LEMMS

Planetary and Space Science 104 (2014) 18–28

Contents lists available at ScienceDirect

Planetary and Space Science journal homepage: www.elsevier.com/locate/pss

Evolution of electron pitch angle distributions across Saturn’s middle magnetospheric region from MIMI/LEMMS G. Clark a,b,n, C. Paranicas c, D. Santos-Costa b, S. Livi b,a, N. Krupp d, D.G. Mitchell c, E. Roussos d, W.-L. Tseng b a

University of Texas at San Antonio, San Antonio, TX, USA Southwest Research Institute, San Antonio, TX, USA c Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA d Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany b

art ic l e i nf o

a b s t r a c t

Article history: Received 13 December 2013 Received in revised form 21 May 2014 Accepted 8 July 2014 Available online 18 July 2014

We provide a global view of
20 to 800 keV electron pitch angle distributions (PADs) close to Saturn’s current sheet using observations from the Cassini MIMI/LEMMS instrument. Previous work indicated that the nature of pitch angle distributions in Saturn’s inner to middle magnetosphere changes near the radial distance of 10RS. This work confirms the existence of a PAD transition region. Here we go further and develop a new technique to statistically quantify the spatial profile of butterfly PADs as well as present new spatial trends on the isotropic PAD. Additionally, we perform a case study analysis and show the PADs exhibit strong energy dependent features throughout this transition region. We also present a diffusion theory model based on adiabatic transport, Coulomb interactions with Saturn’s neutral gas torus, and an energy dependent radial diffusion coefficient. A data-model comparison reveals that adiabatic transport is the dominant transport mechanism between
8 to 12RS, however interactions with Saturn’s neutral gas torus become dominant inside
7RS and govern the flux level of
20 to 800 keV electrons. We have also found that field-aligned fluxes were not well reproduced by our modeling approach. We suggest that wave–particle interactions and/or a polar source of the energetic particles needs further investigation. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Electron pitch angle distributions Electron transport and loss mechanisms Transition region Saturn Cassini

1. Introduction Particle distributions in planetary magnetospheres can be characterized by their intensity and angular distribution. In a planetary dipole, it is expected that the pitch angle distribution (PAD) would reflect quasi-stably trapped particles. Deviations from this type of distribution are very common in planetary data sets, and each deviation is a powerful indicator of magnetospheric structure and/or dynamics. In this paper we explore a persistent feature of pitch angle distributions in the inner to outer magnetosphere of Saturn (i.e. 5–25 Saturn Radii (RS)). Here we are referring to the observation of a persistent pitch angle shape in energetic electrons based on their spatial location. In addition to presenting an extensive summary of Cassini data, we also consider how such distributions are formed and maintained in such an active system. Saturn’s magnetosphere is a clear example of an active magnetospheric system. The rapidly rotating planet has a magnetic field n Corresponding author at: University of Texas at San Antonio, Physics and Astronomy, One UTSA Circle, San Antonio, TX 78249, USA. Tel.: þ 1 210 522 5027; fax: þ1 210 520 9935. E-mail address: [email protected] (G. Clark).

http://dx.doi.org/10.1016/j.pss.2014.07.004 0032-0633/& 2014 Elsevier Ltd. All rights reserved.

strength slightly weaker than Earth, with Enceladus actively pumping
300 kg s  1 of neutral H2O into the magnetosphere which is subsequently dissociated and ionized (e.g. Hansen et al., 2006; Johnson et al., 2006; Pontius and Hill, 2006; Waite et al., 2006, Delamere et al., 2007; Fleshman et al., 2010). Other sources of neutral species in the magnetosphere include rings and other icy satellites. In turn, plasma is accelerated and transported throughout the inner, middle, and outer parts of the magnetosphere. The mechanisms responsible for accelerating and transporting the plasma have been studied for the past three decades with flybys from Pioneer 11 (e.g. McDonald et al., 1980), the two Voyager spacecraft (e.g. Krimigis et al., 1983) and now with Cassini, which has been orbiting Saturn since July 2004 (e.g. Burch et al., 2005; Schippers et al., 2008; Rymer et al., 2009; Carbary et al., 2011). The effects of several types of acceleration mechanisms have been detected at Saturn, such as adiabatic energization (e.g. Rymer et al., 2008 and references therein), pickup acceleration (e.g. Sittler et al., 2006; Rymer et al., 2007), and auroral mechanisms (e.g. Saur et al., 2006, Bunce et al., 2008; Mitchell et al., 2009, Krupp et al., 2009, Schippers et al., 2011). Qualitatively, it is expected that with inward transport of plasma/particles, pitch angle distributions would evolve toward a

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

more trapped shape (maximum near 901), if adiabatic invariants are conserved in the transport. But the neutral gas torus, for instance, complicates this picture and therefore we will rely on observations to help us order the physical effects by their importance to the data. Other types of studies have attempted to relate the particle distribution at each distance with a transport model including losses and sources (e.g. Beutier et al., 1995; Santos-Costa et al., 2003; Lorenzato et al., 2012). Recent analyses by Schippers et al. (2008) and Carbary and Rymer (2014) of low energy electron data (0.6 eV to 26 keV) from the Cassini Plasma Spectrometer (CAPS) (Young et al., 2004) and by Carbary et al. (2011) of higher energy electron data (110 keV to 365 keV) from the MIMI Low Energy Magnetospheric Measurement System (LEMMS) (Krimigis et al., 2004) have identified a boundary near 10 Saturn radii (RS) where PADs morph from a trapped shape (local maximum at 901) to a field-aligned shape (local minimum at 901). Carbary et al. (2011) suggested that fieldaligned PADs may be related to currents coupling the ionosphere to the magnetosphere. However, no clear explanation was provided on the nature of the transition region and subsequent large fraction of trapped distributions inside
8RS. In addition to Saturn, observations of Jupiter’s magnetosphere using Galileo data also revealed a similar boundary in the 10–17RJ region (Tomás et al., 2004a). Tomás et al. (2004b) related their observations to enhanced ionospheric precipitating flux and found the energy flux content to be compatible with the brightness of auroral emissions. Furthermore, studies on Jupiter also discuss wave–particle scattering of keV electrons due to stochastic acceleration processes between 6 and 12RJ (e.g. Horne et al., 2008; Mauk and Fox, 2010; Woodfield et al., 2013). At Saturn, there is currently no accepted explanation of the field-aligned region nor is there a compelling explanation for the similar transition in PAD. In the plasma and suprathermal energy range, there has been discussion of the circulation pattern of electrons as a blueprint for understanding the nature of the butterfly observations (local minima at 01, 901, and 1801) within this region (Burch et al., 2005; Rymer et al., 2009). In addition to local losses, sources, and transport, other possible explanations may include auroral mechanisms (e.g. Mitchell et al., 2009; Saur et al., 2006; Krupp et al., 2009; Schippers et al., 2012) or wave–particle mechanisms (e.g. Menietti et al., 2012; Tang and Summers, 2012). In this paper we present observations from 2004 to 2012 of LEMMS electron PADs between
20 keV to
800 keV. Previous studies of this subject (McDonald et al., 1980; Carbary et al., 2011) were extremely confined either because the data set was limited (in the case of Pioneer 11) or by the use of only a single energy channel. The source of electrons at the energies of interest is not well understood. These electrons are far above the energies associated with corotation or energization through Coulomb collisions with corotating ions. Characterizing the PAD shape in Saturn’s middle magnetospheric region is an essential tool when attempting to understand the loss and acceleration mechanisms present. In Section 3 we outline our analysis technique and in Section 4 we present our analysis results. In Section 5 we compare the results to a theoretical transport model. Section 6 summarizes and discusses the results of our global survey, case study analysis, and the similarities and differences between data and model results.

2. Data Data presented in this paper were obtained from Cassini’s MIMI/ LEMMS sensor, which is described in detail by Krimigis et al. (2004). There are three different sensors that make up MIMI, but our results focus on data obtained by LEMMS. LEMMS is a particle detector with

19

two separate telescopes, a low-energy telescope and a high-energy telescope. The low-energy telescope has eight electron energy channels that span an energy range between 20 keV and 800 keV. A permanent magnetic field is used to separate the electron and ion trajectories, resulting in electron measurements unaffected by ions. The high-energy telescope uses a stack of solid-state detectors to measured energetic electrons between 110 keV and 20 MeV. The low-energy channels (i.e. C0–C7) were subject to background effects such as solar light contamination, whereas the high-energy channels are not susceptible to this effect because they are covered by a 25-micron aluminum shield. Data presented in this paper relied solely on observations from the low-energy channels. A pitch angle distribution analysis was presented by Carbary et al. (2011), which used a single energy channel (110–365 keV) from the LEMMS highenergy telescope. LEMMS measures particle energy, flux, and with the magnetic field orientation provided by the Cassini fluxgate magnetometer (MAG) (Dougherty et al., 2002), we calculated the pitch angle. Data presented here are binned in pitch angles of width 11.251. In early 2005 the LEMMS rotation table became inoperable and was placed in a fixed position (Krupp et al., 2012). Prior to 2005, PADs were obtained at a higher cadence than after that time. Subsequent to that we rely on spacecraft maneuvers and other factors to populate the local pitch angle space with data. For example, the spacecraft rotates about an axis nearly perpendicular to the lowenergy telescope during downlinks (Carbary et al., 2011). The time it takes for Cassini to rotate can range between
23 min to
39 min, therefore LEMMS sweeps through 11.251 in
2.5 min. Data was obtained in half-hour slices (i.e. approximately one spacecraft rotation), which allow pitch angle fluxes to be preserved, while allowing enough time for the spacecraft to build up the full pitch angle distribution. Some electron channels are susceptible to solar light contamination when the low-energy telescope is pointing close to the direction of the Sun. NASA’s SPICE software was used to calculate the angle between the boresight vector of the LEMMS low-energy telescope and the Sun to identify and eliminate potentially contaminated data. If the angle was smaller than the effective field of view (FOV) – the channel dependent FOV to solar light – then the data were discarded. As pointed out above, LEMMS is currently in a fixed position; therefore the boresight angle in spacecraft coordinates is well known and can be accounted for easily.

3. Analysis technique The data was filtered according to the following user-defined constraints before performing a non-linear least-squares fit (Markwardt, 2009) to LEMMS data in units of counts and in linear space before determining the shape of the distribution. (1) Exclude data when the Sun is within a channel’s effective FOV. (2) Consider pitch angle bins that have fluxes larger than 1 cm  2 s  1 sr  1 keV  1. (3) Determine pitch angle coverage to be at least
1101. (4) Confine measurements to the current sheet ( 71RS). Threshold fluxes of 1 cm  2 s  1 sr  1 keV  1 are justified because the average measured background is close to
0.2 cm  2 s  1 sr  1 keV  1. This threshold is large enough to neglect statistical variance, but low enough not to bias large fluxes. We required a minimum pitch angle coverage of
1101 to properly characterize the shape. Requiring the full 1801 pitch angle coverage would significantly reduce the number of events for our analysis because a spacecraft roll does not necessarily point LEMMS into the direction parallel to the magnetic field. Requiring pitch angle symmetry could mitigate this

20

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

Isotropic PAD

Pancake PAD

Field-Aligned PAD

Butterfly PAD

Fig. 1. Typical pitch angle distributions measured in Saturn’s magnetosphere by MIMI/LEMMS and fits to the isotropic, pancake, and field-aligned PAD with a F(α)¼ AsinK(α) and Fourier model. The butterfly PAD was analyzed only using the Fourier model. The black triangles represent measurements (error bars calculated using Poisson statistics) and the red and blue curves represent the fits using Eqs. (2) and (3), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

requirement, but this method was not used in this analysis. Finally, before the distributions were fitted, we identified the location of the current sheet. Saturn’s current sheet is warped by the pressure of the solar wind on the system, especially away from equinox (Arridge et al., 2008a and references therein). Arridge et al. (2008a) modeled the shape of the current sheet and related the vertical distance parallel to the spin axis (ZCS) to the radial distance (r), the magnetospheric hinging distance (RH), and the solar wind latitude (θSUN ). 
 r Z CS ¼ r  RH tanh ð1Þ tan ðθSUN Þ RH The solar wind latitude was determined using the empirical formula provided by Arridge et al. (2008a). We assume a constant hinging distance of 29RS, which Arridge et al. (2008a) shows to have a
95% prediction efficiency in correctly modeling Saturn’s radial magnetic field component. We note that studies (e.g. Arridge et al., 2008b, 2011; Provan et al., 2012) have shown that the current sheet can vary around the mean value (i.e. ZCS). Arridge et al. (2011) (see their Fig. 4 and 7) shows the oscillation amplitude is small for radial distances considered in this study. For example, at distances smaller than 25RS, the current sheet displacement is
1–2RS the majority of the time. However, it can be as high as 4RS. Our criterion has a7 1RS constraint, so some of the displacement is accounted for in our filtering technique. Once the data is filtered to constraints 1–4, we fit the PAD using a standard function of the form: FðαÞ ¼ A sin ðαÞ K

ð2Þ

where α is the local (approximately equatorial) pitch angle, and A and K are constants. The parameters A and K were determined through a non-linear least-squares fitting method (Markwardt, 2009). The standard function (Eq. (2)) has been used in

previous analyses (e.g. Carbary et al., 2011; Rymer et al., 2009; Gannon et al., 2007). The K parameter is the proxy we used to assign distributions to a few principle shapes: |K| o0.1 are defined as isotropic distributions (no local maxima or minima), K o  0.1 are field-aligned or bidirectional distributions, and K 40.1 are trapped distributions. The value of 7 0.1 was chosen based on the model accurately differentiating between the three types of PADs. A reduced chi-square goodness of fit statistic (Χ2ν) was used to test the accuracy of our model to the observed PADs (Bevington and Robinson, 2003). If Χ2ν r
1.6 (changes slightly with the number of degrees of freedom (ν)) then the fit was believed to accurately reproduce (p-value ¼ 0.1) the shape of the observations and therefore passes the goodness of fit test. Examples of theoretical fits to LEMMS pitch angle data are shown in Fig. 1. The black triangles represent particle data and the red curve represents Eq. (2). Error bars were calculated using Poisson statistics. The benefit of Eq. (2) is the simplicity to characterize the shape of the distribution based on the K parameter. However, Eq. (2) cannot fit the butterfly distribution, which is the other general PAD shape found in magnetospheres. Therefore if Eq. (2) fails to accurately fit the PAD (i.e. Χ2ν 4
1.6) then a Fourier series model was used to fit the PAD. Assuming the Fourier series to be odd over the domain between 01 and 1801 reduced the number of free parameters, therefore it can be expressed as: 3

FðαÞ ¼ Ao þ ∑ An sin ðnαÞ n¼1

ð3Þ

where n is an integer, α is the local pitch angle, and the coefficients Ao and An are defined as follows: Z 1 L FðαÞ dα Ao ¼ L L

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

C2

C3

C4

C5

C6

Butterfly PAD

Isotropic PAD

Field-Aligned PAD

C1

Pancake PAD

Mission Average Profiles

C6

C2

Fig. 2. Radial profiles of pancake, field-aligned, isotropic, and butterfly distributions. The PADs are represented as a percentage and normalized to the number of samples in each radial distance bin. Bins are in 1RS. The black, blue, red, purple, pink, and green curves represent the mission averaged profiles for C1, C2, C3, C4, C5, and C6, respectively. The bottom panel illustrates the number of events in each radial bin used for the mission averaged profiles. Here, the blue curve represents C2 and the green curve represents C6. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

An ¼

1 L

Z

L L

FðαÞ sin ðnαÞ dα

We determined the curve was shaped like the butterfly distribution by imposing a series of constraints. First, two maxima and one minimum need to be located within the pitch angle ranges of 251–651, 1151–1551, and 701–1101, respectively. Maxima and minima were determined by calculating the derivative of the fitting function and finding wherepitffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi is equal to zero. Second, there must be at least 3σ (i.e. σ ¼ counts for Poisson statistics) variation between the maxima and minimum to be considered significant. Once these conditions are satisfied and Χ2ν r
2 (p-value ¼0.1 for ν between 5 and 9) then the distribution shape is labeled as butterfly. An example of a Fourier fit to a measured butterfly distribution is shown in Fig. 1 as the blue curve. The Fourier model (Eq. (3)) fits the field-aligned, pancake, and isotropic distributions equally as well as the standard fitting function (Eq. (2)) (Fig. 1). However,
3–5% of PADs that passed our filtering routine were neither characterized by the standard fitting function (Eq. (2)) nor the Fourier model (Eq. (3)). We did not investigate these types of PADs. We hypothesize these PADs could be assigned to one of the four general shapes, although further attention is needed to properly use the Fourier model to pick out all four PAD types. 4. Results In this section we present our results from data obtained with the LEMMS low-energy electron channels between 2004 and 2012, following the data selection criteria and analysis outlined in Section 3. In Section 4.1 we present radial and local time profiles of the angular distributions of electrons as a function of radial

21

distance and local time. Then in Section 4.2 we take a closer look with a case study analysis to see how the PADs are evolving throughout Saturn’s magnetosphere. 4.1. Radial and local time profiles Here we present the radial and local time profiles derived from a comprehensive, statistical analysis using LEMMS data from 2004 to 2012. Fig. 2 shows the fraction of PADs as a function of cylindrical radial distance from the rotation axis (i.e. [x2 þ y2]1/2) using Saturn’s equatorial coordinate system. The fraction was calculated by dividing the total number of each PAD type by total number of PADs in a given radial bin, where radial bins are in 1RS. Each curve represents the mission averaged profile for LEMMS energy channels C1–C7. Black, blue, red, purple, pink, and green curves represent C1, C2, C3, C4, C5, C6, and C7, respectively. The pancake, field-aligned, and isotropic PADs were determined from the standard fitting model (i.e. Eq. (2)), whereas the butterfly PAD was determined from the Fourier model (i.e. Eq. (3)). The bottom panel shows the number of events used for the mission averaged profiles of C2 (blue curve) and C6 (green curve). Inward of
10RS, each radial bin had
20–50 events, which is typical of all the energy channels (C2 and C6 shown). Between
10 to
12RS that number increased slightly between
50–100 events. Subsequently, beyond
12RS, the number of events for lower energy channels (i.e. C1 to C4) increased slightly to
100 or more. In contrast, the number of events for higher energy channels (i.e. C5 to C7) drops of dramatically with increasing energy. The sharp fluctuations of the C6 channel in the mission averaged PAD profiles reflect these poor statistics, which made it difficult to interpret spatial trends. Fig. 2 illustrates a clear spatial organization of the pancake, field-aligned, and butterfly PADs, whereas the isotropic PAD is relatively flat between
5 and 15RS. Observations show that the pancake PAD, in all energy channels, peaks near 100% at 5RS and then the fraction falls off to below 20% by
12RS. In contrast to the pancake PAD, the fraction of field-aligned PADs at 5RS is
0%, but increases to a maximum of
60% by
12RS and continues to remain one of the dominant PAD types out to 25RS. Carbary et al. (2011) observed a similar spatial trend in the pancake and fieldaligned electron PADs in the energy range of 110–365 keV. However, observations presented here suggest that a much larger fraction of isotropic PADs exist throughout the 5–25RS region. In addition, for the first time, we present spatial profiles of the butterfly PAD. The mission averaged profile for channels C1, C3, C4 shows the butterfly PAD peaking
10RS, which makes up
50% of total number of PADs. The fraction of butterfly PADs diminishes between 7
4RS of the
10RS peak. In the higher energy channels (e.g. C5–C7) and the C2 channel the butterfly PAD profile is less significant, peaking at
20%–30%, and appears to a have a flatter distribution relative to the other energy channels. The implications for the larger fraction of isotropic PADs and the behavior of butterfly PADs between
7–13RS are discussed in Section 6. Mission averaged, local time profiles for energy channels C1, C3, C5, and C6 are plotted in Fig. 3. Data are shown as bar charts and the PAD type is normalized to the total number of events for each local time sector. For example, there are 130 total events for 27–40 keV electrons between 06 h and 12 h magnetic local time (MLT), thus each PAD is normalized to 130 and their sum equals 100%. Pancake, field-aligned, isotropic, and butterfly PADs are depicted by the blue, red, green, and purple bars, respectively. The data were binned into local times of 6 h or 901 between the radial distances of 5–15RS. This radial distance was chosen for two reasons: 1) to improve the statistics for discussion, and 2) to cover the transition region where the angular distributions are

22

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

Mission Averaged Local Time Profiles [5-15 RS] 56-100 keV

pancake field-aligned isotropic butterfly

00-06 h

130 Events

168 Events

06-12 h

12-18 h

174 Events

Fraction [%] Normalized in MLT Sector

Fraction [%] Normalized in MLT Sector

Mission Averaged Local Time Profiles [5-15 RS] 27-40 keV

00-06 h

18-24 h

130 Events

00-06 h

06-12 h

172 Events

12-18 h

221 Events

18-24 h

Magnetic Local Time [hours]

133 Events

169 Events

185 Events

06-12 h

12-18 h

18-24 h

[5-15 RS] 265-550 keV Fraction [%] Normalized in MLT Sector

Fraction [%] Normalized in MLT Sector

[5-15 RS] 175-300 keV pancake field-aligned isotropic butterfly

pancake field-aligned isotropic butterfly

pancake field-aligned isotropic butterfly

00-06 h

102 Events

156 Events

129 Events

06-12 h

12-18 h

18-24 h

Magnetic Local Time [hours]

Fig. 3. Normalized fractions of each PAD type to the total number of events in a MLT sector for energy channels C1, C3, C5, and C6. The blue, red, green, and purple bars correspond to the pancake, field-aligned, isotropic, and butterfly PADs, respectively. Data were binned into local time sectors of 6 h or 901 between 5 and 15RS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

dynamically evolving. Unlike the radial profiles, it is difficult to discern any type of organization. A correlation test of each PAD type was explored for trends with MLT. For example, we took the normalized fractions in each MLT sector for a given energy range (e.g. 27–40 keV) and computed the Pearson correlation coefficient. Unfortunately, there are poor statistics (o10 events total) in all energy ranges between 00–06 h MLT, therefore the correlation analysis was based on only three data points (i.e. MLT 06–12 h, 12– 18 h, and 18–24 h). For a correlation to be present we required the coefficient to be greater than 0.8 with a spread larger than 10% in the data points. Under this requirement, we found the fieldaligned PADs between 27 and 100 keV occur slightly more frequently (
15%) between 18 h and 24 h MLT. Similarly, the 27–100 keV electrons have pancake PADs slightly more frequently (
20%) between 06 h and 12 h MLT. All other PAD types show no organization with MLT. A previous study presented the local time dependences for field-aligned and pancake PADs from 10 to 20RS (Carbary et al., 2011) and, in general, the profiles shown here agree with their observations. 4.2. Transition region In this section, the focus is now shifted to the transition region, between
7–13RS, where the PADs evolve from field-aligned to butterfly and then eventually pancake. Fig. 4 shows a pitch angle spectrogram for channels C1, C3, C5, and C7 for the same event (i.e. 2005-267). The top panel of Fig. 4 shows the neutral densities of H2O from the Cassidy and Johnson (2010) as well as H and H2 from Tseng et al. (2011) and (2013) for reference, which is coarsely averaged into 0.5RS bins. During this event (2005-267) Cassini’s trajectory was in the outbound leg of equatorial orbit (i.e. z
0) # 15, in which it traversed the night side of Saturn. Additionally, before
10 UTC and after
18 UTC, the spacecraft stopped rotating and thus poor pitch angle coverage. The data were binned into 11.251 pitch angle bins and collected over 30 min. This figure clearly

illustrates the energy dependent nature of pitch angle evolution as a function of radial distance. Electrons are observed to be primarily field-aligned at
12RS, then at smaller radial distances the electrons are observed to evolve into the butterfly PAD near
11RS, and then subsequently the isotropic PAD farther in near 9RS. Lower energy electrons are observed to isotropize much more rapidly than the higher energy electrons. For example, Fig. 5 shows 27–40 keV electrons isotropizing
10.5RS, whereas 56–100 keV, 175–300 keV, and 510–832 keV maintain their butterfly shape and isotropize much closer to the planet depending on their energy. Therefore is it reasonable to conclude that the higher energy electrons are less likely to be altered as they are transported throughout the system. However, the reason for the abrupt isotropization of 27–40 keV electrons is still unknown and may be complicated by interchange events in the inner magnetosphere. Interchange occurs throughout the inner magnetosphere and affects electrons as high as
100 keV (Chen and Hill, 2008; Paranicas et al., 2010, Fig. 1 and Fig. 3). Interchange events also dominate the local flux, so our hypothesis is that once this process is active, it creates its own pitch angle signatures. We discuss the physical nature of this evolution and the importance of this spatial region in Section 6. In addition to the 2005-267 event, several other events show a similar evolution of PADs as a function of radial distance (Table 1). Fig. 5 shows the differential flux as a function of radial distance and energy for four events, two occurring on the night side and two occurring on the day side. The blue, red, and green curves represent the flux in pitch angle bins 951, 1401, and 1751, respectively. In the 2005-267 event, the anisotropy between pitch angle bins 901 and 1401 increases with increasing electron energy. Similarly, an equivalent anisotropy is also observed in 2011-130 on the night side of Saturn. However, there appears to be a day/night asymmetry in the energy dependence of the PADs because the energy dependent anisotropy is less pronounced in the dayside events of 2007-179 and 2012-88. At the distances we are considering, the magnetic field is no longer entirely due to the

Density [cm-3]

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

H 2O

23

H2

H

RS C1: 27-40 keV

135 90 45

3 104 1.5 104 0 5 102

C7: 510-832 keV C5: 175-300 keV

Pitch Angle

0 180 135 90 45 0 180 Pitch Angle

0

C3: 56-100 keV

Pitch Angle

0 180

135 90 45

Intensity

45

4 104

2.5 102

Intensity

90

0 40

20

Intensity

Pitch Angle

135

Intensity

8 104

180

0

0

Time (UTC) 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 Dipole L (R S) 8.75 9.25 9.73 10.20 10.66 11.11 11.56 11.99 12.42 Fig. 4. Pitch angle spectrograms during 2005-267 for energy channels C1, C3, C5, and C7 (top to bottom respectively). The topmost panel illustrates the neutral densities of H2O, H2, and H. These plots clearly show the energy dependence of the PADs throughout the 8–12RS spatial region. C1 shows that electrons between
20 keV and 40 keV are already isotropized by
10.5RS. Although, LEMMS channel c7 makes it clear that electrons in the 500–800 keV range maintain their butterfly shape down to 9RS.

2005-267 / Night Side C1

10

C3

3

Flux

10

C5

C1

C7

3

8

9 10 11 12 13

Radial Distance [Rs]

10

1

C7

9 10 11 12 13

10

Radial Distance [Rs]

C3: 56-100 keV

10

C5

C5: 175-300 keV C7: 510-832 keV

10

C7

0

10

-1

8

C3

o

C1: 18-40 keV

1

0

-1

-1

C5

10

10

PA = 175

10

2

10

0

0

10

PA = 140 C1

3

C3

2

C7

o

10

3

10

10

10

C1

C5 10

PA = 95o

4

10

10

2012-88 / Day Side 5

10

4

C3

1

1

2007-179 / Day Side

10

10

2

2

10

5

10

10

4

4

10

2011-130 / Night Side 5

5

10

-1

8

9 10 11 12 13

Radial Distance [Rs]

10

8

9 10 11 12 13

Radial Distance [Rs]

Fig. 5. Flux vs. radial distance for four separate events; two occurring during local times sectors on the night side and two occurring on the day side. Blue, red, and green curves represent the fluxes for pitch angle bins 951, 1401, and 1751 respectively for the energy channels C1, C3, C5, and C7. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

planetary dipole, so it is not surprising that day/night asymmetries exist. Since we rely on spacecraft maneuvers for pitch angle coverage, only a small number of events clearly show the radial distance where pitch angle anisotropies develop. Here we have shown the detailed pitch angle evolution for one event occurring on 2005-267. Additionally, we compared the flux as a function of radial distance for four events, occurring both on

the dayside and night side. Here is a brief summary of our observations: (1) the electron flux at pitch angles near 451 and 1351 (i.e. butterfly PAD) dominate in the 8–12RS region for energies between 18 keV and 183 keV; (2) pitch angle anisotropies as a function of energy appear to be largest on the night side; and (3) higher energy electrons maintain their field-aligned or butterfly PAD closest to the planet.

24

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

5. Data comparison to a theoretical transport model The evolution of the electron PAD throughout Saturn’s magnetospheric system cannot be accurately described by a single process alone, but rather is likely due to multiple loss and source mechanisms. In this section we compare a theoretical transport model to LEMMS observations. The model incorporates the physics of radial, adiabatic transport and includes losses due to Coulomb interactions with the neutral cloud. In Section 5.1 we introduce and describe the theoretical model and in Section 5.2 we discuss the results between the model and LEMMS observations.

Table 1 List of events with adequate pitch angle coverage of the spatial region between 7 to 13RS. Year

Start–stop day/UTC

Inbound/outbound orbit

Day side/night side

2004 2004 2005 2005 2006 2011 2011 2012

301/16:00–301/20:00 350/00:00–352/01:00 267/10:00–267/18:00 358/04:00–358/12:00 181/18:00–182/01:00 106/18:00–106/22:00 130/00:00–130/10:00 88/10:00–88/20:00

Inbound Outbound Outbound Inbound Outbound Inbound Inbound Outbound

Day side Night side Night side Day side Day side Night side Night side Day side

5.1. Theoretical model description We examine the transport process of keV-energy electrons using a particle transport code that solves the governing 3-D Fokker-Planck equation (Eq. (4)) (e.g. Santos-Costa and Bolton, 2008). This numerical code – or “physical model” because it is based on diffusion theory – has the capability to compute the time evolution of particle distribution functions in a phase space equivalent to energy, latitude, and radial distance. Threedimensional diffusion theory models have proven to be efficient in determining the dominant mechanisms of source, loss, and transport of radiation-belt particles for the magnetospheric systems of Earth, Jupiter, and Saturn (Beutier and Boscher, 1995; Beutier et al., 1995; Santos-Costa and Bourdarie, 2001; SantosCosta et al., 2003; Santos-Costa and Bolton, 2008). In Saturn’s planetary system, keV-energy electrons undergo Coulomb interactions with the bound electrons of atoms and molecules populating Saturn’s neutral environment (e.g. SantosCosta et al., 2003; Jurac and Richardson, 2005; Paranicas et al., 2007 and references therein). Energetic electrons lose energy and are scattered during the collision with neutrals (Zombeck, 1982). In Eq. (4), Coulomb interactions are characterized by a pitch-angle diffusion (Dyy) term and an energy loss term (dE/dt). These terms are calculated following the methodology of Beutier and Boscher (1995) and models of Saturn’s distribution of neutral constituents are required for their computation. The work of Cassidy and Johnson (2010) provides the spatial distribution of O, OH, and H2O while H and H2 are based on the work of Tseng et al. (2013), (2011), respectively. For the scope of this paper, we use this model as our basis and focus on the transport of 1 keV to 1 MeV energy electrons subject to adiabatic transport and Coulomb interactions with Saturn’s neutral gas cloud. We consider a source of keV-energy electrons in the middle magnetosphere and then calculate a steady state solution (∂f/∂t ¼0). Thus the diffusion transport equation takes the form: 
  ∂f 1 ∂ dE þ 0 ∑ f ðE; y; LÞ ∂t G i ¼ 1;2∂Q i dt     1 ∂ ∂f ðE; y; LÞ 1 ∂ ∂f ðM; J; LÞ ¼ 0 ∑ GDLL þ G0 Dyy ð4Þ ∂Q i G ∂L ∂L G i; j ¼ 1;2∂Q i M; J where f is the particle phase space distribution function averaged over a drift shell. The Jacobian G0 and G are defined as ∂(J1, J2, J3)/ ∂(Q1 ¼E, Q2 ¼ y, L), and ∂(J1, J2, J3)/∂(M,J,L), respectively, with (Ji)i ¼ 1,3 representing the invariants of the elementary motions of trapped particles. M and J (¼J2) are the relativistic magnetic momentum and second invariant, respectively. L is the McIlwain parameter or third invariant (Schulz and Lanzerotti, 1974). The term E is the kinetic energy and y is the sine of the equatorial pitch-angle αeq (y¼sinαeq). DLL is the radial diffusion coefficient term. Two phase spaces are then numerically combined to solve Eq. (4). The (M, J, L) action variable phase space is chosen to model mechanisms that violate the third invariant L-shell (e.g., radial transport)

and the (E, y, L) phase space for modeling processes responsible for changes in E and αeq (e.g. Santos-Costa and Bolton, 2008). Previous studies of the Earth and outer planets assumed a radial diffusion coefficient of the form DLL ¼DoLn, with the power n4 1. For Saturn, Hood (1983) analyzed Pioneer 11 and Voyager 1 particle data and found the power n ¼3 71, while Siscoe and Summers (1981), found the power to vary between n ¼4 and n ¼8 for the region between 3 and 16RS. Santos-Costa et al. (2003) and Lorenzato et al. (2012) developed physical models of Saturn’s electron belts inside 6RS and their simulation results matched spacecraft particle data well with n¼ 3, suggesting a transport of energetic electrons driven by an ionospheric dynamo mechanism (Brice and McDonough, 1973). Moreover, Roussos et al. (2007) showed the power to vary between n ¼6 and n¼ 10 for distances between 4 and 9RS using results derived from the analysis of micro-signatures with Cassini LEMMS. It is clear from the literature that a large range of values for the diffusion coefficients exists that can accurately describe a particular energy of electrons in a given spatial region. Here, a radial diffusion coefficient of the form DLL ¼DoLn is used, where we found energy dependent empirical expressions for the Do and the power n terms. The expression can be written as: DLL ¼ ð37  nðEÞ  4  10  14 ÞLnðEÞ

ð5Þ

where E is the electron energy in keV and n(E) ¼ 7  exp[-0.85  (E/1000)]. This expression was chosen because if E is large (e.g. 1000 keV) then n(E)
3 and the expression takes the form of L3, which is consistent with radiation belt electron studies (e.g. Santos-Costa et al., 2003; Lorenzato et al., 2012). Furthermore, if E is small (e.g. 10 keV) then n(E)
7, which is consistent with the n¼ 6 to n ¼10 dependency that Roussos et al. (2007) derived and was later used by Kollmann et al. (2011). The functional form of Do was also chosen to be in line with these studies. To solve Eq. (4), an explicit finite difference method is sufficient and necessary to compute the steady state solution (e.g. Beutier et al., 1995). Friction and diffusive terms in Eq. (4) usually require the use of a more robust numerical method, such as a Runge–Kutta method of order four or finite volume method, to solve the parabolic differential equation (e.g. Santos-Costa et al., 2003; Santos-Costa and Bolton, 2008). This is not necessary in this study as a limited number of mechanisms (e.g. transport and interaction with neutrals) are taken into account in our simulations. Note that computations were made in the dipolar approximation. Although the field gradually departs from a dipole beyond 6RS to become a smoothly-warped magnetosdisk (e.g. Carbary et al., 2010 and references therein), the dipolar approximation is assumed to be valid for near equatorial orbits at the zeroth order (e.g. Carbary et al., 2009; Roussos et al., 2007). The latest published Schmidt coefficients for the planetary field (Cao et al., 2011) were used to determine the equivalent eccentric dipolar magnetic field in the model. Fig. 6 illustrates the similarities and differences between loss-free adiabatic transport (left panel) and adiabatic transport

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

~100 keV

25

~100 keV L=9

L=7

L=9

L=7

L = 13

L = 13

Fig. 6. Normalized flux (simulated) versus equatorial pitch angle for
100 keV electrons with loss-free transport (left panel) and with losses due to Saturn’s neutral gas cloud (right panel). Each panels shows the evolution of the PAD from the drift shell at L ¼ 13 to L ¼ 7. The blue, red, and purple curves represent the L-shell crossings at 13RS, 9RS, and 7RS, respectively. The source distribution was field-aligned at L ¼ 15. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

including interactions with the neutral cloud (right panel). In each plot, we show the normalized flux versus pitch angle for three radial distances. The blue, red, and purple curves represent the radial distances at 13, 9, and 7RS, respectively. The source distribution was initially field-aligned at L ¼15. It is clear from Fig. 6, that loss-free transport cannot adequately describe the evolution of field-aligned to pancake PADs, as observed in the radial profiles (Fig. 2). However, a weak resemblance of the butterfly distribution can be seen at
9RS in the left panel. The interaction with neutrals is more consistent with the radial profiles (Fig. 2). The
100 keV electrons begin to resemble the butterfly PAD by
10RS and by
9RS it has a well developed shape. Subsequently, at 7RS the
100 keV electrons exhibit the pancake PAD. Next we compare the model with LEMMS results and look at multiple energies. 5.2. Comparison with LEMMS data Here we compare LEMMS data to the output from the theoretical model for the case study event on 2005-267. The numerical box used in the theoretical model extends from 1 to 15RS, and accounts for pitch angles between 0 and 1801 over energies ranging from 1 keV to 1000 keV. For initial conditions we used a distribution function equal to zero everywhere inside the numerical box except for the drift shell at L
12. At L
12 we constrain the model with LEMMS and CAPS data, which is expressed as a Dirichlet boundary condition. CAPS data was used for the1 keV and 10 keV electron distributions, since the energization of these electrons will be measured by the LEMMS C-channels. At
12RS the 1 keV and 10 keV measured distributions were both bidirectional. This also matches the shape of the LEMMS PADs at this radial distance. The boundary condition at
12RS was chosen because it was the farthest distance at which Cassini was still rolling, thus offering the best pitch angle coverage for all energy channels. Since the numerical code uses a finer grid than the LEMMS and CAPS measurements, it interpolates and extrapolates the data at the boundary condition. During the computation of the steady state solution, electrons were allowed to diffuse inward to 1RS and outward to 15RS. Fig. 7 shows the comparison of results between the model and LEMMS data for electron energies of 26.83 keV, 36 keV, and 129.75 keV, and 381.77 keV. These energies correspond to the approximate central pass band energies for the C0, C1, C4, and C6 LEMMS channels. Shown in the top panel of Fig. 7 is the differential intensity as a function of pitch angle for five equatorial L-shell crossings ranging from 12.4 to 5.3RS. The curves represent the results from the model and the symbols represent the results from LEMMS measurements. The black circles represent the L-shell crossing at L ¼5.3. At this radial distance LEMMS pitch

angle coverage was poor. To mitigate the poor angular coverage, we assumed pitch angle symmetry provided by the data shown as solid pink circles to build up the full PAD. Therefore the open circles represent the fluxes of pitch angles between 01 and 451 based on the fluxes of actual measurements from 901 to 1801. The bottom panel of Fig. 7 illustrates the differential intensity as a function of dipole L-shell in terms of Saturn radii. The red solid curve and symbols represent the differential intensity for midlatitude pitch angles (
451) as provided by the model and LEMMS data, respectively. The blue solid curve and symbols represent the differential intensity for equatorial pitch angles (
901) as provided by the model and LEMMS data, respectively. The dotted red and blue curves illustrate loss-free adiabatic transport for
451 and
901 pitch angles, respectively. Error bars were calculated using Poisson statistics, and are often smaller than the symbol size. The PAD evolves differently over the various energies (top panel of Fig. 7). For 26.83 keV and 36 keV electrons the model and results match well from 12.4 to
10RS, but then the data shows a sudden increase of
901 pitch angle electrons by a factor of
4 greater than the model predicts. This may be suggestive of a source due to the injection of electrons. At distances closer to the planet (i.e. 5.3RS) the model does a reasonable job in predicting the flux (within a factor of 3) at pitch angles between
451 and
1351, however it underestimates the flux at pitch angles nearly parallel to the magnetic field. At larger energies (i.e. 129.75 keV and 381.77 keV) the model accurately matches the evolution of the PAD and flux from 12.4RS to below 10RS. Similar to the lower energy electrons, the model does a reasonable job at predicating the flux (within a factor of 3) at pitch angles between
451 and
1351. Pitch angles near 01 and 1801 are grossly underestimated at 5.3RS. It is interesting to note that at higher energies there does not appear to be an injection of electrons at L¼ 10. However, it has been shown previously that injections are an energy dependent process (e.g. Paranicas et al., 2007, 2010). The radial profile of electrons (bottom panel of Fig. 7) suggest that loss-free adiabatic transport is the dominant mechanism between
8 and 12RS. This is supported by LEMMS measurements between
10 and 12RS. However, inside of
7RS interactions with the neutrals are required to reproduce the measured intensities. This suggests that the neutral cloud is a dominant loss mechanism for these electrons at distances less than
7RS.

6. Summary and discussion Based on eight years of Cassini data we show that a distinct PAD boundary exists in the 7–13RS region in Saturn’s magnetosphere. This boundary marks the spatial region where the angular distribution of

26

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

L=12.4 L=11.8 L=11.1 L=10 L=5.3

Loss-free ( ~90o) Loss-free ( ~45o)

Interaction w/ neutrals ( ~45o) Interaction w/ neutrals ( ~90o)

Fig. 7. PAD evolution and L-shell profiles for four different electron energies: 26.83 keV, 36 keV,129.75 keV, and 381.77 keV. In the top panel the green, blue, red, purple, and black curves represent the L-shells of 12.4, 11.8, 11, 10, and 5.3, respectively. Overlaid with circle symbols are the LEMMS data. The open circles represent LEMMS data that was derived from pitch angle symmetry. In the bottom panel the blue, red, and black dash curves represent modeling results for equatorial pitch angles, mid-latitude pitch angles, and loss-free equatorial pitch angles, respectively. Error bars were calculated using Poisson statistics, and are often smaller than the symbol size. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

energetic electrons undergoes a transition from a mixture of fieldaligned and isotropic PADs to butterfly PADs then farther inward to mostly pancake. Similar magnetospheric regions have also been observed at Earth (West et al., 1973) and Jupiter (Tomás et al., 2004a, 2004b). Therefore, similar mechanisms may be present in these magnetospheric systems and responsible for the observed dynamics. We have developed a new technique to fit the butterfly PAD and have statistically quantified its spatial profile. In addition, we also used a standard fitting function (Eq. (2)) to analyze PADs observed by the LEMMS low energy C-channels. Our results of the field-aligned and pancake PADs are in agreement with the Carbary et al. (2011) study. However, we provide new observations that show the butterfly PAD is a significant and persistent feature that occurs within in the transition region (
7–13RS) and brings with it implications on the loss mechanisms in Saturn’s middle to inner magnetosphere. Furthermore, we also provide new statistical information on the isotropic PAD between 5 and 25RS. Results showed the isotropic PAD exhibits a relatively flat trend over the radial distances considered in this study. It was briefly mentioned

that not all PAD types were characterized by our analysis technique. Future work may look into further development of the Fourier series fitting model to characterize all the PAD types. Pitch angle symmetry and pitch angle mapping of high-latitude orbits may increase statistics for the under-sampled areas (i.e. 00–06 h MLT). Case study analyses of the PAD morphology through this transition region revealed interesting signatures. The observations consistently showed energy dependent features. These features displayed that higher energy electrons (4100 s of keV) maintain their fieldaligned or butterfly shape to distances that are much closer to Saturn. In contrast, lower energy electrons (o100 keV) isotropize quickly moving inward, perhaps due to stochastic processes like injections/ wave–particle interactions near 10RS. In addition, the morphology of PAD types in the transition region also corresponded with sharp increases in the density of the neutral gas torus. Electrons passing through a neutral gas medium scatter and lose energy with the effects typically being stronger at lower energies. Previous studies (e.g. Tomás et al., 2004a, 2004b; Carbary et al., 2011) only speculated on the types of processes creating the observed PAD transition regions in Jupiter and Saturn’s magnetosphere.

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

Here, for the first time, we used a diffusion theory model that includes adiabatic transport with pitch angle scattering and energy loss due to Coulomb interactions in Saturn’s neutral cloud. Modeling results, supported by LEMMS data, show that adiabatic transport is the dominant mechanism of energetic electrons between
8 to 12RS, and perhaps beyond to larger radial distances. Furthermore, by including Coulomb interactions and using an energy dependent radial diffusion term the model was able to reproduce flux measurements of electrons with pitch angles between
451 to
1351 reasonably well. However, the model underestimated the fluxes of nearly 01 and 1801 pitch angle electrons. Further work is ongoing to explore the model-data differences, but we speculate that it may be due to a polar source of electrons that have been observed previously (e.g. Saur et al., 2006; Mitchell et al., 2009). Furthermore, local processes such as wave–particle interactions (e.g. Menietti et al., 2012; Tang and Summers, 2012) may be pitch angle scattering electrons to fieldaligned pitch angles. We note that similar processes were also discussed by Tomás et al. (2004a) and here we provide stronger footing for these ideas with our data-model comparison. We conclude that our observations and modeling suggest it is possible to “break up” Saturn’s magnetosphere into distinct regions that are governed by dominant transport and loss processes. This is the first attempt to reproduce the keV-electron distributions and while it does open many additional questions, this study provides the foundation of energetic electron observations throughout Saturn’s magnetosphere and provides an energy and spatial range where adiabatic transport breaks down and interactions with the neutral cloud become important. Here, we present a summary of open questions that are left for future work:

 Is a polar source of electrons responsible for the large differences between our modeling and observational results?

 What is the role of wave–particle activity throughout this region?

 How do dust interactions affect the electron distributions?  How do particle injections affect the energy and spatial distributions of electrons inside
10RS? Do they govern or only reinforce the isotropization of PADs?

Acknowledgements We would like to thank the Cassini MIMI team members for making this work possible. Also, a special thanks to Frederic Allegrini, Chelsea Clark, Anna DeJong, Rob Ebert, Peter Kollmann, Martha Kusterer, Roberto Livi, Barry Mauk, Rebecca Perryman, Abi Rymer, Scott Turner, and John Vandegriff for their help in making this paper possible. The useful comments from the reviewers are also greatly acknowledged. This work was carried out by the MIMI team part of the Cassini mission. References Arridge, C.S., Khurana, K.K., Russell, C.T., Southwood, D.J., Achilleos, N., Dougherty, M.K., Coates, A.J., Leinweber, H.K., 2008a. Warping of Saturn’s magnetospheric and magnetotail current sheets. J. Geophys. Res. 113, A08217. http://dx.doi.org/ 10.1029/2007JA012963. Arridge, C.S., André, N., Achilleos, N., Khurana, K.K., Bertucci, C.L., Gilbert, L.K., Lewis, G.R., Coates, A.J., Dougherty, M.K., 2008b. Thermal electron periodicities at 20RS in Saturn’s magnetosphere. Geophys. Res. Lett. 35, L15107. http://dx.doi.org/ 10.1029/2008GL034132. Arridge, C.S., André, N., Khurana, K.K., Russel, C.T., Cowley, S.W. H., Provan, G., Andrews, D.J., Jackman, C.M., Coates, A.J., Sittler, E.C., Dougherty, M.K., Young, D. T., 2011. Periodic motion of Saturn’s nightside plasma sheet. J. Geophys. Res. 116, A11205. http://dx.doi.org/10.1029/2011JA016827. Beutier, T., Boscher, D., 1995. A three-dimensional analysis of the electron radiation belt by the Salammbô code. J. Geophys. Res. 100, 14,853–14,861.

27

Beutier, T., Boscher, D., France, M., 1995. Salammbô: a three-dimensional simulation of the proton radiation belt. J. Geophys. Res. 100, 17,181–17,188. Bevington, P.R., Robinson, D.K., 2003. Data Reduction and Error Analysis, third ed. McGraw-Hill, New York p. 320. Brice, N., McDonough, T.R., 1973. Jupiter’s radiation belts. Icarus 18, 206–219. http: //dx.doi.org/10.1016/0019-1035(73)90204-2. Bunce, E.J., et al., 2008. Origin of Saturn’s aurora: simultaneous observations by Cassini and the Hubble Space Telescope. J. Geophys. Res. 113, A09209. http://dx. doi.org/10.1029/2008JA013257. Burch, J.L., Goldstein, J., Hill, T.W., Young, D.T., Crary, F.J., Coates, A.J., André, N., Kurth, W.S., Sittler Jr., E.C., 2005. Properties of local plasma injections in Saturn’s magnetosphere. Geophys. Res. Lett. 32, L14S02. http://dx.doi.org/ 10.1029/2005GL022611. Cao, H., Russel, C.T., Christensen, U.R., Dougherty, M.K., Burton, M.E., 2011. Saturn’s very axisymmetric magnetic field: no detectable secular variation or tilt. Earth Planet. Sci. Lett. 304 (1-2), 22–28. http://dx.doi.org/10.1016/j.epsl.2011.02.035. Carbary, J.F., Mitchell, D.G., Krupp, N., Krimigis, S.M., 2009. L shell distribution of energetic electrons at Saturn. J. Geophys. Res. 114, A09210. http://dx.doi.org/ 10.1029/2009JA014341. Carbary, J.F., Achilleos, N., Arridge, C.S., Khurana, K.K., Dougherty, M.K., 2010. Global configuration of Saturn’s magnetic field derived from observations. Geophys. Res. Lett. 37, L21806. http://dx.doi.org/10.1029/2010GL044622. Carbary, J.F., Mitchell, D.G., Paranicas, C., Roelof, E.C., Krimigis, S.M., Krupp, N., Khurana, K., Dougherty, M., 2011. Pitch angle distributions of energetic electrons at Saturn. J. Geophys. Res. 116, A01216. http://dx.doi.org/10.1029/ 2010JA015987. Carbary, J.F., Rymer, A.M., 2014. Meridional maps of Saturn’s thermal electrons,. J. Geophys. Res. Space Phys. 119, 1721–1733. http://dx.doi.org/10.1002/ 2013JA019436. Cassidy, T.A., Johnson, R.E., 2010. Collisional spreading of Enceladus’s neutral cloud. Icarus, 209. http://dx.doi.org/10.1016/j.icarus.2010.04.010. Chen, Y., Hill, T.W., 2008. Statistical analysis of injection/dispersion events in Saturn’s inner magnetosphere. J. Geophys. Res. 113, A07215. http://dx.doi.org/ 10.1029/2008JA013166. Delamere, P.A., Bagenal, F., Dols, V., Ray, L.C., 2007. Saturn’s neutral torus versus Jupiter’s plasma torus. Geophys. Res. Lett. 34, L09105. http://dx.doi.org/10.1029/ 2007GL029437. Dougherty, M.K., Kellock, S., Southwood, D.J., Balogh, A., Smith, E.J., Tsurutani, B.T., Gerlach, B., Glassmeier, K. –H., Gleim, F., Russel, C.T., Erdos, G., Neubauer, F.M., Cowley, S.W. H., 2002. The Cassini magnetic field investigation. Space Sci. Rev., 114. http://dx.doi.org/10.1007/978-1-4020-2774-1_4. Fleshman, B.L., Delamere, P.A., Bagenal, F., 2010. A sensitivity study of the Enceladus torus. J. Geophys. Res. 115, E04007. http://dx.doi.org/10.1029/2009JE003372. Gannon, J.L., Li, X., Heynderickx, D., 2007. Pitch angle distribution analysis of radiation belt electrons based on combined release and radiation effects satellite medium electrons a data. J. Geophys. Res. 112, A05212. http://dx.doi. org/10.1029/2005JA011565. Hansen, C.J., Esposito, L., Stewart, A.I. F., Colwell, J., Hendrix, A., Pryor, W., Shemanksy, D., West, R., 2006. Science, 311. http://dx.doi.org/10.1126/ science.1121254. Hood, L.L., 1983. Radial diffusion in Saturn’s radiation belts: a modeling analysis assuming satellite and ring E absorption. J. Geophys. Res. 88, 808–818. http: //dx.doi.org/10.1029/JA088iA02p00808. Horne, R.B., Thorne, R.M., Glauer, S.A., Menietti, J. D, Shprits, Y.Y., Gurnett, D.A., 2008. Gyro-resonant electron acceleration at Jupiter. Nat. Phys. 4, 301–304. http://dx.doi.org/10.1038/nphys897. Johnson, R.E., Smith, H.T., Tucker, O.J., Liu, M., Burger, M.H., Sittler, E.C., Tokar, R.L., 2006. The Enceladus and OH Tori at Saturn. ApJ 644, L137. http://dx.doi.org/ 10.1086/505750. Jurac, S., Richardson, J.D., 2005. A self-consistent model of plasma and neutrals at Saturn: neutral cloud morphology. J. Geophys. Res. 110, A09220. http://dx.doi. org/10.1029/2004JA010635. Kollmann, P., Roussos, E., Paranicas, C., Krupp, N., Jackman, C.M., Kirsch, E., Glassmeier, K.H., 2011. Energetic particle phase space densities at Saturn: Cassini observations and interpretations. J. Geophys. Res. 116, A05222. http: //dx.doi.org/10.1029/2010JA016221. Krimigis, S.M., Carbary, J.F., Keath, E.P., Armstrong, T.P., Lanzerotti, L.J., Gloeckler, G., 1983. General characteristics of hot plasma and energetic particles in the Saturnian magnetosphere: results from the Voyager spacecraft. J. Geophys. Res. 88, 8871–8892. Krimigis, S.M., Mitchell, D.G., Hamilton, D.C., Livi, S., Dandouras, J., Jaskulek, S., Armstrong, T.P., Boldt, J.D., Cheng, A.F., Gloeckler, G., Hayes, J.R., Hsieh, K.C., IP, W.-H., Keath, E.P., Kirsch, E., Krupp, N., Lanzerotti, L.J., Lundgren, R., Mauk, B.H., McEntire, R.W., Roelof, E.C., Schlemm, C.E., Tossman, B.E., Wilken, B., Williams, D.J., 2004. Magnetosphere imaging instrument (MIMI) on the Cassini mission to Saturn/Titan. Space Sci. Rev. 114, 233–329. http://dx.doi.org/10.1007/978-14020-2774-1_3. Krupp, N., Roussos, E., Lagg, A., Woch, J., Müller, A.L., Krimigis, S.M., Mitchell, D.G., Roelof, E.C., Paranicas, C., Carbary, J., Jones, G.H., Hamilton, D.C., Livi, S., Armstrong, T.P., Dougherty, M.K., Sergis, N., 2009. Energetic particles in Saturn’s magnetosphere during the Cassini nominal mission. Planet. Space Sci. 57, 1754–1768. http://dx.doi.org/10.1016/j.pss.2009.06.010. Krupp, N., Roussos, E., Kollmann, P., Paranicas, C., Mitchell, D.G., Krimigis, S.M., Rymer, A., Jones, G.H., Arridge, C.S., Armstrong, T.P., Khurana, K.K., 2012. The Cassini Enceladus encounters 2005–2010 in the view of energetic electron measurements. Icarus 218, 433–447. http://dx.doi.org/10.1016/j.icarus.2011.12.018.

28

G. Clark et al. / Planetary and Space Science 104 (2014) 18–28

Lorenzato, L., Sicard, A., Bourdarie, S., 2012. A physical model for electron radiation belts of Saturn. J. Geophys. Res. 117, A08214. http://dx.doi.org/10.1029/ 2012JA017560. Markwardt, C. B. (2009), Non-linear least squares fitting in IDL with MPFIT. In: D. Bohlender, P. Dowler & D. Durand (Eds.), Proc. Astronomical Data Analysis Software and Systems XVIII, Quebec, Canada, ASP Conference Series, vol. 411, (Astronomical Society of the Pacific: San Francisco), pp. 251–254. Mauk, B.H., Fox, N.J., 2010. Electron radiation belts of the solar system. J. Geophys. Res. 115, A12220. http://dx.doi.org/10.1029/2010JA015660. McDonald, F.B., Schardt, A.W., Trainor, J.H., 1980. If you’ve seen one magnetosphere, you haven’t seen them all: energetic particle observations in the Saturn magnetosphere. J. Geophys. Res., 85. http://dx.doi.org/10.1029/JA085iA11p05813. Menietti, J.D., Shprits, Y.Y., Horne, R.B., Woodfield, E.E., Hospodarsky, G.B., Gurnett, D.A., 2012. Chorus, ECH, and Z mode emissions observed at Jupiter and Saturn and possible electron acceleration. J. Geophys. Res., 117. http://dx.doi.org/ 10.1029/2012JA018187. Mitchell, D.G., Kurth, W.S., Hospodarsky, G.B., Krupp, N., Saur, J., Mauk, B.H., Carbary, J.F., Krimigis, S.M., Dougherty, M.K., Hamilton, D.C., 2009. Ion conics and electron beams associated with auroral processes on Saturn. J. Geophys. Res. 114, A02212. http://dx.doi.org/10.1029/2008JA013621. Paranicas, C., Mitchell, D.G., Roelof, E.C., Mauk, B.H., Krimigis, S.M., Brandt, P.C., Kusterer, M., Turner, F.S., Vandegriff, J., Krupp, N., 2007. Energetic electrons injected into Saturn’s neutral gas cloud. Geophys. Res. Lett. 34, L02109. http: //dx.doi.org/10.1029/2006GL028676. Paranicas, C., Mitchell, D.G., Roussos, E., Kollmann, P., Krupp, N., Müller, A.L., Krimigis, S.M., Turner, F.S., Brandt, P.C., Rymer, A.M., Johnson, R.E., 2010. Transport of energetic electrons into Saturn’s inner magnetosphere. J. Geophys. Res. 115, A09214. http://dx.doi.org/10.1029/2010JA015853. Pontius, D.H., Hill, T.W., 2006. Enceladus: a significant plasma source for Saturn’s magnetosphere. J. Geophys. Res., 111. http://dx.doi.org/10.1029/2006JA011674. Provan, G., Andrews, D.J., Arridge, C.S., Coates, A.J., Cowley, S.W. H., Cox, G., Dougherty, M.K., Jackman, C.M., 2012. Dual periodicities in planetary-period magnetic field oscillations in Saturn’s tail. J. Geophys. Res. 117, A01209 (doi:10.1029.2011JA017104). Roussos, E., Jones, G.H., Krupp, N., Paranicas, C., Mitchell, D.G., Lagg, A., Woch, J., Motschmann, U., Krimigis, S.M., Dougherty, M.K., 2007. Electron microdiffusion in the Saturnian radiation belts: Cassini MIMI/LEMMS observations of energetic electron absorption by the icy moons. J. Geophys. Res. 112, A06214. http://dx. doi.org/10.1029/2006JA012027. Rymer, A.M., Mauk, B.H., Hill, T.W., Paranicas, C., André, N., Sittler Jr., E.C., Mitchell, D.G., Smith, H.T., Johnson, R.E., Coates, A.J., Young, D.T., Bolton, S.J., Thomsen, M. F., Dougherty, M.K., 2007. Electron sources in Saturn’s magnetosphere. J. Geophys. Res. 112, A02201. http://dx.doi.org/10.1029/2006JA012017. Rymer, A.M., Mauk, B.H., Hill, T.W., Paranicas, C., Mitchell, D.G., Coates, A.J., Young, D.T., 2008. Electron circulation in Saturn’s magnetosphere. J. Geophys. Res. 113, A01201. http://dx.doi.org/10.1029/2007JA012589. Rymer, A.M., Mauk, B.H., Hill, T.W., André, N., Mitchell, D.G., Paranicas, C., Young, D. T., Smith, H.T., Persoon, A. M, Menietti, J. D, Hospodarsky, G.B., Coates, A.J., Dougherty, M.K., 2009. Cassini evidence for rapid interchange transport at Saturn. Planet. Space Sci. 57, 1779–1784. http://dx.doi.org/10.1016/j. pss.2009.04.010. Santos-Costa, D., Bourdarie, S.A., 2001. Modeling the inner Jovian electron radiation belt including non-equatorial particles. Planet. Space Sci. 49, 303–312. http: //dx.doi.org/10.1016/S0032-0633(00)00151-3. Santos-Costa, D., Blanc, M., Maurice, S., Bolton, S.J., 2003. Modeling the electron and proton radiation belts of Saturn. Geophys. Res. Lett., 30. http://dx.doi.org/ 10.1029/2003GL017972.

Santos-Costa, D., Bolton, S.J., 2008. Discussing the processes constraining the Jovian synchrotron radio emission’s features. Planet. Space Sci. 56, 326–345. http://dx. doi.org/10.1016/j.pss.2007.09.008. Saur, J., Mauk, B.H., Mitchell, D.G., Krupp, N., Khurana, K.K., Livi, S., Krimigis, S.M., Newell, P.T., Williams, D.J., Brandt, P.C., Lagg, A., Roussos, E., Dougherty, M.K., 2006. Anti-planetward auroral electron beams at Saturn. Nature 439, 699–702. http://dx.doi.org/10.1038/nature04401. Schippers, P., Blanc, M., André, N., Dandouras, I., Lewis, G.R., Gilbert, L.K., Persoon, A.M., Krupp, N., Gurnett, D.A., Coates, A.J., Krimigis, S.M., Young, D.T., Dougherty, M.K., 2008. Multi-instrument analysis of electron populations in Saturn’s magnetosphere. J. Geophys. Res. 113, A07208. http://dx.doi.org/10.1029/2008JA013098. Schippers, P., et al., 2011. Auroral electron distributions within and close to the Saturn kilometric radiation source region. J. Geophys. Res. 116, A05203. http: //dx.doi.org/10.1029/2011JA016461. Schippers, P., André, N., Gurnett, D.A., Lewis, G.R., Persoon, A.M., Coates, A.J., 2012. Identification of the electron field-aligned current systems in Saturn’s magnetosphere. J. Geophys. Res. 117, A05204. http://dx.doi.org/10.1029/2011JA017352. Schulz, M., Lanzerotti, L., 1974. Particle Diffusion in the Radiation Belts. Springer, New York. Siscoe, G.L., Summers, D., 1981. Centrifugally driven diffusion of iogenic plasma. J. Geophys. Res. 86, 8471–8479. http://dx.doi.org/10.1029/JA086iA10p08471. Sittler, E.C., Johnson, R.E., Smith, H.T., Richardson, J.D., Jurac, S., Moore, M., Cooper, J. F., Mauk, B.H., Michael, M., Paranicas, C., Armstrong, T.P., Tsurutani, B., 2006. Energetic nitrogen ions within the inner magnetosphere of Saturn. J. Geophys. Res. 111, A09223. http://dx.doi.org/10.1029/2004JA010505. Tang, R., Summers, D., 2012. Energetic electron fluxes at Saturn from Cassini observations. J. Geophys. Res. 117, A06221. http://dx.doi.org/10.1029/ 2011JA017394. Tomás, A., Woch, J., Krupp, N., Lagg, A., Glassmeier, K.-H., Dougherty, M.K., Hanlon, P.G., 2004a. Changes of the energetic particle characteristics in the inner part of the Jovian magnetosphere: a topological study. Planet. Space Sci. 52, 491–498. http://dx.doi.org/10.1016/j.pss.2003.06.011. Tomás, A.T., Woch, J., Krupp, N., Lagg, A., Glassmeier, K.-H., Kurth, W.S., 2004b. Energetic electrons in the inner part of the Jovian magnetosphere and their relation to auroral emissions. J. Geophys. Res. 109, A06203. http://dx.doi.org/ 10.1029/2004JA010405. Tseng, W.-L., Johnson, R.E., Thomsen, M.F., Cassidy, T.A., Elrod, M.K., 2011. Neutral H2 and H2þ ions in the Saturnian magnetosphere. J. Geophys. Res. 116, A03209. http://dx.doi.org/10.1029/2010JA016145. Tseng, W.-L., Johnson, R.E., Ip, W.-H., 2013. The atomic hydrogen cloud in the Saturnian system. Planet. Space Sci. 85, 164–174. http://dx.doi.org/10.1016/j. pss.2013.06.005. Waite, J.H., Combi, M.R., Ip, W.-H., Cravens, T.E., McNutt, R.L., Kasprzak, W., Yelle, R., Luhmann, J., Niemann, H., Gell, D., Magee, B., Fletcher, G., Lunine, J., Tseng, W.-L., 2006. Cassini ion and neutral mass spectrometer: Enceladus plume composition and structure. Science 311, 1419–1422. http://dx.doi.org/10.1126/science.1121290. West Jr., H.I., Buck, R.M., Walton, J.R., 1973. Electron pitch angle distributions throughout the magnetosphere as observed on OGO 5. J. Geophys. Res. 78, 1064–1081. http://dx.doi.org/10.1029/JA078i007p01064. Woodfield, E.E., Horne, R.B., Glauert, S.A., Meniett, J.D., Shprits, Y.Y., 2013. Electron acceleration at Jupiter: input from cyclotron-resonant interaction with whistler-mode chorus waves. Ann. Geophys. 31, 1619–1630. http://dx.doi.org/ 10.5194/angeo-31-1619-2013. Young, D.T., et al., 2004. Cassini plasma spectrometer investigation. Space Sci. Rev. 114, 1–112. http://dx.doi.org/10.1007/s11214-004-1406-4. Zombeck, M.V., 1982. Handbook of Space Astronomy and Astrophysics, second ed. Cambridge Univ., Cambridge, U. K.