocity, $q$ is its charge, $\bm{E}$ is the electric field,
$\bm{B}$ is the magnetic field and $t$ is the time.

$m\frac{d\bm{v}}{dt}=q(\bm{E}+\bm{v}\times\bm{B})$ (2.1)

If only an electric field is present, the charged particle will be accelerated
along the direction of the field. The sign of the acceleration will be
determined by the charge, for positive particles in the direction of the
electric field and for negative particles in the opposite direction. The
effect of the magnetic field is more complicated. A particle at rest with
respect to the magnetic field, will not experience a magnetic force. Also, a
particle with its velocity perfectly aligned with the magnetic field will
experience no Lorentz force (since the cross product will be zero). Any
charged particle with a velocity component perpendicular to the magnetic
field, will experience a Lorentz force. Because of the cross product between
velocity and magnetic field, the Lorentz force will always be perpendicular to
the particle velocity and the magnetic field. This force will cause the
charged particle to start gyrating: it will perform a circular orbit around
the magnetic field line, but its velocity magnitude (and energy) won’t change.
The center of the gyration is referred to as the ’gyrocenter’ or ’guiding
center’. The angle between the magnetic field and the velocity vector of a
charged particle is referred to as ’pitch angle’. The gyration for a
positively charged ion and a negatively charged electron are shown in Figure
2.8.

Figure 2.8: Gyration of a positively charged ion and a negatively charged
electron. The magnetic field is into the plane of the figure. Also indicated
is the center of the gyration, the guiding center. [Reprinted/adapted by
permission from Springer International Publishing: Introduction to Plasma
Physics and Controlled Fusion by Francis. F. Chen $\copyright$ (2016)]

This gyrating motion is characterized by two factors: the gyroradius and the
gyrofrequency, these are expressed by respectively Equation 2.2 and Equation
2.3.

$r_{g}=\frac{v_{\perp}}{|\omega_{g}|}=\frac{mv_{\perp}}{|q|B}$ (2.2)
$\omega_{g}=\frac{qB}{m}$ (2.3)

Heavier particles of the same velocity have a larger gyroradius but a smaller
gyrofrequency. The gyroradius linearly scales with the perpendicular component
of the velocity. Larger field strengths lead to higher frequencies but smaller
gyroradii. The direction of the gyration is determined by the charge of the
particle: it is opposite for ions and electrons, this is shown in Figure 2.8.

The gyration of charged particles is associated with an invariant quantity,
referred to as the "first adiabatic invariant". It states that the magnetic
moment of a charged particle can be considered a constant if the frequency of
the field variations is lower than the gyrofrequency. The magnetic moment
$\mu$ is expressed by Equation 2.4.

$\mu=\frac{1}{2}\frac{mv_{\perp}^{2}}{B}$ (2.4)

####  2.2.2 ExB drift

In reality, magnetic fields in solar system or astrophysical environments are
not uniform in space and exist in combination with electric fields. In the
next subsections the motions resulting from these complicating factors is
described. First the case is considered where a magnetic and electric field
occur together in a perpendicular configuration. Such a configuration results
in the motion of the guiding center of the particle, referred to as the ExB
drift. The particle’s guiding center will have a net motion in the direction
perpendicular to the electric and magnetic field. The drift velocity of the
guiding center is expressed in Equation 2.5.

$\bm{v}_{E}=\frac{\bm{E}\times\bm{B}}{B^{2}}$ (2.5)

The ExB drift does not depend on the charge or mass of the particle and is
thus the same for ions and electrons. The ExB motion is shown in Figure 2.9.

Figure 2.9: ExB drift for an ion and a electron. $V_{gc}$ is the same as
$V_{E}$ in Equation 2.5. [Reprinted/adapted by permission from Springer
International Publishing: Introduction to Plasma Physics and Controlled Fusion
by Francis. F. Chen $\copyright$ (2016)]

This drift is the consequence of a varying gyroradius, which is caused by the
introduction of the perpendicular electric field. During one half of the
gyration the electric field accelerates the particle and thereby increases the
gyroradius. During the other half the electric field has a decelerating
effect, thereby decreasing the size of the gyroradius. Thus, during one part
of the gyromotion the gyroradius is larger than during the other, the
consequence of this is a net motion in the direction perpendicular to the
electric and magnetic field. Newly formed ions in Europa’s ionosphere perform
an ExB drift motion.

####  2.2.3 Magnetic gradient drift

A drift motion of the guiding center occurs when there is a gradient in the
magnetic field strength in the direction perpendicular to the field lines. The
drift velocity of the guiding center is expressed by Equation 2.6.

$\bm{v_{\nabla B}}=\frac{mv_{\perp}^{2}}{2qB^{3}}(\bm{B}\times\nabla{\bm{B}})$
(2.6)

This drift motion is perpendicular to the field lines and the gradient in the
field strength. The dependence on charge $q$ indicates that the direction of
this drift is different for positively and negatively charged particles. The
drift arises due to a variation of the gyroradius, this is illustrated in
Figure 2.10. During its gyromotion the charged particle will travel through a
region with a higher and a lower field strength. The gyroradius is larger in
the region with a lower field strength, but smaller in the region with higher
field strength. The effect of this is that the gyro-orbit is not a closed
circle any more, which results in a net motion of its guiding center.

Figure 2.10: Gradient B drift. [Reprinted/adapted by permission from Springer
International Publishing: Introduction to Plasma Physics and Controlled Fusion
by Francis. F. Chen $\copyright$ (2016)]

####  2.2.4 Magnetic curvature drift

The curvature B drift of the guiding center occurs when there is a curvature
in the magnetic field. The drift velocity of the guiding center is expressed
by Equation 2.7.

$\bm{v_{R}}=\frac{1}{q}\frac{\bm{F}_{cf}\times{\bm{B}}}{\bm{B^{2}}}=\frac{mv^{2}_{||}}{q\bm{B^{2}}}\frac{\bm{R}_{c}\times{\bm{B}}}{\bm{R_{c}^{2}}}$
(2.7)

It is a consequence of the centrifugal force
$\bm{F}_{cf}=mv^{2}_{||}\frac{\bm{R}_{c}}{{R}^{2}_{c}}$ experienced by a
charged particle moving along a curved magnetic field. Where $v_{||}$ is the
velocity along the magnetic field and ${R}_{c}$ the radius of curvature.

This drift occurs in the direction perpendicular to the radius of curvature
($R_{c}$) and the magnetic field. The direction of the drift is opposite for
particles with positive and negative charge, because of the dependence on
charge.

Note that the curvature drift always occurs together with the gradient B drift
described previously. This is because a curved magnetic field requires a
change in field strength, a field without this gradient in field strength
would violate $\nabla\cdot\bm{B}=0$. Hence a gradient drift perpendicular to
the field and the gradient occurs. In planetary magnetospheres the combined
curvature drift and gradient B drift causes an azimuthal drift of the
gyrocenter, from the perspective of the planet.

####  2.2.5 Magnetic mirror

The magnetic mirror motion of the guiding center occurs when a charged
particle enters a region of converging magnetic field lines, which is
illustrated in Figure 2.11.

Figure 2.11: Schematic of a magnetic mirror. In the figure converging magnetic
field lines are illustrated by the solid black lines. The horizontal dashed
line indicates the axis of symmetry of the field. On the left a positive ion
is indicated. A gyro orbit about a field line removed from the axis of
symmetry is indicated by the solid circle. The dashed trajectory indicates a
gyro orbit about the axis of symmetry of the field. [Reprinted/adapted by
permission from Springer International Publishing: Introduction to Plasma
Physics and Controlled Fusion by Francis. F. Chen $\copyright$ (2016)]

A gradient in the magnetic field occurs along the field lines shown in Figure
2.11. A particle travelling from left to right in this figure will experience
an increase in magnetic field strength. The particle moving towards the
stronger field experiences a Lorentz force, which is by definition
perpendicular to the field. On the left side of the figure, where the magnetic
field is homogeneous, the effect of the Lortenz force results in a gyration
about the magnetic field. However, when the particle enters the region where
the field lines start converging, the Lorentz force will have a component that
decreases the velocity component of the particle parallel to the field.
Assuming that the first adiabatic invariant is conserved, meaning that the
magnetic moment expressed by Equation 2.4 remains constant, the perpendicular
component of the particle velocity should increase to keep the magnetic moment
constant. However, since the Lorentz force cannot increase the total velocity
of the charged particle, the parallel velocity of the particle will decrease.
Parallel velocity is converted into perpendicular velocity, slowing down the
particle. Essentially the pitch angle of the charged particle is increasing.
When all parallel velocity has been converted into perpendicular velocity the
particle will be reflected away from the converging zone, rather than continue
moving towards it. Particles between two converging field regions will
oscillate (bounce) provided that the condition in Equation 2.8 is met.

$B_{m}>\frac{B_{0}}{\sin^{2}\alpha_{eq}}$ (2.8)

In this Equation $B_{m}$ is the field at the mirror point, $B_{0}$ the
equatorial field and $\alpha_{eq}$ the equatorial pitch angle. This type of
motion is referred to as mirror motion. An example of this is a planetary
magnetosphere, regions of converging field lines occur near the magnetic poles
of the object and charged particles can mirror between these poles, this is
addressed in more detail in the next Section.

####  2.2.6 Trapped particle motion

Planetary magnetic fields combine all aspects discussed above. Field
gradients, curvature and electric fields all lead to the trapping of charged
particles due to a motion that can be decomposed in three elements: gyration,
mirror motion and azimuthal drift. The energetic charged particles that will
be simulated in this thesis are an example of these trapped energetic
particles.

Planetary magnetic fields are often described as a dipole magnetic field. In
that case the magnetic field strength, at a specific radial location $r$ and
latitude $\lambda$ with respect to the center and magnetic axis of the object,
is given by Equation 2.9. In this equation $M_{E}$ is the magnitude of the
magnetic moment.

$B=\frac{\mu_{0}}{4\pi}\frac{M_{E}}{r^{3}}(1+3\sin^{2}\lambda)^{(1/2)}$ (2.9)

In the context of planetary magnetic fields it is often convenient to express
the radial position with respect to the object using the L-shell parameter.
This parameter is the radial distance of a field line at the magnetic equator
$r_{eq}$ divided by the radius of the object $R_{object}$, as shown in
Equation 2.10.

$L=\frac{r_{eq}}{R_{object}}=\frac{r}{R_{object}\cos^{2}\lambda}$ (2.10)

On the right hand side of the equation, $r_{eq}$ is expressed as a function of
any position (expressed in radial distance $r$ and latitude $\lambda$) along
the field line. Planetary magnetic fields are not perfectly dipolar. For
example in the case of Jupiter, the magnetic field is stretched outwards in
the magnetic equator by the coroting plasma, this is depicted in Figure 1.10.
However in such magnetospheres the mirror motion still occurs and does not
change qualitatively.

Figure 2.12 illustrates the different aspects of the trapped particle motion.
2.12A shows the combined effect of the gyration, the mirror motion and the
azimuthal drift. 2.12B shows the motion of the guiding center, that is the
result of the mirror motion and the azimuthal drift. 2.12C shows only the
azimuthal drift.

Figure 2.12: Trapped particle motion, A: gyration, mirror motion and azimuthal
drift, B: motion of the gyrocenter, C: azimuthal drift. [From Kotova (2016)]

The mirror motion is illustrated in Figure 2.13 for an arbitrary planet. This
motion occurs is Jupiter’s magnetosphere, trapped energetic charged particles
are performing mirror motions between the magnetic poles.

Figure 2.13: Trapped particle motion. [From Kotova (2016)]

The latitude of the mirror point is determined by the equatorial pitch angle
of the energetic charged particle, which is defined as the angle between the
velocity vector of the particle and the magnetic field at the magnetic
equator. Equation 2.11 expresses the equatorial pitch angle in a dipolar
magnetic field.

$\sin^{2}\alpha_{eq}=\frac{B_{eq}}{B_{m}}=\frac{\cos^{6}\lambda_{m}}{(1+3\sin^{2}\lambda_{m})^{1/2}}$
(2.11)

In this equation $B_{m}$ is the magnetic field at the mirror point and
$\lambda_{m}$ the magnetic latitude of the mirror point. Particles with an
equatorial pitch angle of zero and 180∘ will travel all the way to the
magnetic poles. A particle with a 90 degree equatorial pitch angle will stay
in the equatorial plane. In Figure 2.13 an intermediate case is shown.

The period of the mirror motion or bounce period is expressed by Equation 2.12
for a trapped particle in a dipole magnetic field, from e.g. Baumjohann and
Treumann (1997).

$\tau_{b}\approx\frac{LR_{E}}{(W/m)^{1/2}}(3.7-1.6\sin\alpha_{eq})$ (2.12)

In this equation L is the L-shell the particle is mirroring in, W the energy
of the particle and $R_{E}$ the radius of the planetary object. The bounce
period is larger for more massive particles and for longer field lines (larger
L). Particles with a higher energy have a shorter bounce period, since the
velocity is higher for these particles. The dependence on equatorial pitch
angle is not very strong. This can be explained by the fact that particles
with a smaller pitch angle have a higher velocity along and the field, but
also have a larger travel distance, and vice versa for particles with a large
pitch angle.

Besides the drift motion between the magnetic poles, the guiding centres of
the trapped particles are drifting azimuthally because of curvature and
gradient B drift. The resulting drift velocity for a trapped particle in a
dipole magnetic field is expressed by Equation 2.13 (see Baumjohann and
Treumann (1997) for a derivation), in which $B_{E}$ is the equatorial magnetic
field on the surface of the planetary object.

$\langle
v_{d}\rangle\approx\frac{6L^{2}W}{qB_{E}R_{E}}(0.35+0.15\sin\alpha_{eq})$
(2.13)

The drift speed depends on the energy per charge of particles. The drift
velocity is therefore the same for ions and electrons of the same energy, but
in opposite direction. The azimuthal drift increases with energy of the
particle, but also with the L-shell. Like the bounce period, the drift period
only depends weakly on the equatorial pitch angle.

###  2.3 Charged particle tracing simulation

Depletions of energetic ions have been observed in the Galileo Energetic
Particle Detector (EPD) data. To determine the origin of these features,
either by impact on the surface or charge exchange with the atmosphere, it is
necessary to simulate the trajectories of the energetic ions. In this section
the Monte Carlo test particle approach that will be used to simulate the
particles is discussed. This code will also be used to simulate trajectories
of neutral and charged particles to make predictions for future measurements.

####  2.3.1 Simulation approach

Figure 2.14: An example of the results of the particle tracing code: a singly
charged oxygen trajectory near Europa, the energy of the particle is 1.7 MeV.

Depending on the application, the motion of charged particles can be simulated
in different ways. Describing the gyration or the mirror motion is not always
needed. Therefore, the periodic aspect of the particle motion can sometimes be
averaged so that only the motion of its guiding center (Figure 2.12B and C)
needs to be followed. For this thesis a full solution of the Lorentz force is
selected as the most relevant approach. The goal is to simulate losses of the
energetic particles that interact with the surface or atmosphere and for this
application the gyration cannot be neglected. The gyroradii of the particles
that will be simulated are of the same size or larger than relevant geometric
scales, such as the altitude of the spacecraft flyby. Thus from an orbital
altitude that is smaller than the gyroradius of certain particles, depletions
of the these particles should be observed. This effect is indeed observed in
the Galileo energetic particle detector (EPD) data, as was discussed in
Section 1.3.2. If the gyroradius were to be neglected in the simulation, these
losses would not occur in the simulation. Therefore the full motion needs to
be described.

The charged particle tracing code used in this thesis is a continuation of the
code originally developed for the Master’s thesis project described in
Huybrighs (2015). It is entirely developed in the programming language Python
and makes use of the NumPy library and the irfpy.util library developed by Dr.
Yoshifumi Futaana at the Swedish Institute of Space Physics
111https://irfpy.irf.se/projects/util. First a summary is provided of the main
aspects of the code as described in Huybrighs (2015). For each aspect it is
indicated by ’ions’ and or ’neutrals’ to which type of simulation it refers to
specifically.

  * •

Test Particle (ions & neutrals): a test particle type of simulation is
employed, this means that individual particles are traced as they propagate
under the influence of the relevant forces (gravity or the Lorentz force). The
effect that the particles have on their environment is not taken into account.
This could be important in particular when dealing with charged particles,
their motion can affect the electric and magnetic fields which affect the
Lorentz force. However, for the simulation of energetic charged particles it
can be assumed that they do not influence the fields, as was discussed in
Section 1.2.4. Ionospheric plasma can also influence the fields (in Section
1.2.4 it was shown how Europa’s ionospheric plasma influences the flow of the
corotational plasma). MHD or hybrid simulation could in principle be employed
to provide self-consistent fields from the plasma dynamics. The test particle
method has a key advantage over these methods. The results of the simulation
depend on multiple parameters. With the test particle method each parameter’s
contribution can be determined by running simulations with increasing
complexity. Furthermore it is less computationally intensive. The simplest
simulation that will be considered is the case with homogeneous fields and no
atmosphere. This case will be compared with simulations taking into account, a
flow deflection, Europa’s dipole and an atmosphere. This way the contribution
of each physical effect on the losses of energetic charged particles can be
characterized. In a self-consistent simulation it would be more difficult to
disentangle the contribution of the different effects to the losses. The
models used to simulate the atmosphere, the flow deflection and the induced
dipole are discussed later in this section.

  * •

Monte Carlo (ions & neutrals): the code generates particles with certain
initial conditions according to the Monte Carlo method. This means that code
generates a large number of particles of which their initial velocity vector
is determined by a certain distribution, which determines the probability that
certain initial conditions occur. The choice of the distribution depends on
the context.

  * •

Particle tracing (ions & neutrals): the code determines the three-dimensional
trajectories of charged particles by numerically integrating Newton’s law of
gravitation (first term of the right hand side of Equation 2.14) for neutral
particles or the Lorentz force (second term on the right hand side of Equation
2.14) for charged particles.

$m\frac{d\bm{v}}{dt}=-\frac{GM}{\bm{r}^{2}}\hat{\bm{r}}+q(\bm{E}+\bm{v}\times\bm{B})$
(2.14)

As was discussed previously, a full solution of the Lorentz force is the most
appropriate for this work. It is assumed that the particles do not exert any
forces on each other.

  * •

Leap frog integration (ions & neutrals): for the numerical integration of
Newton’s law of gravitation and the Lorentz force the method of leap frog
integration is used. Equations 2.15 and 2.16 express how, respectively, the
position and velocity are progressed from time step i to time step i+1 in this
method.

$\bm{x}_{i+1}=\bm{x}_{i}+\bm{v}_{i+1/2}\Delta t$ (2.15)
$\bm{v}_{i+1}=\bm{v}_{i}+\bm{f}_{i+1/2}\Delta t$ (2.16)

The equations are implemented as follows. First, the particle position is
progressed with Equation 2.15. The progression of position depends on the
velocity at step i+1/2. For the first time step (namely, the progression from
i = 0 to i =1/2) the velocity at i+1/2 is calculated with Equation 2.16, by
calculating the force $f_{i+1/2}$ at i+1/2 using the position at step i and
using half a time step $\Delta t$. The force can be either the Lorentz force
or gravity. For the subsequent time step velocity is progressed from v at
i+1/2 to v at i+3/2 with Equation 2.16 and using the time step size $\Delta
t$.

  * •

Super particles (ions & neutrals): the code has the functionality to treat
particles as super particles. This means that each particle in the simulation
represents a number of particles with the same initial conditions that are
travelling together (see for example Holmström (2007)). This aspect of the
code is only used in the simulations for predictions of future measurements
(Chapter 5).

For further technical details on the code the reader is referred to the work
in Huybrighs (2015). Various changes have been made to the code since the
publication of Huybrighs (2015), of particular importance to this thesis are
the following aspects:

  * •

Backtracing (ions):  a crucial new component added to the code for this thesis
is the backtracing functionality. This means that rather than calculating the
trajectories of particles forward in time, they are calculated backwards in
time (see for example Futaana et al. (2003, 2010)). This is achieved
essentially by incorporating a negative timestep in the existing method. This
functionality is very useful when determining the origin of particles that
have reached a spacecraft at a certain position. In the case of forward
calculations one would have to trace many particles from a wide range of
positions to determine which ones reach the spacecraft. In the case of
backtracing calculations one would only have do such a computation for one
position: that of the spacecraft. Thus for this type of simulation, the
backtracing method requires less computational resources, which justifies its
use.

  * •

Particle losses (ions): energetic charged particles in the simulation can be
lost in two ways: by impacting on the surface or by charge-exchanging with
atmospheric neutral particles. The loss due to impact is implemented by
removing particles from the simulation as soon as they obtain a radial
position smaller than Europa’s radius. Losses due to charge exchange are
implemented following the method described on Brieda (2011). The method is
based on Equation 2.17, which expresses the probability $P$ that charge
exchange occurs for a particle located at a certain location where the number
density is given by $n$.

$P=1-\exp(-n\sigma gdt)$ (2.17)

In this equation $\sigma$ is the collision cross section, which is a measure
for the probability of charge exchange between the particle of interest and an
atmospheric particle, $g$ expresses the relative velocity of the particle, and
$dt$ expresses the time step used to integrate the particle trajectory. Charge
exchange is then said to occur if a random generator, that generates numbers
between 0 and 1, generates a number larger than the charge exchange
probability $P$. In this work this is implemented by calculating $P$ for every
integration step. For the calculation of the relative velocity it is assumed
that the atmospheric particles are at rest. Then for each of these steps a
random number is generated. The first integration step for which the random
number is larger than $P$, is then considered as the point where charge
exchange occurs. The particle that charge exchanges is then discarded in the
simulation. Since the simulation is a Monte Carlo approach, a large number of
particles is used and therefore a statistical analysis of the particle losses
by charge exchange is possible. The atmospheric models used to determine the
atmospheric density at every position are discussed in the next section.

  * •

Electric and magnetic fields (ions): assumptions for the electric and magnetic
fields are required to calculate the Lorentz force. These fields can be set as
homogeneous fields, but it is also possible to use analytical equations that
express the fields at every position. An example is the analytical model in Ip
(1996) to express the electrical field near Europa affected by the diversion
of the corotating plasma. The models used in this thesis are discussed in the
next section.

####  2.3.2 Model inputs

In this section an overview is provided of analytical models that are used as
inputs for the simulations of the (energetic) charged particle trajectories.

#### Analytical expressions for the atmosphere and plume

The analytical expression from Saur et al. (1998) is used to determine the
density of Europa’s atmosphere as a function of radial position $r$. The model
is expressed by Equation 2.18 which depends on a surface density $n_{0}$ and
scale height $H$. $r_{sat}$ expresses the radial dimension of the planetary
object.

$n=n_{0}(r_{sat}/r)^{2}\exp{[(r_{sat}-r)/H]}$ (2.18)

This equation is derived in Saur et al. (1998) as a solution of the spherical
continuity equation for radial outflow. Some examples of atmospheric profiles
calculated with this model are shown in Figure 2.15.

Figure 2.15: Several atmospheric profiles, using the model from Saur et al.
(1998)

Jia et al. (2018) uses Equation 2.19 to express the density of a plume as a
function of radial position $r$ and angular distance $\theta$.

$n_{p}=n_{p0}\exp{[(r_{sat}-r)/H_{p}]}\exp{(-\theta/\theta_{p})^{2}}$ (2.19)

It is similar to Equation 2.18 in the sense that it expresses an exponentially
decaying density, determined by a surface density $n_{p0}$ and scale height
$H_{p}$. The difference is a factor that gives the plume an angular width
$\theta_{p}$. We use this model in the simulation to determine the density of
a plume.

#### Induced magnetic field

The induced dipole of Europa can be expressed as a dipole magnetic field, as
shown by Zimmer et al. (2000). An example output of the model from Zimmer et
al. (2000) is shown in Figure 2.16.

Figure 2.16: Europa’s induced magnetic field during the E12 flyby according to
the analytical model from Zimmer et al. (2000). The arrows indicate the
directions of the magnetic field and the colour the magnitude of the field, in
nT. The figure represents Europa’s equatorial plane. The positive y-axis is
towards Jupiter and the positive x-direction is in the direction of the
corotational plasma. For this example it is assumed that the varying magnetic
field components are: 50 nT in direction of Jupiter, 100 nT in the direction
of the corotational plasma and 450 nT in the direction in the plane. The
magnitude of the field is 463 nT.

Equation 2.20 expresses the magnetic field components at a position $\bm{r}$.
Here $\bm{B}_{sec}$ refers to the induced magnetic field.

$\bm{B}_{sec}=\frac{\mu_{0}}{4\pi}[3(\bm{r}\cdot\bm{M})\bm{r}-r^{2}\bm{M}]/r^{5}$
(2.20)

This equation depends on the magnetic moment $\bm{M}$, which is expressed by
Equation 2.21.

$\bm{M}=-\frac{4\pi}{\mu_{0}}Ae^{i\phi}\bm{B}_{prim}\bm{r}_{m}^{3}/2$ (2.21)

$\bm{M}$ on its turn depends on $\bm{B}_{prim}$, which is the varying
component of Jupiter’s magnetic field, as experienced by Europa (see Section
1.1.1). The radius of the moon is expressed by $r_{m}$. The parameters A and
$\phi$ are, respectively, the amplitude and the phase lag, of the induced
dipole moment relative to $\bm{B}_{prim}$. The value of A is between 0.7 and 1
and the value of $\phi$ is zero, according to Zimmer et al. (2000). It will be
assumed that A is 1 for the rest of this work. Inside the radius of the
conductor ($r$ < $r_{Europa}$A-1/3) the magnetic field is given by Equation
2.22.

$\bm{B}_{sec}=[-B_{prim_{x}},-B_{prim_{y}},0]$ (2.22)

#### Flow deflection

To express the deflection of the corotational plasma around Europa the
analytical model from Ip (1996) is used, which was mentioned previously in
Section 1.2.4. The resulting flow field of the model is shown in Figure 2.17.

Figure 2.17: The analytical model of the deflection of the corotating plasma
by Europa’s ionosphere, from Ip (1996). The arrows represent the direction of
the flow, where the arrow length scales with the speed. The colors represent
the speed. The figure represents Europa’s equatorial plane. The positive
y-axis is towards Jupiter and the positive x-direction is in the direction of
the corotational plasma. For this example it is assumed that the upstream flow
velocity is 76 km/s and that it slows down to 40% of the upstream velocity.

The model by Ip (1996) is expressed by Equations 2.23 to 2.26. The model
expresses the velocity vectors, $V_{x}$ and $V_{y}$, with Equations 2.23 and
2.24, outside of the Alfvén wing disturbance ($r$>$R_{c}$). Inside of the
disturbance ($r$<$R_{c}$) $V_{x}$ and $V_{y}$ are expressed by Equations 2.25
and 2.26.

$V_{x}=-2(1-\alpha)V_{0}(R_{c}/r)^{2}xy/r^{2}$ (2.23)
$V_{y}=V_{0}+(1-\alpha)V_{0}(R_{c}/r)^{2}(1-2y^{2}/r^{2})$ (2.24) $V_{x}=0$
(2.25) $V_{y}=\alpha V_{0}$ (2.26)

The diversion of the flow (Figure 2.17) causes the velocity magnitude of the
corotational plasma to vary. Just in front of and behind Europa (from the
point of view of the plasma flow) this results in a slow down of the
corotating plasma. On the flanks, with respect to the plasma flow direction,
the flow is accelerated. Upstream the flow direction is diverted away from
Europa, while downstream the flow returns to its original direction.

The model treats the disturbance of the flow by Europa as a cylinder, not as a
sphere, thereby taking into account the Alfvén wings. The model assumes that
the corotational flow upstream of Europa, $V_{0}$, and the disturbed
components $V_{x}$ and $V_{y}$ are in the same plane. The deflection of the
flow is thus two dimensional. The equations in this model do not vary along
the height of the cylindrical disturbance. Apart from $V_{0}$ the model is
determined by the parameters $R_{c}$ and $\alpha$. $R_{c}$ is the radius of
the disturbance, which is the radius of Europa plus the height of the
ionosphere. The other important parameter is $\alpha$, the interaction
parameter, which has a value between 0 and 1. It expresses the percentage the
upstream velocity $V_{0}$ slows down within the disturbance cylinder.

The electric field resulting from the flow velocity and the magnetic field in
the frame of Europa is expressed by Equation 2.27, the result is shown in
Figure 2.18.

$\bm{E}=-\bm{V}\times\bm{B}$ (2.27)

Figure 2.18: Electric field during the E12 flyby from Equation 2.27 using the
velocity field from Figure 2.17. The arrows indicate the directions of the
field and the colour the magnitude. The magnetic field components are: 50 nT
in direction of Jupiter, 100 nT in the direction of the corotational plasma
and 450 nT in the direction in the plane.

###  2.4 Selected instrumentation and simulation method

In this chapter the methodology that I will use to address the main research
question was discussed. Data analysis and simulations will be combined to find
signatures of Europa’s atmosphere and plumes in the Galileo charged particle
data.

In Chapter 3 the first goal will be addressed: characterize and compare the
charged particle data collected during the Europa flybys to select the best
time period(s) for the search for signatures of the atmosphere or any plumes.
Galileo charged particle data is available for two instruments: the plasma
particle detector PLS and the energetic charged particle detector EPD.

The second goal, the simulations of the data, will be discussed in Chapter 4.