Energetic particle phase space densities at Saturn: Cassini observations and interpretations

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116,, doi: /2010ja016221, 2011 Energetic particle phase space densities at Saturn: Cassini observations and interpretations P. Kollmann, 1,4 E. Roussos, 1 C. Paranicas, 2 N. Krupp, 1 C. M. Jackman, 3 E. Kirsch, 1 and K. H. Glassmeier 1,4 Received 18 October 2010; revised 18 January 2011; accepted 16 February 2011; published 27 May [1] Saturn s magnetosphere has been studied extensively by the Cassini spacecraft during the last 6 years. We present mission averaged energetic proton and electron measurements obtained by the MIMI/LEMMS instrument onboard Cassini in an energy range from several 10 kev to several 10 MeV separated by equatorial pitch angle. We discuss the resulting radial profiles and energy spectra. The measured intensities are converted to phase space densities. The distribution of energetic particles is governed by a large variety of processes. For instance, moons absorb energetic particles, creating macrosignatures or microsignatures. We have found that the moon Rhea is partly responsible for a change in gradient of electron phase space densities. We show that, in contrast to larger distances, the particle distribution for L < 8 is not driven by radial diffusion alone. There, the particle profiles are significantly modified due to Saturn s Neutral Torus, plasma environment, E ring, injection events, and cosmic ray albedo neutron decay. Large parts of our analysis are focused near L = 7. There, protons are lost within the Neutral Torus and not the E ring. For electrons, we find that these two losses are of comparable rate but have discovered that neither process is the dominant driver of loss. We point out that intensity measured by a energy channel, such as in a particle instrument, can actually increase in the region of ring and torus instead of decrease. The importance of injection events is shown to be at least of similar importance as radial diffusion. Citation: Kollmann, P., E. Roussos, C. Paranicas, N. Krupp, C. M. Jackman, E. Kirsch, and K. H. Glassmeier (2011), Energetic particle phase space densities at Saturn: Cassini observations and interpretations, J. Geophys. Res., 116,, doi: /2010ja Max Planck Institute for Solar System Research, Katlenburg Lindau, Germany. 2 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 3 Department of Physics and Astronomy, University College London, London, UK. 4 Institut für Geophysik und Extraterrestrische Physik, Technische Universität Braunschweig, Braunschweig, Germany. Copyright 2011 by the American Geophysical Union /11/2010JA Introduction [2] Saturn and its magnetosphere have been visited up to now by four spacecraft with charged particle instruments: Pioneer 11 [Simpson et al., 1980], Voyager 1 [Krimigis et al., 1981], Voyager 2 [Krimigis et al., 1982] and Cassini [Krimigis et al., 2005]. [3] The first three missions established the pre Cassini understanding of Saturn by providing a wealth of in situ and remote data [Van Allen, 1984]. Since these were flyby type missions, their instruments were providing snapshots of the current configurations. The results were limited to the small spatial coverage of the trajectory, current solar wind conditions and local seasons. Consequently, it has been challenging to distinguish between spatial asymmetries and temporal variability. [4] As an orbiting spacecraft, Cassini completed more than 130 orbits around Saturn between 2004 and 2010 and sampled a wide range of radial distances, latitudes and longitudes. In addition to the observation of single events, it allowed for the very first time to conduct an in situ study of the global configuration in space and dynamics in time. [5] One essential aspect of any magnetosphere is the energetic charged particle population. They have been measured by the instrumentation onboard every mission to this planet in order to understand their physical processes. Energetic particle intensities as a function of energy, pitch angle, position and time provide a powerful tool for understanding the origin and evolution of the particles. For example, spectra of high energy protons show a signature of the cosmic ray albedo neutron decay process (CRAND) [Blake et al., 1983] that acts as a source for protons well above energies of several MeV [Armstrong et al., 2009; Roussos et al., 2011]. Further, the evolution of pitch angle distributions with distance to the planet can indicate how particles are radially transported and which mechanisms govern their transport [Rymer et al., 2008]. Intensities along the spacecraft trajectory can show time dispersed profiles of 1of24

2 injection events [Mauk et al., 2005] that can be modeled in order to understand their evolution [Müller et al., 2010]. Radial profiles of the phase space density have been used to constrain the radial diffusion coefficient of energetic particles [Hood, 1983; Armstrong et al., 1983]. [6] This paper is based on a large data set with almost 6 years of data (section 2). We will present energy spectra and radial profiles of energetic particle intensities (section 3) and phase space densities (section 4.1) as an average over the Cassini era, within a wide energy range and separated for equatorial pitch angles. To provide a direct comparison, this is done for protons as well as electrons. We will discuss the role of radial diffusion and show that there are additional source and loss processes (section 4.2). [7] Beside providing information about the phenomenology and underlying physics of energetic particles, their study also reveals information beyond that. Energetic particles can act as a probe of rings, moons, and neutral gas around Saturn due to interaction and subsequent loss. This has allowed Hedman et al. [2007] to support the discovery of an arc within the G ring and Roussos et al. [2008a] to suggest the existence of another arc near Methone. Another loss of energetic protons is due to charge exchange with neutral gas and goes along with the generation of energetic neutral atoms (ENAs). They can be detected and used to derive properties of Saturn s Neutral Torus [Dialynas, 2010, K. Dialynas, manuscript in preparation, 2011]. [8] In this paper, we also consider the interaction of charged particles with matter. The relative importance of the interaction of energetic particles with ice grains of the E ring and neutral gas of the Neutral Torus has been an open question. Using a thorough mathematical description of this interaction (Appendix A), we conclude that neutral gas is dominant for protons (section 5). For electrons, energy loss to neutral gas and ice grains are equally important (section 5) but are dominated by another process, e.g., pitch angle scattering into the loss cone (section 6.1). At the end of the paper, we deal with the importance of injection events. We will give an estimate on how much particles they transport to a given distance and compare this to other processes (section 6.2). 2. Data Set [9] The basis of this study are long term averages of measurements of energetic protons and electrons in Saturn s magnetosphere during the Cassini era. We use measurements taken by the Low Energy Magnetospheric Measurement System (LEMMS), which is part of the Magnetospheric Imaging System instrument package (MIMI). LEMMS covers the energy range between several 10 kev and several 10 MeV. For protons below 810 kev and electrons below 2.2 MeV, it features a pulse height analyzer (PHA). We use these channels up to 760 kev in case of protons and 1.6 MeV in case of electrons. Depending on energy, they have an energy resolution between 2 kev and 90 kev. Additionally, LEMMS possesses rate channels with lowerenergy resolution but larger energy range and less background signal due to the use of coincidence logic. We use only rate channels with energies above the PHA range. A detailed description of LEMMS can be found by Krimigis et al. [2004], the current rate channel calibration is given by Krupp et al. [2009]. [10] The measured intensities presented here are background subtracted values. The background is retrieved while Cassini was in regions with L 20 (where all channels have a high probability of sampling regions where there is very low foreground) and where LEMMS measures intensities that are constant exclusive of random fluctuations (which is a signature of background). (L is the dimensionless dipole L shell normalized to one planetary radius, defined as 1 R S = km.) [11] Data were taken between July 2004 (Cassini s arrival at Saturn) and June During this time, Cassini had 127 orbits around the planet where it reached minimal distances of L = 1.3 and latitudes up to l 60. The orbital coverage up to July 2008 is described by Krupp et al. [2009]. Within this paper, we limit our considerations to L 20. This corresponds to the nominal dayside magnetopause distance and a region outside of which intensities can be close to background levels. [12] Until early 2005, LEMMS was rotating to sample data from different directions and parts of the pitch angle distribution. For this period, the full time resolution of the data is used within this paper. Currently, LEMMS is not rotating, measuring only two directions with its two detector heads. This increases the time resolution at the respective pitch angles. Since this resolution is not needed for the current studies, the data are averaged over 86 s (duration of one nominal LEMMS rotation). [13] The value of the local pitch angle a loc between the local magnetic field and the detected particles is inferred from the magnetic field measured by the magnetometer instrument (MAG), which is described in detail by Dougherty et al. [2004]. From this and the spatial position of the spacecraft, the equatorial pitch angle a 0 is calculated assuming conservation of the first adiabatic invariant and a model magnetic field. In this work, we use a simple dipole model with a northward offset of R S between the center of the planet and the center of the magnetic field [Dougherty et al., 2005]. Latitudes l and L shells will be given with respect to this and are derived purely from the position of the spacecraft. [14] We excluded three time periods from our data set. In February 2005 and August 2005 an additional radiation belt appeared between the moons Tethys and Dione due to enhanced solar activity [Roussos et al., 2008b]. These events are easy to recognize in data from channels measuring >1 MeV protons at 5 L 6. While the measurements taken there are usually at background levels, the aforementioned events caused a clear foreground signal. The third excluded period was during April At the time where we compiled our data set, there were no precise ephemeris data for this period. [15] If one of the detector heads of LEMMS points toward the sun, it is not operating properly. These usually short time intervals are also excluded. 3. Particle Profiles 3.1. Intensities [16] Throughout our paper, the energetic particle intensities shown in illustrations and conclusions drawn from them 2of24

3 Figure 1. Differential intensities j of (left) protons and (right) electrons. Protons have mean energies of 46 kev, and electrons have mean energies of 91 kev; both species have equatorial pitch angles of a 0 = 10 ± 10. The red points represent single measurements taken between July 2004 and June 2010 (with exceptions, see section 2). The black solid line is the logarithmic average of these points within intervals of 0.5 R S width. Error bars show the associated 1s standard deviations. The increase of intensities for L < 5 is caused by penetrating background and does not represent particles at the mentioned energies. are usually based on measurements averaged within intervals of L. Apart from section 3.2, we also average over all local times because this provides unprecedentedly good statistics. (Local time refers to the azimuthal position with h being closest to the Sun.) [17] Figure 1 demonstrates how the binned values are related to single measurements. It shows one channel of protons and electrons and includes all intensity values within the data set as single points. The values are plotted over L shell without distinguishing between different local times. Overplotted are values derived from logarithmic averaging. We use this type of averaging because the data are also presented on a logarithmic scale and because, in contrast to linear averaging, this is not dominated by the highest values. Additionally, we plot error bars showing the 1s logarithmic standard deviation as a measure of variability. We do not use the median because there is no measure of its error. [18] The large scattering of the single measurements reveals that Saturn s magnetosphere is a highly dynamic system where intensities at the same position but different times can differ significantly. Outside L 10, the 1s intensity error bars can extend over up to 2 orders of magnitude. The 2s error bars can even range over 3 and 4 orders in case of protons and electrons, respectively. The error bars decrease for smaller L and larger energies. The radiation belts are usually very stable. High energy protons at L < 4 vary approximately by a factor of 2. [19] Computing L shells in a dipole model can be a source of imprecision in the averaged intensities. Nevertheless, we do not consider this as a major effect. A dipole field line intersects at every latitude another real field line. When using the Khurana model [Khurana et al., 2006; Carbary et al., 2010] at L = 10, these intersections map to equatorial distances between 10 and 14 R S, depending on latitude. When averaging the intensities of the different latitudes to derive the intensity at the dipole L (as presented here), this creates an error. This error decreases if the data is filtered to a decreasing latitudinal range. In our data set, such a filtering does not cause a significant nor systematic change in the standard deviation. Apparently, the intensity between different field lines is changing slow enough in the region where the dipole model is imprecise, that the error due to the field model is smaller than the time dependent scattering. [20] Calculating a 0 by the use of the dipole also causes imprecisions. We compared the pitch angles calculated from our model with some calculated by the Khurana model. Particles with a local pitch angle in a way that the equatorial pitch angle is a 0 = 10 when the dipole model is used, typically have with the Khurana model equatorial pitch angles between 6 and 11. This is smaller than the a 0 bin size used here. 3of24

4 Figure 2. Differential intensities j of (left) protons and (right) electrons. The intensities are long term averages that are derived as described in Figure 1. Error bars show the standard deviation of the averages. A variety of representative LEMMS channels is shown in different colors; their names and mean energies are explained in the insets of the panels. All curves are for equatorial pitch angles of a 0 = 10 ± 10. If the profiles are shown as thinner lines with modified color, this marks regions where the average intensity is dominated by instrumental background. We cut the profiles for regions that we consider as dominated by radiation belt background. This is the reason why some profiles do not extend below L < 5. Dashed lines mark the outer edge of the main rings and the major axis of the orbits of several moons, which cause the sharp drop offs at small distances. From small to large distances: MR, Main Rings; Ja, Janus; Mi, Mimas; En, Enceladus; Te, Tethys; Di, Dione; Rh, Rhea. [21] In Figure 2, we show solely averaged intensities, but for several channels, representing most of the energy range of LEMMS. If the plotted lines of the average values are thin and the error bars are dashed, this approximately marks regions in L shell and energy where the measurement is background dominated. We use this style for all images shown. [22] Background can be caused by penetrating radiation triggering false counts of the detector. For distances close to the planet (L < 5), the low energy channels measure more penetrating MeV electrons from the radiation belts than particles with energies they were supposed to measure. We will refer to this as radiation belt background. It cannot easily be compensated for this. The precise onset of the radiation belt background dominated area for the different channels is a matter of ongoing investigation. [23] At increasing distance from the planet, LEMMS starts to measure constant average intensities. This is very unlikely since also these distances are expected to be dynamic and differentiated. Therefore, the constant measurement cannot be caused by foreground. Instead, it can be attributed for example to instrumental electronic noise, radiation of the spacecraft s RTG power supply and transient cosmic radiation. We will refer to this as instrumental background. The onset of this feature within the data moves to lower L shells with increasing energy (see left end of thin lines in Figure 2). The background subtraction we apply to our data reduces the instrumental but not the radiation belt background. [24] The intensity profiles shown in Figure 2 can be separated into three regions in L shell: radiation belts, loss region and diffusion region. The radiation belts exhibit large intensities of energetic particles with energies above 1 MeV. For protons they usually extend until L < 5 and seem to be composed of CRAND products at least above 1 MeV [Roussos et al., 2011]. Electrons also have high fluxes in this area but the boundary of the belts is not as sharp as for the protons. The high energy electrons close to the planet mainly originate from adiabatically heated electrons from larger L shells [Paranicas et al., 2010b]. 4of24

5 Figure 3. Spectra of long term averaged differential intensities j of (left) protons and (right) electrons with equatorial pitch angle a 0 = 90 ± 10 for different values of L ± 0.5. Points are given at the mean energies of the respective channels which are defined as the logarithmic average of the energy range. We use several types of channels for this plot that differ in energy range and resolution. Despite ongoing intercalibration, they can show different intensities at similar energies. This can be caused by different background sensibility and energy ranges. In order not to confuse the resulting jumps with real features of the spectra, we mark every transition from one channel type to the next with squares of the same color. The standard deviation of the shown averages is shown exemplary for one L shell. Regions in L and E that we consider as contaminated by any background are not shown. Paranicas et al. [2010c] shows a similar plot on the L shells of the icy moons. [25] Outside the belts, the magnetosphere is populated mainly by particles with lower energies. These are thought to originate from ionized neutral particles at Keplerian energies, which have been accelerated by various processes like pickup, turbulence [Saur, 2004], and adiabatic heating (section 4.1). Inward of 9 R S the intensity is decreasing. As it will be discussed in section 5, this can be attributed to the interaction with matter orbiting Saturn, especially the Neutral Torus, but also the E ring. We therefore call the region within 5 L 9 the loss region. [26] The particles are radially diffusing toward the planet throughout the magnetosphere (section 4.1). This process is the only relevant process acting on the particles for large distances (section 4.2). This gives rise calling L > 9 the diffusion region. A more thorough distinction between loss and diffusion region will be part of section 4.2. [27] Another way of organizing the data is in terms of energy spectra at different L shells. This is done in Figure 3. The spectra there mostly decrease with increasing energy. Measurements of the Cassini Plasma Spectrometer (CAPS) show that maxima are expected at energies <1 kev [Young et al., 2005]. [28] For the protons, the broad peak around 10 MeV is caused by the CRAND process. The spectrum of CRAND protons is expected to extend to even higher energies [Blake et al., 1983; Cooper, 1983] and also to lower energies in the MeV range [Roussos et al., 2011]. [29] In the region of L 7, electrons have a flatter energy spectrum in the energy range from several 10 kev to several 100 kev than outside this range. This has also been observed by the low energy charged particle instrument (LECP) on board of Voyager 2 [Krimigis et al., 1983]. We propose three theories to explain that. [30] The electron intensity that causes the deviation from a power law like falloff can be due to electrons produced by the neutron decay during the CRAND process. These electrons are expected at energies less or equal to the mass defect between a neutron and its decay products which is 5of24

6 approximately 800 kev. This energy approximately fits the high energy end of the flattening. The total number of protons and electrons produced by CRAND should be equal. However, this involves a lot more analysis regarding the full electron and proton spectra and this is beyond the scope of this paper. We plan to pursue this subject further in the future. [31] An alternative hypothesis was advanced by Paranicas et al. [2010b]. They argued that electron injections, which have energies only up to hundreds kev, reach to minimum distances of about L = 5. This could lead to a flux pileup close to this L shell, as it is observed. [32] As a third possibility, the flattening could be explained due to energy filtering at the moon Rhea. As we will show in section 4.1, Rhea absorbs parts of the electrons that have a finite azimuthal velocity relative to it. This is visible in radial profiles of the electron phase space densities and should also leave a signature in the energy spectra. Since Rhea s orbit is located at L 9, this could explain why the spectrum only shows a flattening within this distance. [33] Below 100 kev and 6 R S, protons significantly decrease in intensity. This also was observed by MIMI/ INCA [Dialynas et al., 2009]. The peak at approximately 100 kev is consistent with loss processes due to interaction with the Neutral Torus and the E ring (section 5). These loss processes are energy dependent, being strongest at energies where the decrease is visible. They are also L dependent since they are proportional to the density of interacting material. The density (and therefore the expected loss) maximizes at L =4. [34] A further way of organizing the data would be as pitch angle distributions at different L shells. We do not show this here, because the change in intensity with a 0 is smaller than the standard deviation. Pitch angle distributions taken within short time intervals during one orbit can be found for example by Carbary et al. [2011] and Roussos et al. [2011] and typically show changes less than an order of magnitude Local Time Asymmetries [35] The proton radiation belts are highly symmetric in local time [Paranicas et al., 2010a]. This is different from energetic electrons at 5 < L < 10 that show higher intensities on the night side of the planet [Carbary et al., 2009; Paranicas et al., 2010b]. For this reason, our approach of averaging over all local times yields a simplified configuration of the magnetosphere. For a more detailed view, we divided the magnetosphere in two. Figures 4a and 4b distinguish between day and night side of the planet. These profiles are consistent with previous work on electrons and show additionally that protons are distributed in a similar way. Our data set also reveals that this difference of day and night side exists up to energies of several 100 kev in all pitch angles (not shown in Figure 4). Dividing the data set into dawn and dusk half, as it is shown in Figures 4c and 4d, reveals no significant difference of the averaged intensities. [36] Grodent et al. [2010] demonstrates the existence of a faint outer auroral emission at Saturn s southern polar region, which is stationary at the night side. This emission maps to a region of the equatorial plane between 4 and 11 R S. Energetic electrons in this region can provide enough power to explain the brightness of the aurora. We therefore theorize that the asymmetry of the outer aurora is a signature of the energetic electron asymmetry. [37] One possible cause of the day/night intensity difference is a nonaxisymmetric magnetic field. In case of a steady state magnetosphere, equatorially mirroring energetic particles drift along trajectories of equal magnetic field. If the particles are evenly distributed in drift phase, regions with the same magnetic field show the same intensity of particles. This means that if the magnetic field is axisymmetric, the regions of equal fields are circles and therefore the particle distribution is symmetric in local time. If the field is asymmetric, a circle around the planet (like a dipolar L shell) would have different field strengths at different local times and therefore different particle intensities. [38] Figures 4a, 4b, 4e, and 4f show particle profiles and magnetic field strengths plotted over L shell and split for day and night side. For L < 10 there is indeed a significant difference of intensities between the two halves. This is not the case for the magnetic field, where the differences for L < 10 are small and without trend. Regions (in L and local time) with the same intensity do not have the same magnetic field, which means that at least the long term averaged magnetic field has no local time asymmetries that are strong enough to cause the asymmetry in intensity. [39] We show particles with equatorial pitch angles of a 0 = 80 ± 10 in Figure 4 because we have better statistics for them as for a 0 = 90 ± 10 particles and achieve therefore a higher certainty that the asymmetry is not just resulting from fluctuations. The disadvantage of this approach is that these particles bounce and do not exactly move on trajectories of equal equatorial magnetic field. This leads to L shell splitting [Roederer, 1970]. This implies that the more field aligned the particles are and the more asymmetric the magnetic field is, the more the trajectories deviate from the explained case. We neglected this effect here. [40] Particles with a 0 = 80 ± 10 bounce up to latitudes of l 10. Figure 4f shows the magnetic field at this latitude split for day and night side. It can be seen that it has a similar high symmetry as the equatorial field. Higher latitudes suffer decreasing statistics, but differences between day and night side show no l trend for L < 10 and are supposed to be random. [41] Another possible cause for the particle asymmetry could be the loss mechanism. Neutral gas and ice grains both can deplete energetic particles. There is evidence that neutral gas around Saturn is indeed unevenly distributed in local time [Shemansky and Hall, 1992; Melin et al., 2009] and this is also expected for the E ring [Juhász and Horányi, 2004]. If the asymmetry in the density is stationary in local time and the loss occurs on timescales much faster than the drift period, this would cause an asymmetry in energetic particle intensities. For the E ring the second and for the Neutral Torus the first and second requirement are not expected to hold [Cassidy and Johnson, 2010] (section 5). Additionally one has to take into account that the interaction of protons and electrons with matter is different in mechanism and strength. It would be a large coincidence if these different processes are causing asymmetries for both species of likewise extend at similar energies. Therefore, asymmetries in losses due to E ring or Neutral Torus should not account for the asymmetry. 6of24

7 Figure 4. Differential intensities j and total magnetic field ~B for different local time bins. Protons have energies of hei = 40 kev, and electrons have energies of hei = 118 kev; both are at a 0 = 80 ± 10 pitch angle. (a and b) Differential intensities of (left) protons and (right) electrons split for day/night side of the planet. There is a clear asymmetry for L < 10. (c and d) Same but split for dawn/dusk side. These two sides show no asymmetry. (e and f) Total magnetic field split for day/night side at the magnetic equator and 10 latitude, respectively. All values are logarithmic long term averages. Since the L shell is calculated purely geometrical, it is easily possible to convert the x axis of Figure 4f to radial distance r = Lcos 2 l 0.97L. The right and left end of the pink bar in Figure 4a exemplary marks L shells of the day and night side where particle intensities are equal. They are separated by several R S.Ifthe magnetic field would cause the particle asymmetry, the equatorial magnetic field profiles of day and night side should be separated by approximately the same distance. The pink bar in Figure 4e shows that this is not the case, therefore the field cannot cause the asymmetry. The exact position of the bar has been chosen arbitrarily. The argumentation given here works also for other positions. 7of24

8 [42] Finally, the day/night asymmetry can be caused by a source at the night side. Injection events frequently occur in the L range of the asymmetry [Chen and Hill, 2008] and can act as a source. They mainly originate at the night and morning quadrant of the planet [Müller et al., 2010] before their intensity is deceasing due to losses and dispersion. We and also Paranicas et al. [2010b] therefore advocate that they are the most probable cause for the high intensities on the night side. 4. Radial Diffusion [43] Radial diffusion plays a major role in the distribution of energetic particles in planetary magnetospheres. The use of phase space densities at constant first and second adiabatic invariant is physically more meaningful with respect to particle transport than intensities at constant energy and pitch angle. We will present phase space densities derived from the data and compare them with solutions of a simplified diffusion equation Phase Space Densities [44] The total motion of charged particles within a static dipole field can be decomposed into three different motions acting on different timescales: gyro, bounce and azimuthal drift motion. In addition to that, net radial motions can occur for example due to interchange instabilities [Mauk et al., 2005], the Vasyliūnas cycle [Vasyliūnas, 1983], compressions of the magnetosphere, and radial diffusion (section 4.1). In contrast to the others, the latter process yields a steady and continuous radial flux that is directly related to the gradient in phase space density. It governs the large [Van Allen et al., 1980a] and small scale [Roussos et al., 2007] radial distribution of particles. As we will demonstrate in section 4.2, it is the dominant process for at least L > 12. [45] Radial diffusion can be caused by stochastic [Walt, 1971, 1994] or periodic [Brice and McDonough, 1973] fluctuations of the magnetic or electric field on the timescale of the drift. These effects disturb the drift motion but leave the gyro and bounce motion mostly unaffected and therefore periodic. [46] For every motion, which is periodic in the momentum component p k, the adiabatic invariant J k = H p k dk is conserved. This gives rise to the definition of two conserved quantities associated with gyro and bounce motion. They are EEþ ð 2mc2Þ ¼ 2mc 2 sin 2 ðþ E sin2 ðþ B B K ¼ Z þm m pffiffiffiffiffiffiffiffiffiffiffiffiffiffi B m B ds [47] We refer to m and K as the first and second adiabatic invariants. E is the kinetic energy of the particle, m its rest mass and c the speed of light. B is the magnetic field, which we assume for the calculation of (1) to be an offset dipole. l m is the mirror latitude of the bounce motion, B m qisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the magnetic field at the mirror point. ds = L cos(l) 1 þ 3 sin 2 ðþ dl is the infinitesimal path element along a dipole field line. The approximation given in (1) is for nonrelativistic velocities and for the ð1þ energies considered here valid for protons. The equation for K is exact for the relativistic as well as for the nonrelativistic case. [48] Equation (1) can be numerically solved for energy E(m, K, L) and equatorial pitch angle a 0 (m, K, L), revealing that they change during the diffusive process with L. This means that particles gain energy while diffusing toward the planet, a process that is called adiabatic heating. [49] If the distribution of particles is given at constant m and K and in terms of phase space density f, it can be described via the following diffusion equation [Schulz and DL ð L þ f t Here, f/ t is the change in phase space density and therefore particle number with time. We assume that the longterm averaged phase space density presented here is equivalent to a steady state situation. For a (nearly) steady state, f/ t is zero (smaller than all other terms). [50] The right hand side of (2) shows how a change in f can occur: Particles can spatially diffuse away (D is the radial diffusion coefficient) or be lost or be supplied by other processes (df/dt is the sum of losses and sources). [51] The phase space densities that will be shown in this paper are derived like this: In general, f is related to the differential intensity j, which is particles per time, area, space angle and size of the energy interval, by [Walt, 1994] f ð; K; LÞ ¼ j ð ; K; L Þ p 2 ð; K; LÞ [52] Energetic particle detectors do not measure j but a quantity proportional to j, which is averaged over E and a 0. Using this, we cannot exactly derive f but a quantity that is approximately the same and we call f. [53] To calculate f (m, K, L) from j(e, a 0, L) we first derive j(m, K, L). For this, we compute E(m, K, L) and a 0 (m, K, L). Then we retrieve j at these energies and pitch angles from the data. Since LEMMS does not provide intensities for arbitrary E and a 0, we use interpolation and binning for this, which is described next. [54] The size of the energy bins are between 4% and 8% of the central energy value for the used LEMMS PHA_A, PHA_E and PHA_F1 channels and between 16% and 335% for the used rate channels A, P and E. (The central energy is defined as the logarithmic average of the lower and upper limit of the energy range.) To derive intensities at exactly E(m, K, L), we interpolate the measured intensities assuming a power law spectrum. Due to apertures of a finite size (15 for A and all PHA channels, 30 for P and E channels), intensities measured at a given (central) pitch angle also include contributions from the neighboring angles. Therefore, we bin intensities not only in L but also in a 0 (around a 0 (m, K, L)). [55] The described procedure together with equation (3) provides a tool to convert intensities to phase space densities. Since the result is based on interpolated values of j, we call it f. For j j it is approximately the same as f. [56] Figure 5 presents the most comprehensive computation of profiles based on MIMI data to date. They are based ð2þ ð3þ 8of24

9 Figure 5. Long term averaged phase space densities f of (left) protons and (right) electrons p ffiffiffiffi with constant first and second adiabatic invariants m and K. Their units are given in MeV/G and R S / G, respectively. In all cases the equatorialppitch ffiffiffiffi angle changes from a 0 (20 R S ) = 10 to a 0 (2 R S ) = 4. Protons with m = 20 MeV/G and K = 3.34 R S G change their energy from E(20 RS ) = 110 kev to E(2 R S ) = 17 MeV. Electrons with the same m and K change from E(20 R S ) = 100 kev to E(20 R S ) = 3.7 MeV. If the profiles are plotted with thinner lines in a modified color, this marks regions, where the average intensity is dominated by instrumental background and the profile is not reliable. We cut some of the profiles shown here if the region was too extended. Error bars are the 1s standard deviation of the average and are exemplarily shown only for one profile that is representative. There is a change in gradient within the electron profiles at L = 9. We show the black lines, which are linear fits, to guide the eye in this region. The squares mark the transition between different channel types equal to Figure 3. Dashed lines mark the outer edge of the main rings and the major axis of the orbits of several moons, which can cause dropouts or gradient changes of the profiles. on our long term averaged data set, which provides much better statistics and coverage than the flyby missions. We show protons and electrons for the full range of adiabatic invariants covered by LEMMS. The equatorial pitch angle of the particles shown there is approximately 4 a 0 10 within the L range shown. The difference to profiles with other pitch angle ranges is part of the following discussion. [57] An overview on the phase space densities from previous missions can be found by Van Allen [1984]. For selected Cassini orbits, electron phase space densities at energies lower than LEMMS are given by Rymer et al. [2007]. [58] In Figure 5, the proton radiation belts are visible for L < 5 as a region of large phase space density. We do not provide phase space densities of the electron belts because most of the electron channels are contaminated by radiation belt background and the remaining ones do not provide sufficient spectral information for a reliable energy interpolation. [59] For L > 5, the profiles show a general decrease toward the planet, which is consistent with previous works [Van Allen, 1984]. In case of the displayed pitch angles, the profiles become flat in the region around 10 R S for small m. More field aligned particles (not shown here) have profiles that are always increasing (approximately logarithmically). [60] On top of the general decrease of phase space density toward the planet, electron profiles also show a sharp change in gradient at L 9, which is the orbit of Saturn s moon Rhea. A profile of this kind is consistent with electrons being absorbed by Rhea and is discussed in section 5.4 in more detail. [61] Van Allen et al. [1980a] observed a similar gradient change at L 10. Various displacements between the expected 9of24

10 and observed L shells of moon signatures have been reported before [Roussos et al., 2005]. They can be attributed to errors of the magnetic field model and the negligence of electric fields. Both can modify the drift path of the electrons and therefore the positions where the presence of moons influences the electron distributions. [62] Electron densities at thermal energies (<100 ev) show a change in gradient at L 14 [Schippers et al., 2008]. In the same region, at L = 15.5, the ring current proposed by Connerney et al. [1981] has its outer boundary. For the energies in the LEMMS range, even the average electron phase space densities show large fluctuations at L > 9.In contrast to the lower energies there is no feature obvious in our profiles that would consistently occur throughout all possible sets of adiabatic invariants (Figure 5 only shows a subset). [63] In contrast to the intensities presented in Figure 2, the distinction between loss and diffusion region for L > 5 is not obvious anymore. A more careful analysis in section 4.2 will reveal that this also exists in the phase space density profiles and prove that there are indeed different processes acting in the two regions. [64] Usage of the dipole model causes an error in phase space density. f at a given L is a function of energy and pitch angle, which are derived from m and K that depend on the magnetic field. An error in the magnetic field will therefore ultimately cause an error in f. For a typical spectrum with a spectral index of g 2 we estimate the error in phase space density of equatorial particles being Df 3f. Outside the radiation belts, this is well within the error bars (see Figure 5) and can be neglected Importance of Diffusion [65] The diffusion equation given in (2) can be solved analytically under the assumption of a steady state ( f/ t = 0) and absence of sources and sinks (df/dt = 0), which gives rise to a simplified diffusion DL L ¼ 0 [66] The radial diffusion coefficient D(L) can be described as a power law in L: D ¼ D 0 L n [67] The parameters of the power law have been determined from LEMMS measurements by Roussos et al. [2007] in the region of 4 < L < 9. We neglect dependencies on energy and pitch angle and assume n = 10, which is still consistent with Roussos et al. [2007]. [68] For n 3, the solution of (4) is a power law with exponent en =3 n f ¼ 1 L ~n en þ 2 [69] The phase space density f in equation (6) is independent of D 0 and only has the diffusion exponent n as a ð4þ ð5þ ð6þ free parameter. x 1 and x 2 are constants and can be derived from two boundary conditions. We use the values of the phase space densities at the inner and outer edge of the considered region for this. [70] In Figure 6, measured phase space densities within the loss and the diffusion region are shown in combination with phase space densities derived from equation (6) for different exponents n. The plots reveal that a general decay of phase space density toward the planet can be achieved without any losses occurring in the analyzed area. Nevertheless, the precise shape of the profiles depends on the detailed processes like the L dependence of the diffusion coefficient. [71] Within the loss region (Figure 6, left) pure diffusion does not fit the data even within the large error bars for E 200 kev and m 125 MeV/G. Even assuming unrealistic, negative values of n results in theoretical profiles that do not match the observation. We attribute this to processes other than diffusion, namely sources and losses. [72] At higher energies and m values these processes are apparently weaker or even vanishing. There, and also within the diffusion region (Figure 6, right), the data does not contradict the assumption of pure diffusion and there is no evidence that other processes play a major role here. The profiles shown in this and similar figures are mostly concave (middle of the curve is bend toward higher values). This requires a positive value of en, which is true for n > 3, which matches our expectations. n < 3 would cause a convex profile. 5. Modeled Sources and Losses [73] Energetic charged particles can be lost or changed in energy by a variety of processes. Major effects at Saturn are caused by interaction with neutral gas, and ice grains. We will discuss these effects in detail and give estimates for the loss timescales of equatorially mirroring particles at L =7.It is not possible for us to consider the peak region of gas and grains at L = 4 because LEMMS data is contaminated there by background from the radiation belts. At L = 7 this problem does not exist. This region also has the advantage that it is within a relatively wide gap (2.5 R S wide) where no orbits of major moons are nearby that also can have an impact on the particle profiles. We focus on equatorially mirroring particles because their lifetime only depends on the equatorial density of gas and grains while lifetimes of more field aligned particles also depend on the latitudinal profile of Neutral Torus and E ring, which is poorly known. [74] We will compare the derived lifetimes of different effects with each other. Also, we will discuss qualitatively the effects of the moons, pitch angle scattering to the loss cone, injection events of several types, and CRAND. In section 6, we will compare our results to lifetimes derived directly from the phase space density profiles Charge Exchange [75] Saturn s Neutral Torus consists mainly of neutral O, H, OH and H 2 O [Jurac and Richardson, 2005; Melin et al., 2009]. There is no evidence or reason for other species 10 of 24

11 Figure 6. Phase space densities f of protons within the (left) loss and (right) diffusion p region. ffiffiffiffi Colors of the curves mark different values of m. The units of m and K are given in MeV/G and R S / G, respectively. The scattered profiles are measured, long term averaged phase space densities. The standard deviation of the average is exemplarily shown at one profile and is similar for the others. Every measured profile is compared to two theory curves, which are the smooth lines. These are solutions of the simplified diffusion equation (4) for two different exponents n of the radial diffusion coefficient. The upper curves are for a realistic value of n = +10 and approximately match the observations within the diffusion region. The lower curves are for a unrealistic value of n = 10. Even this scenario cannot fit the low m profiles within the loss region. The squares are color coded for the approximate energy at the given position. They illustrate that while left and right images show phase space densities of different m values, they still cover about the same energy range. The pitch angle of the shown particles is a 0 = 90 ± 10 for all L. being important. The neutral particles originate to a large extension from the plumes of Enceladus [Burger et al., 2007], which is the reason why their density is highest close to its orbit at L 4. [76] Energetic protons interact with neutral particles essentially via charge exchange (this process does not apply to the electrons). During this process, an electron is transferred from the neutral particle to the proton. The energies of both particles are changed little. Since the created neutral atom is not bound to the magnetic field anymore, it escapes as an ENA, if it is not stripped again during its exit. The created charged particle is accelerated by the corotating electric field but remains below energies that LEMMS detects. Therefore, we consider charge exchange a loss process. It is usually considered even as the dominating process at least for protons below several 100 kev [Paranicas et al., 2008]. We will give proof for this in the following. [77] The appropriate loss term is carefully derived in Appendix A and yields e f t ¼ ven e rf ¼ e f CE e f is the phase space density. In contrast to f, it can be measured at any l l m and is therefore independent of l (see (A4) for definition). We define t CE as the proton lifetime against charge exchange. The smaller the lifetime, the faster the protons will be lost. v is the total velocity of the protons, s the interaction cross section for charge exchange, en the neutral density averaged over the path of the proton: ð7þ en r ¼ 1 Z TB n r ðl;ðþ; t Þdt ð8þ T B 0 11 of 24

12 [78] There, t is time and T B the bounce time. Keep in mind that en r is not equivalent to the density averaged over l. The integration over time used here weights the latitudes. This is necessary since the particle s parallel speed maximizes at the magnetic equator, so that it experiences the density there for only a short time. [79] To obtain a relation between en r and the peak density n 0 of the torus, we assume that its latitudinal distribution can be described by a Gaussian profile n r (l) =n 0 exp( l 2 /l r 2 ), and that its thickness is varying slowly with L so that l r ArcTan(z r /L) is a good approximation. Here, l r and z r is the latitude and height above the ring plane, where the torus density drops to 1/e of the equatorial value. [80] For a torus with 2z r =1R S that is at L = 7 traversed by a 0 = 10 particles, the average density yields en r = 0.06 n 0. This is different from a 0 = 90 particles that always experience the density at the equator so that en r =1n 0. Considering more field aligned energetic particles is therefore equivalent to assuming smaller densities of neutral gas. [81] Values for the charge exchange cross section s can be found in literature for H, O, and H 2 O [McEntire and Mitchell, 1989; Toburen et al., 1968] but not OH, since this molecule is highly reactive and cannot be studied easily in the lab. Theoretical work has been done in calculating cross sections that couldalsobeappliedtooh in the future [Houamer et al., 2009]. All cross sections exhibit strong energy dependence: between 10 kev and 100 kev, s decreases by about 1 order of magnitude, between 100 kev and 1000 kev about 4 orders. Although s depends on the species, the differences between them are usually smaller than 1 order of magnitude. [82] There is a lack of agreement about precise values of the Neutral Torus density and the relative abundance of different species [Richardson et al., 1998; Jurac and Richardson, 2005; Shemansky et al., 2009; Melin et al., 2009; Smith et al., 2010]. We assume here that all neutral particles are O, in order to derive energetic particle lifetimes. Since all major species have similar charge exchange cross sections, this assumption is not critical. Nevertheless, it implies that our assumed density of effective O has to be larger than the real O density. If all 4 major species would be equally abundant and have exactly the same cross sections, the difference between effective and real O density would be a factor of 4. [83] For the effective density of all neutrals, we use n 0 (7 R S ) = 10 8 m 3 as the equatorial peak value. This is roughly consistent with O densities given by Melin et al. [2009], Smith et al. [2010], Cassidy and Johnson [2010], Dialynas [2010, also manuscript in preparation, 2011] and approximately 1 order of magnitude less than the peak value at L = 4. As values of the charge exchange cross section, we use the O cross sections from McEntire and Mitchell [1989]. [84] The resulting lifetimes are shown in Figure 7 (left) as red crosses. It can be seen that they strongly depend on energy and vary between days and years within the considered energy range. Comparisons with other effects will be drawn in sections 5.2, 5.3, and Energy Loss in Ice Grains [85] Protons and electrons also interact with the E ring components [de Pater et al., 2004; Kempf et al., 2008]. This is a faint and extended ring outside the main rings, which is supplied by the plumes of Enceladus and therefore has its peak density roughly along its orbit. It consists mainly of grains of water ice. [86] Energetic particles lose energy while passing through matter and ultimately can get stopped in it. Protons can also capture electrons during the passage. This is called neutralization and acts as an immediate loss process. It is dominant for energies below 100 kev but can be neglected above that [Mauk et al., 1998; Kreussler and Sizmann, 1982]. Here, we do not consider it. [87] The energy loss in matter is described by the energy loss per distance de/dx, which is usually referred to as stopping power or stopping cross section. Values for this can for example be derived from Berger et al. [2010]. Protons with low energies (<1 kev in case of ice [Miller and Green, 1973]) mainly scatter at nuclei and at electrons for higher energies, causing impact ionization. Electrons lose energy mainly due to impact ionization. For very high energies (>10 MeV for ice [Berger et al., 2010]), radiative bremsstrahlung losses start significantly contributing to the loss. [88] A loss in energy is not directly equivalent to a loss of particles, which makes this interaction more difficult to treat than the charge exchange or neutralization process. To derive the relation between a loss in energy and a loss within a particle population, one first has to define this population. If defined only by the species and the fact that the particles are moving freely, it is necessary for them to lose all of their kinetic energy to be considered as lost. We call the typical time for this to happen global lifetime t glob. This case is usually treated in literature [Thomsen and Van Allen, 1979; Van Allen, 1983]. [89] The global lifetime is important to characterize the evolution of energetic particles but is not appropriate to explain the decrease of particles with a given energy. The use of a detector that distinguishes between energies (or energy intervals) implicitly defines the population not only by species but also by energy. In this case, a particle is lost after losing enough energy to leave the energy range of the detector channel. This decreases the intensity measured by the channel. Particles with initially higher energies that lose energy can end up in the considered channel (if they do not overshoot). This increases the intensity. Depending on the energy spectrum, for a given channel, energy loss can therefore act as a loss or source process. We call the typical time to enter or leave a channel the channel lifetime t. [90] The loss and source rates of the phase space density of a given channel is derived in Appendix A. The net sum of these two rates turns out to be hf i t ¼ R E o E i ðf = L ÞdE þ R E o ðf = S ÞdE R Eo ¼ hf i de hi E i f is the phase space density of particles with the precise energy E. E i and E o are the lower and upper limit of the considered channel, respectively. h f i is the mean phase space density in this range (see (A8) for exact definition). Because we mainly utilize the PHA channels, which are narrowly spaced in energy, it is h f i f. [91] We will refer to the first term of (9), which is the loss rate of the channel without considering its gain, as the pure loss. ð9þ 12 of 24