The Structure and Dynamics of Jupiter’s Magnetosphere
Thesis Proposal
Marissa F. Vogt
Department of Earth and Space Sciences
University of California, Los Angeles
April 2011
Abstract
This thesis will consist of three distinct but related projects in which I investigate the
structure and dynamics of Jupiter’s magnetosphere. The first project is a survey of
magnetometer data throughout the Jovian magnetotail to identify events related to
reconnection and flow. Such events have been previously studied through analysis of
energetic particle data and are thought to be driven predominantly by internal process.
My thesis contributes the first complete survey of reconnection signatures in the available
magnetometer data. I will discuss the event distribution, occurrence rate, and location
inside or outside of a putative neutral line, as functions of radial distance and local time.
Results will be compared to those from previous studies of flow bursts and particle
anisotropies and placed in context of our current understanding of Jovian magnetospheric
dynamics. The second project also addresses global dynamics by determining the size
and location of Jupiter’s polar cap. The boundary between open and closed flux in the
ionosphere is not well defined because, unlike at the Earth, the main emissions at Jupiter
are likely associated with the breakdown of plasma corotation. Additionally, the
magnetospheric mapping of Jupiter’s polar auroral emissions is highly uncertain because
global field models are inaccurate beyond ~30 RJ. In the second part of my thesis I map
contours of constant radial distance from the magnetic equator to the ionosphere in order
to understand how auroral features relate to magnetospheric sources. Instead of following
model field lines, I have mapped equatorial regions to the ionosphere by requiring that
the magnetic flux in some specified region at the equator equals the magnetic flux in the
area to which it maps in the ionosphere. Finally, I will test the idea that Jupiter’s rapid
rotation can explain local time asymmetries in the plasma sheet through use of a largescale kinetic simulation. Specifically, this simulation will examine whether particle
anisotropies develop as rotating flux tubes stretch, as they do in Jupiter’s magnetosphere
between noon and dusk. If possible, I will compare results to the available particle data.
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1. Overview
It is often said that Jupiter’s magnetosphere is one of superlatives. Jupiter’s
magnetic field is the strongest, its standoff distance is the largest (in both absolute and
relative terms), and the planetary rotation period is the fastest in the solar system. These
properties combine to make Jupiter a unique and exciting target for comparative
magnetosphere studies.
Seven spacecraft have now visited the Jovian system and obtained a wealth of
information about the magnetosphere and aurora, both of which have proved to be very
different from what we observe at the Earth. For example, the primary source of plasma
in Jupiter’s magnetosphere is not the solar wind but an internal source: the volcanically
active moon Io, which produces about 1 ton of plasma per second. Another major
difference is that Jupiter’s magnetospheric dynamics appear to be dominated by the
planet’s rapid rotation period (~10 hours). At Jupiter, the potential energy from corotation
is ~50 times larger than the solar wind induced potential in the polar cap, while at Earth
this ratio is closer to ~5, meaning that the solar wind plays a relatively larger role there.
My thesis addresses unanswered questions about the structure and dynamics of
Jupiter’s magnetosphere through three distinct but related projects. The first is a survey of
magnetometer data to 1) identify signatures of reconnection in Jupiter’s magnetotail and
2) characterize the spatial distribution, recurrence period, and other properties of these
events. The second part of the thesis is an improved mapping, through flux equivalence,
of Jupiter’s auroral features to their sources in the middle and outer magnetosphere. The
final project is a kinetic simulation that will examine the effects of rotation and field line
stretching.
These three projects are directly related to the topic of global magnetospheric
dynamics at Jupiter. The first project contributes a new understanding of where and how
often reconnection occurs, an important process that allows for the release of mass and
energy from the system. In particular, the local time distribution of reconnection events
provides useful clues to the relative importance of the solar wind in driving reconnection.
The second part of the thesis, a mapping of the polar aurora, also addresses the relative
role of the solar wind in global dynamics because it allows identification of the size and
location of the polar cap. Knowing how much flux may be open in the polar cap gives us
insight into how much flux may be opened by the solar wind on the day side, and whether
Dungey cycle-like reconnection may be required. The mapping also enables us to identify
the source regions of polar dawn spots, auroral signatures which are thought to be
associated with the inward flow of tail reconnection, with respect to a statistical
separatrix. Finally, the simulation project will test an idea put forward by Kivelson and
Southwood [2005] that discusses the effects of rotation on plasma sheet thickness and
magnetospheric dynamics.
The projects, though separate, all also have relevance to the magnetospheric
structure. The spatial distribution of reconnection events provided by the first part of the
thesis enables identification of a statistical separatrix separating inward and outward
flow. The second project identifies the source regions of three very different polar auroral
regions; the varying nature of the auroral emissions in these regions suggests that there
are very different processes occurring in the different magnetospheric source regions.
Additionally, I am able to more precisely identify the magnetospheric source region of
the main oval emissions, which are associated with corotation enforcement currents and
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are expected to map to ~20-30 RJ, though the distance may vary with local time. Such
variations could be explained by a local time dependence of the plasma outflow rate or
the current sheet density and thickness. Finally, the kinetic simulation project directly
addresses the topic of magnetospheric structure because it tests a theory which explains
local time asymmetries in the plasma sheet thickness.
In the rest of this thesis proposal I will describe the research projects in more
detail, including an overview of our current understanding of each individual topic, how
my work builds on previous studies, my methods, and results or expected results as
applicable.
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2. Properties and periodicities of reconnection events in Jupiter’s magnetotail
The first part of my thesis is a statistical analysis of the properties and distribution
of reconnection events in Jupiter’s magnetotail. I have used magnetometer data to
identify signatures of tail reconnection and compile a list of reconnection events that
satisfy certain criteria. From that list, I am able to describe where and how often
reconnection occurs. I am particularly interested in the local time distribution of events
and whether they display any periodic recurrence, as these properties give important
clues to the importance of the solar wind in driving dynamics.
2.1 Current understanding of magnetotail dynamics
Dynamics in the Jovian magnetosphere are likely rotationally driven rather than
solar wind driven as they are at the Earth. This in part results from Jupiter’s short rotation
period (~10 hours) and the vast size of the Jovian magnetosphere, both of which
contribute to the dynamical importance of rotational stresses. An additional factor
distinguishing Jupiter’s magnetosphere is the presence of an internal plasma source from
the volcanically active moon Io, which releases about one ton of plasma per second.
Ultimately the plasma must be removed from the system; one likely mechanism is
magnetic reconnection and subsequent plasmoid release.
In the model of rotationally-driven dynamics first proposed by Vasyliūnas [1983],
reconnection occurs on mass-loaded flux tubes, which are stretched, pinch off, and form a
plasmoid, as can be seen in Figure 1. The stretching of the flux tubes dragged from
Jupiter’s day side results from centrifugal acceleration of rotating particles. The stretched
flux tubes eventually pinch off, releasing a plasmoid that can escape down the tail. In the
model of Vasyliūnas [1983], a magnetic x-line forms across the tail, beginning just before
midnight local time and extending forward in local time and until it encounters the
magnetopause. The x-line is accompanied by a magnetic o-line at larger radial distances.
More recently, observations of local time asymmetries in the plasma sheet thickness have
been shown to result from dynamics that are consistent with the Vasyliūnas model
[Kivelson and Southwood, 2005]. The plasma sheet is observed to be thinnest at dawn
and to thicken as it rotates through the dusk sector, where it is thickest. On the night side
where the plasma is no longer constrained by the magnetopause and is free to flow down
the tail, the plasma-field configuration is unstable and plasma is centrifugally accelerated
outward down the tail. As a result, the plasma sheet thins. Flux tubes break and are
depleted of plasma then continue to rotate through the nightside to dawn. The empty flux
tubes are carried inward via interchange motions as they rotate through the night side,
while full flux tubes are carried outward. Kivelson and Southwood [2005] suggest that the
stretching and pinching-off continues for all nightside local times across the tail, and that
the location for the stretching and pinching off moves radially inward as the flux tubes
rotate from dusk to dawn.
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Figure 1. Schematic showing the mass loading and release process of the Vasyliūnas
cycle [figure from Vasyliūnas, 1983].
Other models suggest that reconnection at Jupiter is to a significant degree solar
wind-driven [e.g., Cowley et al., 2003]. Solar wind-driven reconnection could occur on
the dayside low latitude magnetopause for a northward-oriented interplanetary magnetic
field, with the opened flux closing through reconnection at a tail x-line, similar to the
Dungey cycle at the Earth. However, the Dungey cycle x-line at Jupiter would likely be
restricted to the dawn side because of the strong outward flows, associated with
corotation and the Vasyliūnas cycle, that oppose sunward flow in the dusk and midnight
sectors [Khurana et al., 2004]. McComas and Bagenal [2007] suggest that at Jupiter the
magnetic flux opened via dayside reconnection with the solar wind need not close in the
magnetotail as at the Earth. Instead, they propose that the flux closes on the
magnetopause, near the polar cusps, rendering tail reconnection unnecessary.
Ultimately the models of Jovian magnetospheric dynamics must account for the
reconnection and plasma flows that have been observed in magnetic field and particle
data from the Jovian magnetotail.
2.2 Building on previous studies that used particle data
Much of what we currently know about Jovian magnetospheric dynamics on a
global scale is based on analysis of data from Galileo’s energetic particle detector (EPD)
instrument. The EPD data can provide particle anisotropies, which can in turn be used to
infer magnitude and direction of plasma flow, to identify intervals of magnetospheric
disturbances, and define a possible separatrix. For example, Woch et al. [2002] studied
inferred flow bursts at distances out to 150 RJ (1 RJ = 1 Jovian radius = 71,492 km) in the
tail and identified a statistical separatrix separating inward and outward flow bursts. The
flow bursts and separatrix are shown in Figure 2. Outside of ~100 RJ in the post-midnight
sector they observed primarily outward flow bursts. In the pre-midnight sector they drew
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two possible lines that could separate flow directions, recognizing that the limited data in
the dusk sector did not establish its location in that region.
Figure 2. Location of a statistical separatrix identified from flow bursts. From Figure 3a
in Woch et al. [2002].
Particle anisotropies have also been studied by Kronberg et al. [2005, 2007, 2008]
with good agreement between the inferred flows and magnetic field data. The authors
identified 34 “reconfiguration events” which include disturbed intervals that are
characterized by increases in the radial and corotational anisotropies occurring at the
same time as increases to the north-south component of the magnetic field. Large,
positive (negative) radial anisotropies occur at the same time as large negative (positive)
Bθ signatures, both of which are consistent with outward (inward) flow. With one
exception, the reported reconfiguration events are located in the post-midnight sector.
These disturbed intervals display a ~2-3 day periodicity consistent with the periodic
modulations in the plasma flux described by Woch et al. [1998]. The periodicity is
thought to be related to the time scale of the internally driven mass loading and release
process at Jupiter [Kronberg et al., 2007].
Whereas particle data have been used to examine magnetospheric dynamics on a
global scale, studies that make primary use of the magnetometer data have thus far
focused on individual events or orbits. Two of the most prominent reconnection events
were reported by Russell et al. [1998]. The events occurred a few days apart in the G8
orbit, both in the post-midnight sector. These events are characterized by an increase in
the magnitude of Bθ, the north-south component of the magnetic field, and in the total
field magnitude. In one event the spacecraft was tailward of the x-line, and in the other
the spacecraft was planetward of the x-line.
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Since previous studies of the magnetometer data have been restricted to individual
orbits or events, my work in this thesis provides the first complete survey of reconnection
events in the Jovian magnetotail from the magnetometer data. The work also serves as a
nice complement to previous studies of flow bursts and anisotropies from the particle
data. One potential contribution of my work is to resolve the ambiguity regarding the
location of the Woch et al. [2002] separatrix in the pre-midnight local time sector.
Additionally, I compare my events, their distribution in radial distance and local time,
and any periodic recurrence to the intervals of increased radial anisotropies identified by
Kronberg et al. [2005]. Many of the studies that noted the 2-3 day periodicity in
reconfiguration events or flow bursts have considered only isolated intervals or a subset
of spacecraft orbits (Galileo orbits G2, C9, and E16). This chapter extends the analysis to
the entire spacecraft magnetometer data set.
2.3 Method: Identifying reconnection events in magnetometer data
In order to study the properties of reconnection events in Jupiter’s magnetotail, I
have surveyed the available magnetometer data for signatures consistent with
reconnection, such as reversals or significant increases in Bθ over background levels. (For
a complete description of the quantitative identification criteria I used, please see Vogt et
al. [2010].) Bθ is the north‐ south component of the magnetic field, over background
levels, and positive increase in this component implies reconfiguration to a more dipolar
field. Such a reconfiguration is shown in Figure 3. In the top panel I have drawn the
initial field configuration, which is primarily radial except near the current sheet. In the
second panel I have drawn reconnected field lines, noting the expected field orientation
and flow directions. On either side of the reconnection point the field becomes more
dipolar than prior to reconnection, and |Bθ| increases.
Figure 3. Reconnection in the Jovian magnetotail, illustrated here in a meridional view.
The top panel shows the initial field configuration, and the second panel shows the
reconfiguration to reconnected field lines, noting the expected field orientation and flow
directions.
Though the magnetometer does not directly measure flow, the sign of Bθ can be
used to infer the radial flow direction. It has been shown to be statistically correlated
during disturbed intervals with the flow direction as deduced from particle anisotropies
[Kronberg et al., 2008; Vogt et al., 2010]. Figure 3 also shows how the sign of Bθ can be
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used to indicate the spacecraft’s position with respect to a reconnection x-line, and
therefore, to infer flow direction. A large, positive Bθ indicates that the spacecraft is
located on the planetward side of the x-line (position 1 in the second panel). A reversal in
Bθ indicates that the spacecraft is located on the tailward side of a reconnection x-line
(position 2 in the second panel). Using the sign of Bθ as a proxy to flow allows me to
compare my events and their properties and distribution to those of intermittent flow
bursts inferred from particle anisotropies in previous studies [Kronberg et al., 2005,
2007].
2.4 Results
This study has been completed and the results were published in Journal of
Geophysical Research [Vogt et al., 2010]. I will summarize the results here, as they will
be incorporated into my thesis.
Surveying the available magnetometer data for reconnection events yielded a list of
249 events, all characterized by an increase in |Bθ| over background levels. One example
is shown in Figure 4. During this event Bθ reached -11.6 nT, more than 10 times the
background level. The event is interesting because we observe both positive and negative
Bθ during the period of enhanced |Bθ|, indicating that the reconnection x-line moves in
over the spacecraft. The event occurred during one the reconfiguration event intervals of
Kronberg et al. [2005].
Figure 4. Magnetic field data from an example reconnection event which occurred on 20
September, 1996, during orbit G2.
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The 249 reconnection events I identified are distributed over nearly all radial
distances and local times that I surveyed (outward 30 RJ, and 18:00-06:00 LT). Events
were observed in radial distance from 33 to 155 RJ, and in local time from ~19:00 to
~06:00 hours. The events have an average duration of 59 minutes, ranging in duration
from 10 minutes (imposed as a lower cutoff) to just over 5 hours. An equatorial plane
view of the event locations is given in Figure 5.
The events in Figure 5 are colored according to the dominant flow direction, as
inferred from the sign of Bθ. Red events, indicating inward flow and positive Bθ, are
found at all local times, and are dominant inside of 75 RJ. Blue events, indicating outward
flow and negative Bθ, are generally located outside of ~75 RJ. There is little available data
at large distances pre-midnight, and there are only a few negative Bθ events in this local
time sector. Events with enhanced both positive and negative Bθ signatures, as was shown
in Figure 4, are plotted in green, and can be found at ~60-90 RJ post-midnight and ~90120 RJ pre-midnight. A statistical separatrix separating inward and outward flow is
shown as a thick purple line; this separatrix begins at ~90 RJ near dawn and moves
outward to ~120 RJ near 22:00 LT. The results qualitatively agree with the Woch et al.
[2002] separatrix in the post-midnight local time sector.
Figure 5. Distribution of reconnection events, shown in the equatorial plane. The events
are colored according to the dominant sign of Bθ, and events that were also identified by
Kronberg et al. [2005] are plotted as triangles. A statistical separatrix separating inward
and outward flow is shown as a thick purple line.
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It is clear from inspection of Figure 5 that more events are observed in the postmidnight local time sector than in the pre-midnight sector. From a total of 249 events,
only 57 events occurred pre-midnight. However, we must also consider the distribution of
available data and the duration and frequency of the events in order to fully understand
the distribution of these dynamic processes. For example, though fewer events were
observed pre-midnight than post-midnight, more data are available in the post-midnight
region at large radial distances so one might naturally expect to find more events in this
region.
The event occurrence rate versus local time is plotted in Figure 6. Here I define
the event occurrence rate as the duration of all events within a bin divided by the amount
of data in a bin. From this perspective, the event frequency appears relatively symmetric
across the different local time sectors, though there is a curious decrease just prior to
midnight. There is a peak in the occurrence rate between 02:00 and 04:00 LT.
Figure 6. Event frequency as a function of local time.
It is of interest to compare my events to the so-called ‘reconfiguration events’ of
previous studies [Kronberg et al., 2005, 2007]. These events were characterized by
intermittent flow bursts inferred from particle anisotropies. Returning to the event
distribution shown in Figure 5, we see that many of my events were previously identified
in the particle data (triangle symbols), though I identified scores of new events in the
magnetometer data, particularly in the pre-midnight local time sector. This result is
particularly important because we expect that the x-line associated with solar wind-driven
reconnection to be restricted to the dawn sector at Jupiter [Cowley et al., 2003]. This xline is analogous to the terrestrial near-Earth neutral line, and as in the terrestrial case, we
would expect a distant reconnection line to exist farther down the tail. The available
spacecraft observations are limited in their radial extent, so we do not expect to find
direct evidence of the distant x-line. However, our events do support the presence of a
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near-Jupiter x-line that favors the dawn local time sector, where we observe planetward
reconnection events inside of an x-line at ~90 RJ and tailward events outside. Events in
the dusk sector are primarily planetward, and can be interpreted equally well as coming
from the distant x-line or from centrifugally driven reconnection.
The reconfiguration events have been observed with a 2-3 day periodicity; this
periodicity is also visually apparent in my events during selected interval or orbits (G2,
G8, C9, and E16). One example, which was also studied by Kronberg et al. [2007], is
shown in Figure 7. However, using the Rayleigh power spectrum, I found that there is no
statistically significant periodic signal in my events for this interval or on longer time
scales. The Rayleigh power spectrum can be used to determine whether a statistically
significant periodic signal is present among the occurrence times of discrete events. It has
been used to study periodicities in quantities such as proton flare occurrences [Bai and
Cliver, 1990]. For a more complete discussion of the Rayleigh power spectrum, its usage,
and its limitations, I refer the reader to Vogt et al. [2010], Mardia [1972], and Lewis
[1994].
Figure 7. Magnetic field and particle data for 21 September to 6 October 1996. My
events are shown by the red traces in the top panel.
Given the absence of a persistent, statistically significant periodic signal, I
concluded that the 2-3 day time scale is unlikely to be characteristic of internal processes
driving reconnection in the Jovian magnetotail. Instead, the reconnection events during
intervals displaying the 2-3 day periodicity could be at least partly influenced by external
factors such as magnetospheric interaction with the solar wind. Overall, I concluded that
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the observed distribution and recurrence of reconnection events at Jupiter are consistent
with both internally-driven and solar wind-driven reconnection, and that there is not
strong evidence that one process is favored over another. Therefore, I would disagree
with the suggestion by McComas and Bagenal [2007] that solar wind-driven
reconnection does not occur in the magnetotail, and that flux opened by the solar wind is
instead closed on the magnetopause flanks.
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3. Jupiter’s polar cap: Where is the open/closed flux boundary?
In the second part of my thesis I investigate the link between regions in Jupiter’s
equatorial magnetosphere and the polar aurora. I have mapped auroral features to their
magnetospheric sources by using flux equivalence rather than by tracing field lines from
a model. This approach allows me to relate polar auroral features to different regions in
the magnetosphere and to identify the size and location of open flux in Jupiter’s polar
cap.
3.1 Overview of Jupiter’s auroral emissions
Observations of Jupiter’s aurora at ultraviolet, infrared, and visible wavelengths
show that the emissions can be classified into three main types: the satellite footprints, a
main oval (main emissions), and the mysterious polar emissions [Clarke et al., 1998].
These features are seen in Figure 8, which shows a polar projection of the UV aurora as
seen by the Hubble Space Telescope. These auroral observations, along with interpretive
theoretical studies, have helped to constrain global magnetic field models and improve
our understanding of magnetospheric dynamics.
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Figure 8. UV observations of Jupiter’s aurora as imaged by HST. The three main types
of aurora (satellite footprints, main emissions, and polar aurora) can be seen. The polar
emissions can be further categorized into three regions: the active, dark, and swirl
regions. Modified from Figure 5 in Grodent et al. [2003b].
The main oval emissions at Jupiter fall in a relatively constant, narrow (1º-3º
latitudinal width) band that is fixed with respect to System-III longitude [Grodent et al.,
2003a]. In the northern hemisphere, the main emissions are not actually shaped like an
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oval, but display a kidney bean shape due to a “kink” that is also fixed in longitude. The
Jovian main auroral emissions are believed to be associated not with magnetospheric
interaction with the solar wind but instead with the breakdown of plasma corotation in the
middle magnetosphere [Cowley and Bunce, 2001; Hill, 2001; Clarke et al., 2004]. Plasma
from the Io torus diffuses radially outward through flux tube interchange, and must
decrease its angular velocity in order to conserve angular momentum. Because the field is
frozen into the flow, field lines in the magnetosphere are swept back azimuthally as the
plasma’s angular velocity decreases. A current system develops which features a fieldaligned current coming out of the ionosphere on L-shells beyond ~20, an outward radial
current in the equator, and a returning field-aligned current into the ionosphere at larger
L. This current system is shown in red in Figure 9. The upward (out of the ionosphere)
field-aligned current is carried by downward-moving accelerated electrons which
stimulate the main oval emissions. In the equatorial plane, the radial current provides a
j ´ B force in the direction of corotation, increasing the azimuthal velocity of the plasma
back towards corotation.
The polar emissions are located poleward of the main oval and include many
interesting features, such as flares, a dark region, and swirling aurora. These features are
yet to be reliably linked to a magnetospheric source region or process because field
models are inaccurate at these high latitudes. In the northern hemisphere the UV polar
emissions can be organized into three regions: the active, dark, and swirl regions
[Grodent et al., 2003b], based on their average brightness and temporal variability. The
active region is very dynamic and is characterized by the presence of flares, bright spots,
and arc-like features. It is located just poleward of the main oval and maps roughly to the
noon local time sector. Pallier and Prangé [2001] suggested that the bright spots of the
active region are the signature of Jupiter’s polar cusp, or possibly dayside aurora driven
by an increase of the solar wind ram pressure.
The crescent-shaped dark region is located just poleward of the main oval in the
dawn to pre-noon local time sector. As its name suggests, the dark region is an area that
appears dark in the UV, displaying only a slight amount of emission (0-10 kiloRayleighs)
above the background level [Grodent et al., 2003b]. The dark region is thought to be
linked to the Vasyliunas-cycle [Vasyliūnas, 1983] return flow of depleted flux tubes
[Cowley et al., 2003].
The swirl region is an area of patchy, ephemeral emissions that exhibit turbulent,
swirling motions. The swirl region is located poleward of the active and dark regions, and
is roughly the center of the polar auroral emissions. It is generally interpreted as mapping
to open field lines. Pallier and Prangé [2001] interpreted the area poleward of their inner
arcs as being analogous to a polar cap for Jupiter; this area roughly matches the location
and shape of the swirl region.
An additional feature of the polar auroral emissions is the presence of transient
spots located at the equatorward edge of the dark region. These polar dawn spots have
been associated with the internally driven reconnection process and especially with the
inward-moving flow initiated during reconnection [Radioti et al., 2008, 2010].
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Figure 9. Illustration of the current system that develops to speed plasma back up toward
corotation and produces Jupiter’s main auroral emissions. Modified from Figure 1 in
Cowley and Bunce [2001].
3.2 The need for a better model to map the polar aurora and identify the polar cap
Auroral emissions have been observed at the footprints of Io, Ganymede, and
Europa [Connerney et al., 1993; Clarke et al., 2002]. These satellite footprints are useful
for constraining global field models because the satellites’ orbital locations are known.
The footprint’s ionospheric location can, therefore, be linked reliably to a radial position
in the magnetosphere. The longitudinal position can also be inferred, although with some
small uncertainty as a consequence of the signal propagation time between the satellite
and the Jupiter’s ionosphere. Thus satellite footprints provide a check for field model
accuracy at the orbital distances of Io (5.9 RJ), Europa (9.4 RJ), and Ganymede (15 RJ),
and as a result one can confidently map from the inner magnetosphere to the ionosphere.
The VIP4 field model [Connerney et al., 1998] was developed to match the
Voyager 1 and Pioneer 11 magnetic field observations and to ensure that the model field
lines traced from 5.9 RJ matched the Io footprint in the ionosphere. The model does a
good job of fitting the Io footprint, except in the auroral “kink” sector that gives the Io
footprint its characteristic kidney bean shape. Recently, Grodent et al. [2008b] have
shown that addition of a magnetic anomaly in the northern hemisphere can improve the
agreement between the model and footprint observations in the northern hemisphere,
especially in the “kink” sector.
Even with recent improvements such as the inclusion of a magnetic anomaly, the
available field models are still accurate only within distances of ~30 RJ in the equatorial
plane. Beyond these distances there are no satellite footprints to constrain the field
models, and azimuthal currents stretch field lines and compromise the mapping. As a
result, the magnetospheric mapping of the polar aurora is uncertain.
In this thesis I map contours of constant radial distance from the magnetic equator
to Jupiter’s ionosphere by performing a flux equivalence calculation rather than by
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following field lines according to a model as is often done at Earth. This approach allows
me to relate auroral features to their magnetospheric sources at a large range of radial
distances and local times, a result that was previously inaccessible due to the lack of field
models accurate beyond ~30 RJ. It provides a reliable mapping of the three polar auroral
regions, improving on the current models, which are only able to infer that the polar
aurora emissions map to equatorial regions beyond ~30-50 RJ because they lie poleward
of the main oval.
Another contribution of this work is to map the location of the dayside
magnetopause, thereby establishing possible locations of a portion of the open/closed flux
boundary in Jupiter’s polar cap. The extent to which Jupiter’s polar cap is open to the
solar wind is a question of particular importance because the answer has consequences
for our understanding of global magnetospheric dynamics at Jupiter. For example, if
Jupiter’s magnetosphere is closed, as suggested by McComas and Bagenal [2007], then
one expects Jupiter’s polar cap to be small (up to ~10º across as observed by Pallier and
Prangé [2004]). However, if cusp reconnection is unable to close all of the flux opened
on the day side, as Cowley et al. [2008] argue, and the magnetosphere is open, then
Jupiter’s polar cap would correspond to a more significant fraction of the area inside the
main auroral oval.
A related outstanding issue is how and to what extent the solar wind influences
the main emission brightness and position. It has been predicted that solar wind
compressions will decrease auroral emissions: the inward moving plasma will increase its
angular velocity to conserve angular momentum, decreasing the strength of the fieldaligned current system that drives the main auroral emissions [Cowley and Bunce, 2001;
Southwood and Kivelson, 2001]. Simultaneous HST observations of the aurora and
Cassini data of the upstream solar wind conditions showed that the auroral emissions
brightened by a factor of ~2 during a period of changing solar wind dynamic pressure;
however, it remains unclear whether the brightening was associated with the
magnetospheric compression or with the magnetospheric expansion [Nichols et al.,
2007]. My work contributes the first steps toward understanding the influence of the solar
wind on the main oval emissions by allowing an accurate mapping of the main emissions,
which are not expected to map to a constant radial distance [Grodent et al., 2003a].
Another potential use for such a mapping is to establish how reconnection or
reconfiguration events [Kronberg et al., 2005; Vogt et al., 2010] and the associated x-line
[Woch et al., 2002] compare to observed auroral polar dawn spots [Radioti et al., 2008].
Previous studies have mapped the polar dawn spots to their magnetospheric source
regions (and vice-versa) by tracing field lines from the available field models [Radioti et
al., 2008b; Ge et al., 2010]. However, these models are not accurate beyond ~30 RJ and
both the tail reconnection events and the polar dawn spots occur on L shells beyond this
distance. Therefore, a mapping model that is accurate in the middle and outer
magnetosphere will be useful to further confirm polar dawn spots as an auroral signature
of tail reconnection.
3.2 Methods: Mapping through flux equivalence
I wish to relate Jupiter’s polar auroral features to their magnetospheric sources.
One approach to such a mapping is to trace equatorial magnetic field lines from the
magnetosphere to the ionosphere, as is frequently done in studies of the terrestrial
17
magnetosphere. However, that method requires an accurate global Jovian magnetic field
model, and field models are highly uncertain at radial distances beyond ~30 RJ. The error
arises, in part, because an azimuthal current flows through the equatorial plasma and
stretches field lines at all local times. Though the available global field models are
accurate only in the inner to middle magnetosphere, spacecraft observations of the
magnetotail are available out to ~150 RJ, and I wished to consider auroral features that
may map to the outer magnetosphere. I, therefore, took a different approach in my
mapping, using a flux equivalence approach.
I started the mapping at the orbit of Ganymede, where the link to the auroral
ionosphere can be determined from emissions identifiably linked to the moon.
Thereafter, rather than following field lines along a field model, I mapped equatorial
regions beyond Ganymede’s orbit to the ionosphere by requiring that the magnetic flux
threading a specified region at the equator must equal the magnetic flux in the area to
which it maps in the ionosphere. The method is illustrated in Figure 10 and is briefly
summarized in this proposal.
A flux equivalence analysis has been used previously to estimate currents, flows,
and magnetic mapping of Jupiter’s ionosphere [Cowley and Bunce, 2001], although they
used a simplified axisymmetric magnetic field model to estimate the magnetic flux. A
key contribution of our work is that I calculate the magnetic flux through the equator
using a two-dimensional data-based fit that accounts for local time asymmetries. This
allows me to reliably map the source(s) of dawn-dusk asymmetries in the auroral
emissions.
To begin, I identified the ionospheric footprint of an equatorial circle at 15 RJ, the
orbit of Ganymede and a distance where field models are reasonably accurate, by
following model magnetic field lines [Grodent et al., 2008] from the equator to the
ionosphere. This step is represented in Figure 10 by the solid green field lines, which
connect the 15 RJ equatorial curve (black circle) to the 15 RJ ionospheric reference
contour (black). I then calculated the magnetic flux through an area pixel in the equator
(dA1). The magnetic flux in the equator depends on BN,equator, a the normal component of
the magnetic field at the equator, which I represented with a model developed from a fit
to available spacecraft data. This model was specifically chosen to be a function of both
radial distance and local time to reflect local time asymmetries in the field strength
(strongest in the noon-afternoon local time sector). The data and fit are shown in Figure
11.
After evaluating the equatorial magnetic flux through a typical pixel, I then
determine how far to move the ionospheric contour poleward, given by the distance dn, to
match the equatorial flux. This gives the mapping of a pixel linked to the 20 RJ
equatorial circle (in blue in Figure 10); iteration provides the ionospheric mapping of
successively distant circles (illustrated in Figure 10 by the red curves representing the
mapped 25 RJ equatorial circle). I continued the flux equivalence calculation out to a
radial distance of 150 RJ, the limit of the magnetic field data coverage in the magnetotail
and the valid region of the BN fit. For a more thorough discussion of my method I refer
the reader to Vogt et al. [2011, in press].
18
Figure 10. Illustration (not to scale) of the method used to map equatorial magnetic flux
to the ionosphere by equating flux in the two regions.
19
Figure 11. Values for BN (left) from spacecraft measurements and equivalent values
from a model fit (right) plotted vs. radial and local time in the equatorial plane. In both
the data and the model the field in the current sheet is strongest in the noon to dusk local
time sector and weakest in the early morning.
3.3 Results
This study has been completed and the results were accepted for publication in
Journal of Geophysical Research [Vogt et al., 2011, in press]. I will summarize the
results here, as they will be incorporated into my thesis.
I have mapped radial distances from 20 to 150 RJ in the equator into Jupiter’s
ionosphere using the mapping procedure and flux equivalence calculation outlined in
section 2.2. That calculation involves BN, which is a function of local time, and therefore
the mapping results depend on how the ionosphere is oriented with respect to the Sun, or
local noon. In Figures 12 (northern hemisphere) and 13 (southern hemisphere) I present
mapping results for four different viewing orientations, with local noon at 0º, 90º, 180º,
and 270º SIII left-handed longitude.
In these figures I have plotted the contours corresponding to constant radial
distances, every 10 RJ from 20 RJ to 150 RJ. The outermost black dashed line is the 15 RJ
reference contour, matching Ganymede’s auroral footprint. In all panels the Sun’s
direction is to the bottom of the page, so field lines to the left generally map to the
morning and pre-dawn sector, while field lines to the right generally map to the dusk
sector. The auroral contours have the largest separation on the right side because the
equatorial BN is strongest in the afternoon sector (see Figure 11). As a result, the area of
open flux is shifted toward the predawn to dawn side (left/upper left).
I terminate the contours where the field lines map to the Joy et al. [2002]
magnetopause (~60 RJ at noon and ~85 RJ at dawn/dusk for the compressed case, and
~90 RJ at noon and ~130 RJ at dawn/dusk for the expanded case, shown here). The white
(green for northern hemisphere, subsolar longitude 180º) or empty area interior to the
20
colored contours maps beyond 150 RJ on the night side and beyond the magnetopause on
the day side; I interpret these areas as open flux.
Figure 12. Mapping results for the northern hemisphere, expanded magnetosphere.
21
Figure 13. Mapping results for the southern hemisphere, expanded magnetopause.
With models of the link between different magnetospheric regions and their
magnetic footprints in the ionosphere established, it is of interest to compare the results to
UV observations. I focused on auroral observations in the northern hemisphere, for which
more observations are available than for the southern hemisphere as a consequence of the
viewing geometry [Grodent et al., 2003b].
In Figure 14 I present a composite of mapping results for central meridian
longitude (CML) 160º SIII left-handed longitude and the corresponding UV auroral
observations [modified from Figure 5 in Grodent et al., 2003b]. Also shown are contours
delineating the active (green), dark (yellow), and swirl (red) regions in the polar aurora,
originally drawn by Grodent et al. [2003b]. The inner dashed white contour shows the
location of the fixed dark polar region (f-DPR) from the IR auroral observations of
Stallard et al. [2003].
22
Figure 14. Composite of mapping results and UV auroral observations.
Comparison with the auroral observations shows that the active region maps to
field lines just outside the dayside magnetopause, plausibly open field lines in the polar
cusp. The swirl region maps to tail field lines at distances larger than 150 R J, plausibly
open field lines; the Stallard et al. [2003] f-DPR (stagnant flow) lies within that region.
The dark region maps to both open and closed field lines near dawn local time. The main
oval radial mapping changes with local time: ~15-30 RJ near dawn, ~30-50 RJ near noon,
and 50-60 RJ at ~15:00 LT.
I also compared the mapping results to UV auroral observations for CML 220º
(not shown here) and found similar results. The dark region mapping was the most
variable, mapping almost entirely to open field lines for CML 220º and to both open and
closed field lines for CML 160º. The auroral observations for CML 220º include two
spots, one in the dawn sector and one nightside spot, that are thought to be the signature
of magnetic reconnection in the tail [Grodent et al., 2004]. The polar dawn spot maps to
~50-80 RJ and ~0200-0400 LT, and the nightside spot maps to ~50-90 RJ and ~21002400 LT. That both spots map to equatorial regions planetward of a statistical x-line
23
[Vogt et al., 2010] supports the association with inward moving flow released during tail
reconnection, as has been shown in Radioti et al. [2010] for the polar dawn spots and
recently in Radioti et al. [in press] for the nightside spots.
On the basis of the above comparison with auroral observations I interpret the
polar auroral active region as forming Jupiter’s polar cusp, and the swirl region as
Jupiter’s polar cap. It is also clear that there are several ways in which to explain the
absence of emissions in the dark region. Where the dark region maps to open field lines
the relative lack of auroral emissions can be explained by an exceptionally low plasma
density. On closed field lines coupled to the dark region, one potential explanation for the
relative lack of auroral emissions is the presence of downward (into the ionosphere)
closure currents, analogous to the terrestrial black aurora that are also associated with
downward field-aligned currents on closed field lines [e.g., Marklund, 2009]. My
interpretation is in line with the previous discussion of Cowley et al. [2003], who
suggested that aurorally dark regions at Jupiter might be associated with either open field
lines or downward (into the ionosphere) currents on depleted flux tubes as part of the
Vasyliunas-cycle return flow.
The flux equivalence calculation was performed only out to R = 150 RJ, the limit
of data availability and the valid region of the BN fit; however, the Jovian magnetotail is
known to extend as far as ~9000 RJ based on Voyager 2 data [Lepping et al., 1983]. By
assuming that field lines that cross the equator beyond 150 RJ are open, I have
undoubtedly overestimated the region of open flux in the ionosphere. I can correct for
this overestimate by assuming a radial dependence for BN and integrating the function
from 150 to 9000 RJ to account for the magnetic flux that closes through the tail.
Kivelson and Khurana [2002] found that BZ, which on average is normal to the current
sheet and can be considered equivalent to BN, is given by:
(1)
Bz (R) = 4.32 ´10 4 R-2.44
where Bz is in nT and R is in Jovian radii. The magnetic flux closing through the
magnetotail can therefore be given by integrating this expression from 150 to 9000 RJ.
Inclusion of the additional flux through the tail shrinks the size of the polar cap by
only ~a few degrees of latitude (see red shaded region in Figure 12). I then identify the
green shaded regions in Figure 12 as the polar cap. Its area is equivalent to that of a circle
around the pole with an ~11º latitudinal width – only slightly smaller than the ~15º
latitudinal width of the polar cap at the Earth.
If the polar cap is accurately identified, the open flux linked to that region in the
ionosphere should equal the tail lobe flux. I calculated that the open flux through the
region I have identified as the polar cap in the northern ionosphere is ~1.41 × 105 nT RJ2
(~720 GWb). A similar calculation for the southern hemisphere finds that the amount of
open flux through the southern hemisphere is ~1.49 × 105 nT RJ2 (~762 GWb). The
calculated values closely match the amount of open lobe flux in the magnetotail;
magnetometer data show that BR ~ 7 nT at R = 80 RJ, where the magnetotail width varies
from 115 RJ (compressed) to 165 RJ (expanded) [Joy et al., 2002]. Assuming a
compressed magnetosphere, the lobe flux, ∫ B ∙ dA, is 7 nT × π × (115 RJ)2 × ½ = 1.45 ×
105 nT RJ2 (~741 GWb), very close to the amount of open flux through both the northern
and southern ionospheres.
The main oval emissions are associated with corotation enforcement currents and
are not expected to map to a constant radial distance [Grodent et al., 2003a]. Indeed, our
24
analysis shows that the main oval mapping varies with local time. Near dawn, the main
emissions map to ~20-30 RJ, while near dusk they map farther out, ~50-60 RJ. These
results suggest that either the radial location of the corotation enforcement currents varies
with local time, or the plasma outflow rate differs among local time sectors, or both. In a
recent study of nine years of HST data, Grodent et al. [2008a] found that the main oval
location has shifted over time by as much as 3º in latitude. They proposed that the
latitudinal shift could be explained by variations in the current sheet density or thickness
and not just by a response to changing solar wind conditions. Similarly, we suggest that
the main oval variation with local time seen here could be explained by a local time
dependence on these current sheet properties or the plasma outflow rate.
25
4. Effect of rotation on particle anisotropy
The final part of my thesis will be a simulation project to test whether centrifugal
forces, which are important in Jupiter’s rapidly-rotating magnetosphere, can contribute to
pressure anisotropy. This theory was suggested by Kivelson and Southwood [2005] to
explain heating and thickening of the plasma sheet as it rotates from noon to dusk local
times. To test the effect of rotation on particle anisotropy, I will follow particles in a
large-scale kinetic (LSK) model and examine what happens as field lines rotate and
stretch. I am currently working on the analysis for this final part of the thesis.
4.1 Local time asymmetries in Jupiter’s plasma sheet
Observations show that Jupiter’s plasma sheet is thinnest in the post-midnight to
dawn local time sectors, thickens as it rotates through the morning sector through noon,
and becomes thickest near dusk [Kivelson and Khurana, 2002]. The plasma sheet heating
and thickening near noon can be explained as a response to increased pressure from the
magnetopause, as the magnetopause distance decreases by ~50 percent from dawn to
noon. However, one might then expect that the plasma sheet would thin in response to the
reduced pressure as the magnetopause distance increases from noon to dusk, but
observations show that the opposite is true.
This local time asymmetry is illustrated in Figure 15, which presents a
comparison of magnetometer data from the dawn (thick lines) and dusk (thin lines) local
time sectors. The top panel shows the radial component of the magnetic field, which
reverses with a 10-hour periodicity due to the 10 degree dipole tilt (note, however, that
the data in this figure are plotted versus radial distance, not time). The sign of BR reverses
every ~5 hours as the current sheet moves over the spacecraft. In the dawn sector the
spacecraft easily enters the lobes, as can be seen by the square, flattened peaks in |BR|.
However, the current sheet is much thicker in the dusk sector and the spacecraft, which
reaches peak magnetic latitudes of +/- ~10º degrees, does not completely exit the current
sheet, so the BR fluctuations are more rounded. The second panel of Figure 15 shows Bθ,
the north-south component of the magnetic field. This component of the field is much
stronger, indicating a thicker current sheet, in the dusk (thin lines) local time sector than
at dawn.
26
Figure 15. Magnetic field data as a function of radial distance for orbit G2 (thick lines) in
the dawn local time sector and orbit C23 (thin lines) in the dusk local time sector. From
Figure 24.19 in Khurana et al. [2004].
These local time asymmetries have been previously discussed by Kivelson and
Southwood [2005] in the context of global magnetospheric dynamics. They attribute the
dusk side plasma sheet heating and thickening to centrifugal forces due to the
magnetosphere’s rapid rotation. They suggest that as a result of rotation, particles gain
parallel velocity as plasma moves outward, and the resulting anisotropy makes the
plasma sheet become unstable as follows:
¶v
Kivelson and Southwood [2005] use the chain rule to rewrite m || such that the
¶t
parallel momentum equation for a particle in guiding center motion is given by
¶v
¶B
(2).
mv|| || = (mw 2 r - 2mw ´ v )|| - m
¶s
¶s
From this equation we can see that for a particle moving from its mirror point (labeled
subscript 1), where the parallel velocity v|| = 0, to point 2:
v2
m¶ ||
2 = mw 2 r
(3)
2
¶r
and
27
¶v|| 2
r2
=¶
2w 2
2
(4)
which leads to
v|| = (r2 - r1 )w 2
2
2
2
(5)
(their equation 7), where r is cylindrical, or measured perpendicular to the spin axis. So a
rotating particle bouncing from its mirror point at r1, where v|| = 0, to r2 > r1, will gain
parallel velocity, by equation 5. The resulting pressure anisotropy makes the plasma sheet
unstable because the perpendicular force,
é
B2 ù æ
B 2 ö RC
2
(6)
F^ = -Ñ^ ê p^ +
+
p
p
ç
÷ 2 + rw r - 2 ´ v ^
ú
//
^
2m 0 û è
m0 ø RC
ë
(
)
is no longer ~ 0. (The second term in equation X is the dominant one, such that force
B2
balance implies that p// - p^ » 0 near the current sheet crossing, which no longer
m0
holds if there is pressure anisotropy.) These stresses lead to ballooning and release of
plasma “bubbles”.
In the final part of my thesis, I will test this idea of Kivelson and Southwood
[2005] by tracking particle motion using a large-scale kinetic (LSK) model. A kinetic
approach will allow me to test the key physical processes in their theory, which cannot be
modeled using magnetohydrodynamics (MHD) because I am interested in the effects of
rotation and large spatial scales on individual particles. This simulation project will be a
relevant and interesting part of my thesis because it directly addresses an issue relating to
both the magnetosphere’s structure and its dynamics.
4.2 Methods: Using a LSK model
The goal of the third part of my thesis is to test whether rotation and field line
stretching can produce particle anisotropy and an increase in net energy. I will use a
large-scale kinetic (LSK) model [Ashour-Abdalla et al., 1993] to follow particles,
initially in an isotropic distribution, as they move in specified time-dependent electric and
magnetic fields. This approach is preferable to an MHD simulation because I am
concerned with the differences in responses of particles with parallel and perpendicular
velocities and therefore cannot use a fluid approximation. Specifically, we will assume
that the second adiabatic invariant, or the integral of the parallel velocity/parallel
momentum over a bounce period, is violated because bounce times are ~ hours, a
significant fraction (or longer than) the time for rotation from noon to dusk.
LSK models integrate particle orbits by solving the Lorentz force equation,
dv
(7),
m = q E+v´B
dt
where E and B are specified global electric and magnetic fields, respectively. The
model I have adapted for my use solves the Lorentz force equation with a fourth-order
Runge-Kutta method, which is a common approach to numerically solve differential
equations.
(
)
28
In simulations of the Earth’s magnetosphere, the electric and magnetic fields may
come from models (e.g., one of the Tsyganenko models) or results of global MHD
simulations. E will be represented by the corotation electric field. For the magnetic field,
I will use a modified version of the Goertz et al. [1976] Jovian field model, which
represents the observed Jovian field (from Pioneer 10 measurements) to a reasonable
degree of accuracy as an axisymmetric dipole plus current sheet field. The Goertz et al.
[1976] field model is desirable because it can be written in an explicit form, which will
minimize the computing time required for the simulation. Additionally, the model can
easily be modified to reproduce the stretching that occurs as field lines rotate from noon
to dusk.
Following Stern [1970], Goertz et al. represented the magnetic field B in terms
of two scalar stream functions f and g, such that
(8)
B = Ñf ´ Ñg
which is possible because B is divergenceless. Both f and g are constant along a field
line. Goertz et al. constructed their field model so that the stream function g contains the
field bendback or spiral shape:
(9)
g(j, r ) = j +175(er /500 -1)
and the stream function f contains the contributions of the dipole field (first term) and the
stretching due to the current sheet (second term):
r2
é
ù
(10).
f = MJ
+ h ( r, z ) êlog cosh z
+ C ( r )ú
3
D
ë
û
2
2 2
z +r
(
)
( ( ))
Here r , j , and z are the axes of the cylindrical coordinate system, M J is the Jovian
dipole moment, D and C are constants, and h is a function such that
-b
(11),
h ( r ) = a0
r
where a and b0 are constants and r 2 = r 2 + z 2 .
From equations X-X, the field can be written as
ì 1 ¶f ¶g ¶f 1 ¶f ü
(12)
B = í,
,
ý
î r ¶z ¶r ¶z r ¶r þ
such that
z
tanh
b
D - ab0 z éln æç cosh z ö÷ + C ù
Br = a0
ê
ú
r Dr
r a+2 r ë è
Dø û
Bj = - r Br ´ 6.12 ´10-3 e r /500
(13)
ab0 é æ
zö ù
ln ç cosh ÷ + C ú
a+2 ê
r ë è
Dø û
[Khurana, 1997]. The constants (a, b0 , C, D) = (9000 Gauss, 0.7, 10, 1 RJ). The resulting
field is shown in Figure 16 as projected onto a surface of constant g (not quite a meridian
plane cut, but a plane that follows the field sweep back).
Bz =
29
Figure 16. The field model of Goertz et al. [1976], taken from their Figure 4. The thick
solid line is the trajectory of Pioneer 10.
I am interested in the effect of field line stretching, which occurs over ~3-5 hours
as the field lines rotate from noon to dusk. (In the middle and outer magnetosphere, field
lines are swept back and lag corotation, so rotation from noon to dusk will take longer
than the ~2.5 hours it would take at corotation speeds.) The equatorial crossing point of
the flux tube can move up to ~35 RJ in this time, as the magnetopause is located at 60
(compressed) or 90 (expanded) RJ at noon and ~85 (compressed) or ~125 (expanded) RJ
at dusk. One way to mimic this stretching is to vary the ring current intensity in time.
Inspection of equations 10 and 11 shows that this can easily be achieved by varying the
term b0 .
I will begin with an isotropic particle distribution at energies chosen so that their
bounce periods are ~long compared to the time for rotation from noon to dusk. For
example, 30 keV particle in a stretched magnetic field (the unpublished Khurana model)
extending as far as 60 RJ will have a bounce time of ~3-4 hours depending on the pitch
angle and the precise field model or configuration. Before proceeding, I will need to more
precisely calculate particle bounce times at different energies for the Goertz et al. [1976]
field model to ensure that I begin with particles of appropriate energies/bounce times.
Next, I will follow the particles as they move through the time-dependent
magnetic field according to the Lorentz force equation. The magnetic field will vary such
that the field lines become stretched by ~50 percent in ~3-5 hours. I will include virtual
“detectors” in the code that record the time when a particle passes a specified point, as
well as relevant properties about that particle such as its energy and pitch angle. The final
product of the simulation is the “data” collected by these virtual detectors. Specifically, I
will be looking for signs of particle anisotropy and heating, following the theory
proposed by Kivelson and Southwood [2005].
As currently proposed, this simulation will not be done self-consistently, that is, I
will assume that the particles do not affect the field configuration. However, I may find
that I need to iterate after launching the particles and tracing their motion to obtain a selfconsistent magnetic field after the particles become anisotropic. On long time scales the
increase in v// could stretch the field lines, which would alter the magnetic field model
from the time-dependent Goertz et al. [1976] model that I intend to use. I will also be
30
interested in whether pitch angle scattering can return the particles to an isotropic
distribution, and over what time scale.
4.3 Current progress and expected results
The final part of the thesis, i.e. the LSK simulation project, is yet to be completed.
I expect that the analysis will be completed by late May. I have obtained the code needed
to run the LSK model and have run it for a single particle in a dipole magnetic field with
an electric field. I have verified that the procedure is working correctly by examining the
particle’s motion and other properties such as its mirror point and changes to the total
energy or first adiabatic invariant, and comparing these to the expected values.
Modifying the code that I have already written so that it can push many particles
through the Goertz et al. magnetic field will be trivial. Adding virtual “detectors” that
record when a particle passes over a given point or set of points (to be determined) will
be a slightly more time-consuming endeavor. These virtual detectors will record
properties such as pitch angle and energy, and write the data to a file. I will analyze the
data collected by the virtual detectors and look for evidence of heating and increased
parallel pressure. If time allows and data are available, I will compare the simulation
results with measured pitch angle distributions.
31
5. Proposed schedule and outline
The thesis will include five major sections:
 Introduction – In this section I will introduce my thesis topic and a motivation for
and descriptions of the questions I will address. This section will also include a
review of the literature and current debates for each subtopic. I estimate writing
this section will take 4 weeks.
 Reconnection event survey – I will describe the motivation, methods, results, and
conclusions of this project. I estimate writing this section will take 4 weeks.
 Auroral mapping model – I will describe the motivation, methods, results, and
conclusions of this project. I estimate writing this section will take 4 weeks.
 Simulation Project – I will describe the motivation, methods, results, and
conclusions of this project. I estimate writing this section will take 8 weeks,
including time to write, submit, and revise a JGR paper summarizing my results.
 Conclusions – I will summarize the contributions of my thesis. I estimate writing
this section will take 4 weeks.
Time to completion of the thesis is 4 months of analysis for the LSK simulation
project, followed by ~6 months (24 weeks) of thesis and paper writing, with a target
completion date in mid-November.
32
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ionospheric flows: Theoretical interpretation, Geophys. Res. Lett., 30(5), 1220.
Cowley, S. W. H., S. V. Badman, S. M. Imber, and S. E. Milan (2008), Comment on
“Jupiter: A fundamentally different magnetospheric interaction with the solar wind” by
D. J. McComas and F. Bagenal, Geophys. Res. Lett., 35, L10101,
doi:10.1029/2007GL032645.
Ge, Y.S., C. T. Russell, and K. K. Khurana (2010), Reconnection sites in Jupiter’s
magnetotail and relation to Jovian auroras. Plan. Space Sci.,
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Goertz, C. K., D. E. Jones, B. A. Randall, E. J. Smith, and M. F. Thomsen (1976),
Evidence for open field lines in Jupiter’s magnetosphere, J. Geophys. Res., 81, 3393.
33
Grodent, D., J. T. Clarke, J. Kim, J. H. Waite, and S. W. H. Cowley (2003a), Jupiter's
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