Plasma Structures at the Enceladus Plume

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FYSMAS1012

Examensarbete 30 hp December 2013

Plasma Structures at the Enceladus Plume

Ilka A. D. Engelhardt

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Teknisk- naturvetenskaplig fakultet UTH-enheten

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Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0

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Box 536 751 21 Uppsala

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018 – 471 30 03

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http://www.teknat.uu.se/student

Abstract

Plasma Structures at the Enceladus Plume

Ilka A. D. Engelhardt

Cassini-RPWS high resolution (20 Hz) Langmuir probe data was analyzed to find the source of fast variations in the electron density especially in the Enceladus plume region. The spatial scale on the variations is between 1 and 10 km in size. The approaches were to check for correlations between the plasma density and its variations on one hand, and boundary conditions such as the cracks on Enceladus surface as well as dust and single jets on the other hand. None of these mechanisms could be identified as the only or dominating source of observed fine structure, though partial correlation can sometimes be found and the comparison to dust presence is qualitative more than quantitative. Along the way the charging mechanism in the plume was found to be most likely due to solar UV ionization since the maximum electron density was found to be around 200km altitude. Also the

deformation of the plume in the corotation direction is visible in the 20 Hz data.

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Saturn is a very interesting Planet with a prominent ring and many moons.

One of these moons is called Enceladus and is special for scientists. Enceladus is a moon covered in ice with an ocean below it. It is not the biggest moon but it is one that spews out gas, dust and ice particles of its south pole region.

Some in form of thinner jets, the rest more as a big blob. Because of this, and other interesting findings, Enceladus is believed to be very geologically active. After a closer look at Enceladus five prominent cracks in the ice, called Tiger Stripes, were identified as the source.

Since the discovery of the plume in 2006 the Cassini space mission to Saturn flew past Enceladus about 20 times collecting heaps of data to analyze.

Among these is the Radio and Plasma Science group data which is used to search for clues on the plasma environment around Saturn.

In this group is one experiment, one small metal sphere on a boom (Langmuir Probe), that collected data on ion and electron densities. Earlier studies suggest that suddenly the electron density increased in the plume region but the ion density increased much more. The instrument, in its high resolution mode, can measure changes in the electron density on average down to 500 m.

Our measurements show that the electron density can change a lot over small distances, as short as 1 to 10 km in size.

In this report we tackle the question on where does it all come from and go on a quest to find the source of the fast variations.

Why? Because what we find at Enceladus can in the future help us understand other objects such as comets. The idea is to apply this information to the Comet 67P/Churyumov-Gerasimenko that the Rosetta space mission is going to pay a visit and travel with it in 2014.

We found that even though the gas comes out of the Tiger stripes, there is no correlation between the exact location of these versus density peaks in the

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data. Also dust particles of minimum a micro meter size did not recover the peaks. We also looked at times when the spacecraft was hit by dust grains to see if there was any change in the plasma density going with the dust, but could find at least no obvious signs that this is the case. Looking at the specific jets Enceladus is spewing out gave the conclusion that for them to be the source they need to be very thin along the way out to far distances and upon reaching those, the jet usually has smeared out.

Since footprints of Enceladus in the Aurora of Saturn have been observed, the idea of the magnetic field and current systems in the atmosphere as sources emerged. On first approximation also this did not correlate in-situ.

But there is much more to find out.

Even though the quest for the source in the fast variations was not yet successful, on a larger scale some other observations could be made along the way. We can say that the dust particles get charged along the way due to ionization and have their maximum density around an altitude of 200 km, and do not leave Enceladus already charged. On another note also a plume deformation was observed in the electron density data.

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Master thesis research is in general a collaboration performed with others.

At this time I want to take the opportunity to acknowledge some people.

The eight months working at the IRF have been very important to me both to develop my scientific skills and to experience how exciting research is.

I have really enjoyed to work there and had a rewarding time with the entire staff both personally as well as professionally. In particular I would like to thank Anders Eriksson as my main supervisor and the originator of the idea for the thesis, Jan-Erik Wahlund and Michiko Morooka who helped me a lot in the project and for letting me participate in the Cassini Project Science Group meeting and last but not least Mats André as head of the research program in Space Plasma Physics.

I also want to thank my friends and colleagues, especially Oleg Sheban- its, Shotaro Sakai, David Andrews, Stephan Buchert and Nicklas Edberg who supported me during the start-up of my work and final stage in end- less discussions. All the others which are not mentioned by name are not forgotten.

Last but not least I thank my family for making my studies in particular in Sweden possible.

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1 | Introduction

1.1 | Background

Saturn is one of four gas giants in our solar system and has been known since the ancient times. Galileo Galilei was the first to gaze at Saturn with a telescope in 1610. Christiaan Huygens discovered Saturn’s rings in 1659 and later in 1675 Jean-Dominique Cassini discovered a gap in the rings. Saturn is not the only planet that has rings around it but no other rings are as prominent as Saturn’s [NASA, 2013b].

The Cassini mission had the objective to find out more about Saturn, Titan and its icy moons. It consists of the Cassini spacecraft and the Huygens probe and is a joint project between NASA, ESA and ASI¹. Launched for its mission to Saturn on the 15th of October 1997 from Cape Canaveral in Florida it arrived at Saturn in 2004. [Pailharey and Vignaux, 2004; NASA - JPL, 2012]. The Huygens probe separated 25th of December 2004 from Cassini and landed on Titan 14th of January 2005. Cassini was left to orbit Saturn and its icy moons.

Cassini is already in its second extension phase of the mission. It started with the four-year prime mission which lasted from July 2004 to July 2008. After successful operation and in good state of health NASA granted two mission extensions. The first one is the Equinox mission, from July 2008 to October 2010 and the second extension, the Solstice mission, is planned until May 2017 [Buffington, 2011].

Measurements received from Cassini revealed interesting findings. One for example is the perturbation of the magnetic field in the vicinity of Saturn’s moon Enceladus. The

1Italian space agency

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flow of the rotating plasma is slowed down there [Dougherty et al., 2006; Wahlund et al., 2009]. This was interpreted as a signature of mass loading of the plasma by matter flowing out from the moon, which led to the detection of the Enceladus plume also by other instruments on Cassini, e.g. [Porco et al., 2006].

Saturn’s moon Enceladus was discovered in 1789 by William Herschel. Enceladus is the 6th largest moon, with a mean radius of 252 km, in Saturn’s system. It orbits Saturn in the densest region of the E-ring at a distance of about 4 RS, with Saturn’s equatorial radius being RS= 58 232 km [NASA, 2013a]. With the Cassini mission it has been found that Enceladus is a geologically active moon and shows out-gassing in form of a plume.

An example of geological activity are jets of dust and ice that leave the surface at the south polar region. Large cracks in the surface (about 100 km long [NASA, 2013a]), dubbed tiger stripes, seem to be very young and much warmer than the surrounding surface which is covered by ice. Enceladus probably is a major source of gas, plasma and dust feeding the E-ring [Dougherty et al., 2006; Jones et al., 2009; Morooka et al., 2011; Wahlund et al., 2009]. The plume of nm sized water-ice and dust particles [Hill et al., 2012] seems to extend several RS into space.

The plume has been a target for study since it was first discovered in 2008. In total there have been 20 flybys of Enceladus. Four in the prime mission, 8 in the Equinox mission and 8 in the Solstice mission with 3 more to come in 2015 [Buffington, 2011].

1.2 | Report Outline

This masters thesis is a continuation of a project work which started in 2012, [Engelhardt, 2013], from here on called "the project work". It was carried out at the Swedish Space Institute (IRF) in Uppsala and the Department of Physics and Astronomy, division of Astronomy and Space Physics, at Uppsala University. Since the present report is an extension of the previous some sections are edited and reused, in particular chapters 2 and 3 and sections 1.1, 4.1 and 5.2.

The first chapters, chapters 1 to 3, give some background information on the mission, the instruments from which information is used in this report as well as on the coordinate systems and the visualization of data. Chapter 4 gives an overview on the Langmuir

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1.2 Report Outline

probe measurements in general, an overview of the Enceladus flybys and a first estimation on some plasma parameters.

From the project work, it has been concluded that there are fast variations¹ in electron density in the Enceladus plume. A possible source could be that the outflow is shaped by the topographical cracks on the surface on the South polar region of Enceladus.

Subsequent ionization of the outflowing gas could then give rise to similar spatial structures in the plasma as in the gas. The correlation between these cracks and the small scale plasma structures was therefore examined. The general large-scale changes in the plasma density fits well, meaning that higher densities are apparent in the plume region. In this report, we go deeper into this, looking for correlation on a larger scale, chapter 5.

Structures in plasmas can be generated internally by local processes, or imposed externally by boundary conditions. For plasma structures in the Enceladus plume, the most obvious external cause would be structures in the gas outflow from the planet. The fact that the outflow is concentrated into jets correlating with cracks in the ice Spitale and Porco [2007] made that idea sound very likely at the beginning of this study. However, our investigations suggest this is not the case.

In the project work, an attempt to correlate the fine structures observed in-situ in the plume plasma to jet source operations by the camera system on Cassini failed to show any obvious correlation, section 2.5. Another attempt which is included in this work, chapter 6, is to correlate the observed finestructure in-situ to micrometer sized dust hits observed by a Radio and Plasma Wave Science (RPWS) instrument, section 2.2. Second, some theoretical considerations presented in chapter 7 made clear that fine structures imposed by the ice cracks could hardly be responsible for fine structure at the level we observe it in-situ in the plume – this would require very well collimated jets at the surface, and that these jets would not diverge at all, which seems quite unrealistic.

The next step was to look quantitatively on the plume plasma fine structure, chapter 8.

This resulted in the fact that regions of higher density correlates to regions of richer fine structure, but not the other way around.

1Variations here are considered due to the spacecraft moving through structures in the plume although eventual time variations should not be ignored.

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A second external structure generator could be filamentation of field-aligned currents in the plasma, like what is observed in the auroral footprints of the moons at Jupiter and Saturn [Pryor et al., 2011]. Field aligned currents can lead to electron acceleration, and when the accelerated electrons reach a denser region, like a planetary atmosphere in the case of auroras or in this case the Enceladus plume, they can cause ionization of neutrals, leading to higher plasma density. In this way, structuring of the currents can be mirrored by structures in the plasma density. To find if this is the case, a comparison with the data from the Cassini magnetometer instrument, section 2.4, is added in chapter 9.

A general result and a summary of the thesis work can be found in chapter 10.

The appendices A, B, C.1, C.2 and D include plots of all flybys that have not been added to the main report as they would take too much space and they are not essential for illustrating the main points. However, they are reproduced in the appendices as they constitute important material behind the findings presented.

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2 | Instrumentation

The Cassini spacecraft carries many different instruments. The data analyzed for this project comes mainly from the Radio and Plasma Wave Science (RPWS) instrument (P.I. institute: University of Iowa). The RPWS includes electric field sensors, a magnetic search coil assembly, a Langmuir probe and a spectrum analyzer [NASA - JPL, 2012;

Gurnett et al., 2004]. The main source of data are the 20 Hz measurements of the Langmuir probe, section 2.1. Figure 2.1 shows the Cassini spacecraft and the location of the RPWS sensors. The spectrum analyzer used for dust measurements and the electric and magnetic antennas are described in sections 2.2 and 2.3, respectively.

Some data are also taken from the magnetometer (MAG), section 2.4 and a cartographic map of the south polar region produced by the Imaging Science Subsystem (ISS), section 2.5.

2.1 | Langmuir Probe

The Langmuir probe (LP), provided by the IRF (Swedish Institute of Space Physics), measures resulting currents between the plasma and the probe while set on a given potential. From that data one is able to infer the electron temperature, electron density and estimate the potential of the spacecraft with respect to the plasma [Wahlund et al., 2009]. On the Cassini(-Huygens) mission, the LP used has a diameter of 5 cm. In the deployed configuration, the LP itself is about 1.5 m away from the closest spacecraft surface [Gurnett et al., 2004].

The LP has two main measurement modes. The first one is a 512 point voltage sweep,

± 32 V, measuring the current that it produces. This mode usually operates every

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Figure 2.1: Model of the Cassini spacecraft showing the locations of the instruments of the RPWS. Adapted from Gurnett et al. [2004, figure 14].

10 minutes [Wahlund et al., 2009]. For the second mode, the bias is set to a constant voltage, usually chosen to be +11.5 V and the resulting current is measured with a sampling frequency of 20 Hz. Figure 2.2 shows a photograph of said LP with its boom assembly in stowed configuration.

2.2 | Spectrum Analyzer

In the present study, we use the spectrum analyzer for dust and upper hybrid frequency detection. It consist of a high frequency receiver providing measurements from two selected antennas (3.5 kHz to 16 MHz) and a medium frequency receiver providing intensity measurements from a single selected antenna (24 Hz to 12 kHz) [Wang, 2006].

The antennas are three 10 m long conducting cylinders with a diameter of 2.86 cm.

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2.3 Electric and Magnetic Antennas

Figure 2.2: A photo of the Langmuir probe in its stowed configuration. Adapted from Gurnett et al. [2004, figure 17].

2.3 | Electric and Magnetic Antennas

The electric and magnetic antennas were used together with the spectrum analyzer for calibration during the previous project work. The magnetic field is measured by a tri-axial search coil magnetic antenna. For more detailed specifications see Gurnett et al.

[2004].

2.4 | Magnetometer

Magnetometer (MAG) data is used for comparison with the electron density variation in chapter 9. The magnetometer is a direct sensing instrument. It measures the magnitude and direction of the magnetic field. For more information see Kellock et al. [1996]. Mag data has been collected from Automated Multi Dataset Analysis (AMDA).

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2.5 | Imaging

The cartographic map of the southern hemisphere of Enceladus used in the analysis is provided by the Imaging Science Subsystem (ISS). It provides a narrow angle camera, a reflecting telescope, and a wide angle camera, a refractor. For more specifications on the instrument see Porco et al. [2004]. More information on how the map is retrieved from the images is provided in Roatsch et al. [2008]. The map is also used for jet positions and directions.

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3 | Coordinates and Visualization

Three coordinate systems have been used. The co-rotating, the Enceladus geographical and the Kronocentric Solar Magnetospheric (KSM) coordinate systems. The co-rotating coordinates and KSM are represented in a Cartesian system, whereas the geographical coordinates are used for the polar representation of the trajectory. For all coordinate systems, along-track line plots are generated as well.

The ephemeris data is taken from the Cassini RPWS page of the University of Iowa¹.

3.1 | Co-rotating Coordinates

For general trajectory plots, the Enceladus Interaction Coordinate System (ENIS) is used [Dougherty et al., 2006]. It is given as a system co-rotating with Saturn. The z-axis lies along Enceladus’ axis of rotation, pointing roughly toward ecliptic north. The y-axis always points toward Saturn. Then the x-axis completes the right handed coordinate system in the direction of motion of Enceladus around Saturn. Because of the phase locking of Enceladus rotation to its motion around Saturn, the ENIS system can in practice be regarded as a Cartesian representation of a geographical system (see below).

With these coordinates, different useful plots have been created. The first version is the usual Cartesian plane cut. This means, showing the x-y plane, the x-z plane and the y-z plane. Another illustrative representation is to take the rotation axis, z, versus R =p

x²+ y² of the flybys, i.e. going to cylindrical coordinates. These trajectory plots

1The data can be retrieved from the RPWS Team page under ’Geometry Tools’. However access to the data is restricted and needs login. http://cassini.physics.uiowa.edu/cassini/

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are useful to determine which of the flybys are going through the plume and determine which to use for the analysis.

3.2 | Geographical

For geographical coordinates the longitude is defined increasing in westward direction where zero longitude is centered on the Saturn facing side of Enceladus. These coordinates are used for the trajectories on the surface of Enceladus itself to be able to connect in-situ data to the topographic features of Enceladus south pole. Used as a map is fig. 3.1.

3.3 | Kronocentric Solar Magnetospheric

The Kronocentric Solar Magnetospheric (KSM) coordinate system gives the position of Enceladus with respect to Saturn and the Sun. The x-axis points from Saturn to the Sun, the z-axis is chosen so that the Saturn axis of rotation lies in x-z plane and the y-axis completes the right handed system which is perpendicular to the axis of rotation and points in the general direction of local dusk [MAPSview].

3.4 | Along Track Plots

The last point to mention here is an along-track line plot. Here the electron density is given in color coding of the trajectory. Additionally a line plot is added where the trajectory is used as the new x-axis for the measurements. This along-track line plot is possible in both the ENIS and the geographical coordinates.

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3.4 Along Track Plots

Figure 3.1: Map of the south polar region of Enceladus, used for ground track plots.

Image Credit: NASA/JPL/Space Science Institute, Image Addition Date:

2010-03-03

http://photojournal.jpl.nasa.gov/catalog/?IDNumber=PIA12566

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4.1 | Langmuir Probe Measurements

Saturn’s magnetosphere is influenced by the solar wind, but at this heliocentric distance (about 9.5 AU¹) the solar wind is less strong compared to Earth (1 AU). Cassini is orbiting Saturn in a plasma environment. A plasma is defined as a quasineutral gas of charged and possibly also neutral particles, exhibiting a collective behavior, meaning that the motion of the single particles are not only dependent on local conditions but also on the state of the plasma in remote regions [Chen, 1984]. With the help of the Langmuir probe, section 2.1, plasma parameters such as the electron density can be determined.

The Langmuir probe records the resulting current from a pre-set bias potential. For sufficiently low densities, this current is linearly proportional to the electron density and therefore can be considered as a good electron density estimate. The proportionality is given by Wahlund et al. [2009] in the following equation.

Ie∝ n_e_LPp Te

1 +USC+ Ubias

Te

, (4.1)

The bias potential, Ubias the spacecraft potential, USC, and the electron temperature Te, measured in electron volts [eV], is assumed to be constant.

Physical processes of ionization, recombination, collisions and charge exchange are expected to be apparent in the entire plume, meaning that the plasma density likely varies a lot. Whereas the electron temperature is not expected to vary widely. Assuming

11 AU = 149.6 · 10⁶km

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4.2 Flyby Geometry

the electron temperature to vary within a factor of 10 results in a current change of a factor of 3 because of the 1/√

Te dependence in eq. (4.1). Observed variations in the LP current are of several orders of magnitude. Since the variation in the electron temperature likely explains only a small part of the variations when analyzing probe current data, the electron temperature can often be considered as a constant to first approximation.

For sufficiently dense plasmas, like those we find around Enceladus, the spacecraft potential only depends weakly on the density of the plasma and the random current carried by plasma particles dominates over the photoelectron current. The spacecraft potential is usually about 2-4 V around Enceladus, which for a fixed bias of 10 V translates into a 20-40 % variation compared with the several orders of magnitude variation of the probe current.

4.2 | Flyby Geometry

Figure 4.1 shows an overview of all flybys, color-coded in current, given in a cylindrical coordinate system, with z versus r = px²+ y². The logarithm mentioned throughout the report is in base 10.

The average spacecraft velocity with respect to Enceladus is 10 km/s. With 20 samples per second, this translates to one measurement point around every 500 m. With the slowest flyby E13¹, the highest spatial resolution measurements would be every 300 m.

In table 4.1 an extended list for date, time and altitude of closest approach and the average velocity with respect to Enceladus is shown. Flybys that pass Enceladus on the northern hemisphere parallel to the equatorial plane are marked by a dagger (^†). The ones passing Enceladus from north to south, going through the plume, are marked by an asterisk (*). The flybys where no calibration is available are marked by an apostrophe (’). Flybys not marked are parallel to the equatorial plane on the southern hemisphere.

The geometry of all flybys can be found in appendix A. Here the red line are the along track measurements of the electron density in arbitrary units.

1Passing Enceladus on the northern hemisphere.

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Figure 4.1: Overview of the geometry of every flyby combined in one figure: z versus r =p

x²+ y². The colorbar gives the 10-logarithm of the probe current in ampéres.

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4.2 Flyby Geometry

Flyby Date DoY UT Altitude [km] hvSCi[km/s]

E0^†’ 2005-02-17 048 03:30:30 1264.003 6.7

E1’ 2005-03-09 068 09:08:03 497.034 6.6

E2*’ 2005-07-14 195 19:55:22 165.034 8.2

E3* 2008-03-12 072 19:06:12 47.674 14.4

E4* 2008-08-11 224 21:06:19 49.421 17.7

E5* 2008-10-09 283 19:06:40 24.586 17.7

E6* 2008-10-31 305 17:14:51 169.073 17.7

E7 2009-11-02 306 07:41:58 98.909 7.8

E8 2009-11-21 325 02:09:56 1596.595 7.8

E9’ 2010-04-28 118 00:10:17 100.434 6.5

E10’ 2010-05-18 138 06:04:40 437.068 6.5

E11 2010-08-13 225 22:30:52 2555.235 6.9

E12^†’ 2010-11-30 334 11:53:59 45.763 6.3

E13^†’ 2010-12-21 355 01:08:27 48.394 6.3

E14 2011-10-01 274 13:52:26 98.906 7.5

E15’ 2011-10-19 292 09:22:11 1230.756 7.5

E16’ 2011-11-06 310 04:58:53 496.578 7.4

E17 2012-03-27 087 18:30:09 74.166 7.5

E18 2012-04-14 105 14:01:38 74.104 7.5

E19 2012-05-02 123 09:31:29 73.133 7.5

Table 4.1: List of flybys used with corresponding date, day of the year (DoY), time of closest approach and altitude of closest approach. As well as average velocity with respect to Enceladus.

* Pass Enceladus from pole to pole

† Pass Enceladus on the northern hemisphere

’ No calibration available

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4.3 | Estimation of Gyration Radii

It is important to know an approximate size of the gyration radius for determining the regime of the plasma processes: the size, L, of the observed structures is at least for stationary structures expected to be much larger than the gyration radius, rg. Therefore the following relation needs to be fulfilled.

L r_g (4.2)

To calculate the electron and ion gyration radius some more information is needed. The magnetic field is about 330 nT [Jia et al., 2010] outside of the plume. Furthermore we have the standard values for electron and ion mass (for hydrogen) and the electron charge.

me= 9.1 · 10⁻³¹kg mi= 1.67 · 10⁻²⁷ kg e = 1.6 · 10⁻¹⁹ C

The equation for the gyration radius is given by

r_g = mαv_th,α

eB (4.3)

where m is the particle α’s mass, vth its velocity, e the elementary charge and B the magnetic field. The thermal velocity, with temperature Tα given in [eV] is given by

v_th=r eT_α

mα (4.4)

For ions and dust particles it is difficult to calculate the gyration radius since mass loading and other effects should be taken into account. As an approximation for water- like ions with a mass of 18 · mi and considering an electron temperature of about 50 eV outside of the plume gives a gyration radius of 9 km outside of the plume.

Following Morooka et al. [2011], the used electron temperature for the thermal velocity is taken to be 2 eV, giving an electron gyration radius of about 10 m.

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5 | Large-Scale Plume Structures

5.1 | Introduction

During the analysis of data one feature seemed to come up at a few flybys that have a geometry parallel to Enceladus’ equatorial plane. The feature mentioned is a decrease of electron density downstream of the plume in plasma flow direction. Also in some flybys this decrease, though less prominent, exists upstream of the plume as well.

The flybys used for analysis in section 5.3 are summarized in table 5.1. Note that these data have been calibrated and the calibration factor is listed in the table. See section 5.2 for the methodology.

Flyby Date Altitude [km] Calibration Factor [cm⁻³/A] Mission

E7 2009-11-02 99 9.17 · 10⁸ Equinox

E8 2009-11-21 1597 6.11 · 10⁸ Equinox

E11 2010-08-13 2555 6.71 · 10⁸ Solstice

E14 2011-10-01 99 1.20 · 10¹⁰ Solstice

E17 2012-03-27 74 9.44 · 10⁹ Solstice

E18 2012-04-14 74 6.95 · 10⁹ Solstice

Table 5.1: List of flybys used in section 5.3 with corresponding date, altitude of closest approach Calibration factor and the mission.

All flyby geometries are available in appendix A with an uncalibrated along track reference plot of the electron density measurements.

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5.2 | Calibration

The calibration of the density was done in the project work. It is only applied to the data in this chapter 5. For completeness the methodology is presented here.

There are three methods for inferring the electron density nefrom the RPWS instrument.

One that is important for calibration is the upper hybrid resonance frequency which can be identified in the electric field spectra. The other, which is the main source of information, is the LP 20 Hz data measuring the total electron number surrounding the spacecraft [Wahlund et al., 2005].

The upper hybrid emission is a function of electron plasma density [Farrell et al., 2010].

Together with the magnetic field strength the number density of the electrons can be inferred. The upper hybrid frequency, fuh, is a combination of the gyration frequency, f_ge, and the Langmuir frequency, fpe.

f_uh² = f_ge² + f_pe² . (5.1)

The Langmuir frequency is given by eq. (5.2), where ne is the electron density, e the electron charge, 0 the permeability of free space and me the electron mass.

(2πfpe)² = ω_pe² = nee²

0me (5.2)

For completeness, the gyration frequency, eq. (5.3), is given by

(2πf_ge)² = ω_ge² = |e|B

me (5.3)

with B the magnetic field.

As a result one can get the electron density by combining these equations as follows

ne= 4π²0me

e² f_uh² − f_ge² . (5.4)

To acquire the upper hybrid emission a Java program can be downloaded from the Cassini website of the University of Iowa. It is called ’Cassini Spectrograms Digitizer

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5.3 Observations

(beta)’ ¹. After carefully finding the upper hybrid emission line in the program, the data is saved to a file. This already contains the calculated electron density which will be used for the calibration.

Since the electron density and probe current are proportional to each other and eq. (4.1) holds, a reasonable calibration factor, C, can be found by setting the electron density of the LP equal to the electron density of the RPWS measurements with the upper hybrid frequency, eq. (5.5). This leads to eq. (5.6) for finding the calibration factor, C.

ne_uh = ne_LP (5.5)

C = neuh

Ie (5.6)

To find the factor, the received electron density from the upper hybrid frequency measurements and the LP current are then compared. This is done outside of the plume because the upper hybrid frequency can not be identified within it. Various values are then tested, until a reasonable fit is found. From this the various calibration factors C are then noted down per flyby and used for further analysis.

5.3 | Observations

Using the calibration factors obtained from the project work² and combining E14 (blue), E17 (green) and E18 (red) because of their similarity in the geometry and their closeness in time, figs. A.15, A.18 and A.19, shows that a similar large-scale structure is visible, fig. 5.1. It is apparent that those compare pretty well. Just before and after the plume density peak a decrease in density, depletion, is observed especially nicely overlapped in the x direction.

Note that a sudden jump in density level in E17 and E18 is appearing at about the same position in the x coordinate, x = −1.5. At this point a jump in the spacecraft potential can be observed [Pers. comm. J.E. Wahlund]. The ground tracks of these flybys on the moon’s surface are shown in fig. 5.2(a). Note that they are quite close together.

1http://cassini.physics.uiowa.edu/das2/demo-apps.html. However the access to the data is restricted and needs login.

2The calibration factor for E7 however has been updated.

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(a)x direction

(b)y direction

Figure 5.1: E14 (blue), E17 (green) and E18 (red). The density versus x, fig. 5.1(a), and y, fig. 5.1(b) is shown.

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5.3 Observations

(a)E14, E17 & E18

(b)E8, E11, E14, E17 & E18

Figure 5.2: Ground track of E14, E17 and E18, fig. 5.2(a), and also including E8 and E11, fig. 5.2(b), in the region from south polar (-90° to -60°).

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The flybys used in fig. 5.1 have a closest approach altitude of less than 100 km. Now adding E8 (magenta) and E11 (brown), at altitudes of approximately 1600 km and 2600 km, respectively, one can see that the electron density of these flybys is generally lower, fig. 5.3 Note that along the x axis, fig. 5.3(a), the density minima downstream of the plume passing along these two flyby trajectories is found between around x=0.7 (E8) and x=1 (E11) and not close to zero. Upstream the density dip nicely overlaps around x=-0.4. Along the y axis only E11 does not seem to overlap with the other flybys downstream. This is taken as an indication of the deformation of the plume with the plasma flow, moving in the positive x direction. The general lower density is due to the fact that those flybys happend much further out in plume and most of the charge has been picked up and spread out.

Looking at the position of the flybys with respect to Saturn and the Sun in the KSM reference system¹, E8 (magenta) and E11 (brown) are not positioned in the shadow of Saturn. They are exposed more to sunlight than the others, fig. 5.5, and the plume can get ionized much more. The ground tracks of all of those flybys are shown in fig. 5.2(b).

Now returning to an altitude of less than 100 km, using E14, E17 and E18 and adding one more flyby, E7 (black), fig. 5.4. Note that the ground track on Enceladus surface of this flyby E7 is in a different direction than the rest as well as its position relative to Saturn and the Sun, fig. 5.5. In fig. 5.4(a) the electron density during E7 (black) is generally lower than the others outside of the plume. Even though it was positioned closer to the Sun. This can be explained due to the fact that the Sun was at a solar minimum in 2009, when flyby E7 took place, fig. 5.6.

1The explanation on the KSM reference system is given in section 3.3

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5.3 Observations

(a)x direction

(b)y direction

Figure 5.3: E8 (magenta), E11 (brown), E14 (blue), E17 (green) and E18 (red). The density versus x, fig. 5.3(a), and y, fig. 5.3(b) is shown.

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(a)x direction

(b)y direction

Figure 5.4: E7 (black), E14 (blue), E17 (green) and E18 (red). The density versus x, fig. 5.4(a), and y, fig. 5.4(b) is shown.

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5.3 Observations

(a)x-y plane

(b) y-z plane

Figure 5.5: The position with respect to Saturn and the Sun in the KSM reference system.

The sun is in the positive x-direction and Saturn is the black circle in the middle. Figures 5.5(a) and 5.5(b) show the x-y plane and the y-z plane, respectively.

Flybys shown are E7 (black), E8 (magenta), E11 (brown), E14 (blue), E17

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Figure 5.6: Sunspot records and predictions made by Hathaway, NASA and MSFC taken from

http://solarscience.msfc.nasa.gov/images/ssn_predict_l.gif,

5.4 | Conclusions

From this one conclusion is that not only the calibration procedure is quite consistent with little random error, but also that the Enceladus environment is rather stable.

Flybys E17 and E18 are roughly two weeks apart. From this the conclusion is drawn that the continuous outflow variations on a timescale of weeks are small. Variations due to electron temperature and the floating potential were not included in this analysis, since these effect were assumed to be small, as discussed in section 4.1.

From the figures including E8 and E11, further away from Enceladus, one can observe that the plume is being dragged in the flow direction. One explanation for this would be electromagnetic forces or particle collision of the plasma particles with dust that interact with the plume. The sketch in fig. 5.7 shows what is meant by the drag in the flow direction.

From all the flybys that have been included here one observes that there exists an electron density depletion downstream, and less prominent upstream of the plume. What causes this depletion needs to be further investigated in another setting since it is beyond the scope of this thesis.

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5.4 Conclusions

Figure 5.7: Sketch of the plume being tilted in the positive x-direction, the plasma corotation flow.

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6.1 | Introduction

A possible source of fast variation in the electron density is the presence of dust. If there is plenty of dust around, a large fraction of the electrons in the plasma can get stuck on the dust grains, meaning a drop in the density of free electrons measured by the Langmuir probe. The probe will collect the negatively charged dust grains as well, but as they are much heavier than the electrons, they are much harder to accelerate toward the positively biased probe. In consequence, dust can lead to lower current of attracted electrons to a probe, as has for example been observed in the E-ring by Morooka et al.

[2011]. Hence, one could expect some degree of anti-correlation between dust and plasma density. On the other hand, in some to circumstances it could also be possible to find dust and plasma density correlate. If both originate from the same source, as they should do when considering the dust and gas outflow from Enceladus, one may indeed expect them to correlate. What actually can be seen will depend on the detailed physical processes, so comparing the variations of dust and plasma should give some clue to what goes on. To do such an investigation, some independent method for dust detection is needed. One such method is to look for broad-band short-time bursts in the wave data [Kurth et al., 2006; Wang et al., 2006; Farrell et al., 2010], caused by plasma clouds generated when dust particles hit the spacecraft. For the orbital speed of Cassini, this mechanism requires quite large dust grains, of micrometer size and larger, for giving a detectable signal. While this is larger than the manometer size range expected for the dust grains to be mainly responsible for the collection of electrons [Morooka et al., 2011], it is still worth investigating if any obvious correlation or anti-correlation between dust

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6.2 Observations

and plasma can be found.

The data used for this analysis comes from the spectrum analyzer section 2.2. The dust observed are footprints of bursts of micro-meter sized dust, see for example [Omidi et al., 2012, fig. 2]. To do this, broad-band signals in the spectrum are checked if they coincide in time with local maxima in the probe current data.

6.2 | Observations

In the figures, the plume region is taken from the spectrum analyzer with the frequency range of 0 to 100 kHz¹, indicated on the left side of the graph. The black line is the overlay of the probe current and its logarithmic scale is indicated on the right side of the graph, where the x axis is time. This analysis has only been done for flyby E3 and E5 because no strong enough correlations were found in those.

For E3, fig. 6.1, mainly narrow band emissions are apparent and even those do not coincide with local peaks in the probe current measurements. There are also some broad band emissions indicative of dust impacts, e.g. for the 6 seconds following 19:06:50, but they show little detailed correlation to small scale structures in the probe current. The general fluctuation level in the probe current is indeed higher in this interval than the preceding one, but on the other hand it is even higher in the following seconds where the spectra rather suggest less of micrometer-sized dust impacts. The data are thus inconclusive.

In E5, fig. 6.2, there are several peaks in the probe current visible.

Some of them, like those shortly after 19:06:50 UT, about 19:06:02 UT and at 19:07:05 UT, do nicely correlate to broad-band signatures in the spectral data which is interpret as micrometer-sized dust impacts, [Kurth et al., 2006; Wang et al., 2006; Farrell et al., 2010].

However, there is also at least one example of a current maximum without any obvious dust signature in the spectrogram, just before 19:06:00 UT. Around 19:06:46 UT at about 60 kHz, narrow band emissions are apparent and they are likely to be signatures of wave structures.

1The label shows frequency Hz but actually kHz is plotted. This is an error in the program provided at the University of Iowa web site.

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Figure 6.1: Plot of the spectrum analyzer data for E3 with an overlay of the electron density measurements from the Langmuir probe at fixed bias voltage (black line). The vertical axis on the left indicates the frequency range for the spectrum analyzer (0-100 kHz) and on the right the values for the electron density. The horizontal axis indicates the position in time and space of the spacecraft. Lon (longitude) and Lat (latitude), LT (local time) and L (L-shell) is given in the Saturnian system.

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6.2 Observations

Figure 6.2: Plot of the spectrum analyzer data for E5 with an overlay of the electron density measurements from the Langmuir probe at fixed bias voltage (black line). The vertical axis on the left indicates the frequency range for the spectrum analyzer (0-100 kHz) and on the right the values for the electron density. The horizontal axis indicates the position in time and space of the spacecraft. Lon (longitude) and Lat (latitude), LT (local time) and L (L-shell) is given in the Saturnian system.

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6.3 | Conclusions

The observations compare well to estimates made in previous studies where larger size dust particles were not considered to be measured by the Langmuir probe and the resulting probe current was mainly due to free electrons in the plasma [Engelhardt, 2013, sec. 6.1].

However effects of smaller sized negatively charged dust particles are not being considered here. Such particles, which would not give as clear broad-band signatures in the spectra due to their smaller impact energy, could be one of the reasons why we get varying and inconclusive results when looking for dust-plasma correlations. This would need further investigation but how to actually do a deeper investigation of this is not so clear.

One way of finding nanodust particles is by comparing ion and electron densities: if finding a shortage of electrons, this is an indication of the presence of nanodust particles absorbing many of the electrons [Morooka et al., 2011]. However, this requires either Langmuir probe bias sweeps, which we only have quite infrequently, every ≈24 s, or simultaneous use of two probes, one measuring ions and the other electrons. We do not have the latter on Cassini but will have on Rosetta when it arrives at its target comet in 2014, thus opening this possibility for dust-plasma interaction studies. For Cassini, we have to live with what we have, and a way forward would probably have to involve the use of models or assumptions. Nevertheless, just extending the number of flybys checked could give a clearer picture, and this should be done as the logical next step in a continued investigation.

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7 | Modeling of the Jets

One possible source of the fine structure in the data could be due to localized sources of out-gassing on the moon. Those localized sources can be jets that have been identified by Spitale and Porco [2007]. The ion density variation with altitude has been modeled thoroughly for example by Saur et al. [2008]; Fleshman et al. [2010]. However, there exists no model¹ for the electron density variation with altitude, which would be helpful to interpret the 20 Hz data from the Langmuir probe.

A first step is to plot the directions of the jets inferred by Spitale and Porco [2007] and this is shown up to an altitude of 504 km from Enceladus surface in fig. 7.1. The relative trajectory of the spacecraft, for all southerly flybys, and the jet directions are available in appendix B.

The actual modeling of a jet is based on assumptions. The first approximation is to use the same approach as Saur et al. [2008]; Fleshman et al. [2010] and put the source of the electrons in the center of Enceladus, fig. 7.2(a) and section 7.1. Since most of the outgassing comes out of the cracks the natural next step is to put a spherical source in the cracks on the surface of Enceladus fig. 7.2(b) and section 7.2. One can then specify an arbitrary angular width and shape of the beam, thus modelling more realistic scenarios.

1I could not find any evidence in the published literature.

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Figure 7.1: Direction of the jets in a 3D plot up to an altitude of 5 RE. The co-rotation flow is to the lower left direction, Saturn to the upper left and south to the top.

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(a)Center (b)Surface

Figure 7.2: Coordinates used in the formulas. Figure 7.2(a) shows the Enceladus radius, R, and the radial distance from the center of Enceladus, r. Figure 7.2(b) shows the radial distance from the center of the spherical source on the surface of Enceladus, x, and the radius of the source on the surface of Enceladus, a. For both figures, the angular distance from the center of the plume is denoted by ω, and the angular width of the plume by Hω.

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7.1 | Source at the Center of Enceladus

The first approach is to have a source at Enceladus center from which a constant stream of neutrals is ejected within a certain opening angle. Two sinks are included in the model:

electron loss due to radial expansion and due to ionization starting at the surface. Here the plasma is considered to be collisionless, T = 0. Only source terms are taken into account, meaning that no magnetic field transport or any recombination is considered.

Another assumption is that ionization is due to solar UV radiation only.

The radial expansion, superscript re, without ionization, is given by

n^(re)_n = n0

R r

2

(7.1)

To derive the ionization term, superscript io, using the continuity equation given as

∂n_n

∂t + ∇ · (n_n~v) = Q − L (7.2)

In the source term, Q, only ionization by solar UV radiation is considered and the loss term, L, is excluded in the assumptions.

∂n_n

∂t + ∇ · (n_n~v) = −νn_n = −1

τn_n (7.3)

Assuming nn to be constant in time

∂n_n

∂t = 0 (7.4)

and using the spherical divergence

∇ · F = 1 r²

∂(r²F_r)

∂r + 1

r sin θ

∂(F_θsin θ)

∂θ + 1

r sin θ

∂F_φ

∂φ (7.5)

the resulting equation is

1 r²

∂

∂r(n_nvr²) = −1

τn_n (7.6)

Assuming v to be constant the equations needing to be solved is given by

∂

∂r(n_nr²) = − 1

vτ(n_nr²) (7.7)

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7.1 Source at the Center of Enceladus

This then solved by

nn= A r² exp

− r vτ

(7.8)

with A an integration constant. The boundary condition at the surface is nn = n₀ at R = r which then gives the final result for neutral ionization

n_n(r) = n₀ R r

2

exp

−R − r vτ

(7.9)

The electron density then is the difference between the pure radial expansion and the radial expansion including ionization

n_e= n^(re)_n − n^(io)_n (7.10)

This computes to the total electron density as given in eq. (7.11). The first term includes electron loss due to radial expansion and the second due to ionization starting at the surface. The last term in the equation is a width effect with a Gaussian curve distribution for the electron density.

Thus the electron density for one jet and a source at Enceladus center equates to:

n_e(~r) = n₀ R r

2

| {z }

radial expansion

1 − exp

−r − R τ v

| {z }

ionization

exp −

ω H_ω

2!

| {z }

width

(7.11)

Here n0 is the initial neutral density at the center of the plume at the surface, r the radial distance from the center of Enceladus, v is the flow speed, τ is the ionization lifetime, ω is the angular distance from the center of the plume and Hω is the angular width of the plume. For each jet n0, v and Hω are different.

The values used for this calculation are given in table 7.1.

Figure 7.3 shows the resulting density distribution. On the x-axis the angular distance, in degrees, and on the y-axis the distance from the surface, in kilometers.

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Variable Value Source

R 252km [NASA, 2013a]

v 300m/s derived from the escape velocity τ 10⁶s [Johnson et al., 2006]

n₀ 4.8 · 10⁸cm⁻³ [Saur et al., 2008, Source I]

H_ω 10° [Saur et al., 2008, Source I]

Table 7.1: Used values

Figure 7.3: Model of a jet with a point source at Enceladus’ center. The x-axis shows the angular distance in degrees and the y-axis the distance from the surface in km. The peak density is at 252 km altitude.

Plasma Structures at the Enceladus Plume