Modeling the electron and proton radiation belts of Saturn

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 20, 2059, doi: /2003gl017972, 2003 Modeling the electron and proton radiation belts of Saturn D. Santos-Costa, 1 M. Blanc, 1 S. Maurice, 2 and S. J. Bolton 2 Received 15 June 2003; revised 16 September 2003; accepted 29 September 2003; published 28 October [1] We present results from a three-dimensional model of the Saturnian radiation belts. This model draws on preexisting physical radiation-belt models, developed to study the belts of the Earth and Jupiter. In the present work, transport processes and interactions with dust and gas clouds, moons, and plasma are considered to determine the trapped particle distribution in Saturn s inner magnetosphere. The results of the modeling are: absorption by dust is the dominant loss effect in the innermost region while local losses from satellites act as the prominent physical process in the outer part of the inner magnetosphere. Results suggest strong energetic neutral atom emission and weak synchrotron emission. Comparisons between data and model results are presented. INDEX TERMS: 2720 Magnetospheric Physics: Energetic particles, trapped; 2730 Magnetospheric Physics: Magnetosphere inner; 2756 Magnetospheric Physics: Planetary magnetospheres (5443, 5737, 6030); 2753 Magnetospheric Physics: Numerical modeling. Citation: Santos- Costa, D., M. Blanc, S. Maurice, and S. J. Bolton, Modeling the electron and proton radiation belts of Saturn, Geophys. Res. Lett., 30(20), 2059, doi: /2003gl017972, Introduction [2] Pioneer-11 and Voyager encounters with Saturn provided important snapshots of the Saturnian system. A more in-depth and complete investigation of the system will be possible with Cassini currently en route to Saturn. In preparation for future Cassini data analysis, we have developed a model of the Saturn s radiation belts that includes processes related to the rings, satellites, plasma, gas clouds and transport processes. [3] Modeling radiation belts provides opportunities to estimate trapped particle fluxes along spacecraft s trajectory and their emissions (synchrotron radiation and Energetic Neutral Atom emission). In previous works, a physical model for the Jovian electron radiation belts was able to reproduce both spacecraft measurements and radio data [Santos-Costa, 2001]. Based on the modeling of the physical processes and the study of their role on the radiation belts dynamics, this physical model has expounded the high-energy electron distribution functions in the inner magnetosphere of Jupiter and the Jovian synchrotron brightness distribution [Santos-Costa et al., 2001]. [4] An early empirical model was developed based on a limited set of measurements obtained along the Pioneer-11 and Voyager trajectories [Divine, 1990]. This model was used to calculate the trapped electron and proton fluxes in 1 Laboratoire d Astrophysique de l Observatoire Midi-Pyrénées, Toulouse, France. 2 Jet Propulsion Laboratory, Pasadena, California, USA. Copyright 2003 by the American Geophysical Union /03/2003GL Saturn s magnetosphere in preparation of the Cassini mission. In this paper we present a new model of the trapped particle population of Saturn developed based on existing models of the Jovian electron radiation belts [Santos-Costa et al., 2001] and the terrestrial proton radiation belts [Beutier et al., 1995]. The new model will be used to improve our understanding of the radiation-belt population as observed during the Pioneer and Voyager flybys, before being used to predict radiation-belt fluxes and emissions for the Cassini Mission in a subsequent study. 2. The Modeling [5] During the 1990s, three-dimensional physical models of the electron and proton radiation belts of the Earth have been developed [Beutier and Boscher, 1995; Beutier et al., 1995] and more recently, the terrestrial electron model has been adapted to Jupiter [Santos-Costa and Bourdarie, 2001; Santos-Costa et al., 2001]. These models draw on of adiabatic invariant theory and solve the governing Fokker-Planck transport equation to determine the trapped particle population in the inner magnetospheres. The 3-D equation [e.g., Beutier, 1993; e.g., Santos-Costa, 2001] describes the time evolution of the distribution functions in a phase space equivalent to energy, latitude and þ X2 i¼1 SSC f fric D i¼1 j¼1 j þ L D þ L ¼ X2 Here, f is the particle phase space density averaged over a drift shell, J 1 (or M) corresponds to the first invariant, J 2 (J) is the second invariant and L is the McIlwain parameter [Schulz and Lanzerotti, 1974]. The determination of D ij and (@J i /@t) fric (diffusion and non-stochastic coefficients, respectively), and the source (S) and loss () terms is required to solve the equation. These terms depend on the interactions occurring between radiation-belt particles and planetary environments, and the sources. [6] The physical modeling of the Earth s radiation belts has allowed to define the terms coming from interactions between trapped particles and neutral particles (atmospheric particles), charged particles of plasma environment, and waves [e.g., Beutier, 1993]. Interactions with neutral and charged particles engender energy degradation terms) for electrons and protons, but also pitch-angle diffusion for the electrons (D MM,D JJ,D MJ terms are generated). Moreover, trapped protons interact with neutrals thru charge exchanges: neutral particles are ionized (engendering a source term for plasma) and charged protons are neutralized (a loss term ( absorption) is then

2 SSC 6-2 SANTOS-COSTA ET AL.: MODELING THE RADIATION BELTS OF SATURN defined) [Beutier et al., 1995]. Wave-particle interactions induce pitch-angle diffusion terms (D MM,D JJ,D MJ )[Beutier and Boscher, 1995]. [7] The investigation of Jupiter s radiation belts has provided a fundamental understanding of effects on energetic electron population from processes associated with the satellites, dust rings and synchrotron emission [e.g., Santos- Costa, 2001]. Satellites contribute to the absorption of energetic electrons during their transport within the magnetosphere, engendering a loss term in the transport equation [Santos-Costa and Bourdarie, 2001]. Trapped electrons can also be absorbed as they pass through the ring systems (loss term), with high-energy electrons experiencing both energy loss and deflection (engendering energy degradation (@M/@t and pitch-angle diffusion (D MM, D JJ, D MJ ) terms) [Santos-Costa, 2001]. Synchrotron radiation causes electron energy degradation and consequently a decrease in the trapped electron pitch-angle (@M/@t terms appear in the equation) [Santos-Costa et al., 2001]: electrons lose energy and are transported along the field lines from the magnetic equator to the loss cone. [8] Taking into account the different Kronian components, modeling the radiation belts of Saturn for particles (electrons and protons) with energies between 10 kev and 5 MeV needs to consider interactions of the radiationbelt particles with the extended neutral environment (atmospheres and gas torii), plasma, dust (ring systems), waves and particle transport and the particle sources. The current model does not account for wave-particle interactions and interaction with the Saturnian atmosphere. This will be done in a subsequent work and in this work we assume that these interactions induce weak effects compared with those caused by the other physical processes. [9] Interactions with neutral particles forming the gas torii have been modeled based on the work of Beutier [1993] (interaction with the terrestrial atmosphere). The resulting equation terms D MM, D JJ, D MJ ) were determined by considering different neutrals: H, H 2 O, OH, O, H 2 and O 2 (Neutral H density comes from Hsieh and Curtis [1988] while H 2 O, OH, O, H 2 and O 2 densities come from Ip [1997]). [10] Interactions with cold plasma have been modeled based on Beutier et al. [1995], and using the distribution of thermal ions and cold electrons in Saturn s magnetosphere computed by Richardson [1995]. [11] Effects of synchrotron radiation on the electron trapping and moons on radiation-belt populations have been estimated based on Santos-Costa and Bourdarie [2001]. Eleven satellites located in the Saturnian region (2.2 to 4.89 Rs) have been considered. [12] Absorption, energy degradation (and pitch-angle diffusion only for electrons) occurring when trapped particles pass through rings have been determined by updating the work of Santos-Costa [2001]. We have revised the formulae for the protons and modified the ring model to be consistent with Saturn s more substantial ring system. Furthermore, a full description of the interaction between trapped protons and dust has been completed including the production of Energetic Neutral Atoms (ENA) during charged particle dust crossing. As described by Mauk et al. [1998], the production of ENA by this process removes the low-energy trapped proton population (tens to hundreds kev) in Saturn s system and introduces a supplementary absorption term in the transport equation. Information given by the National Space Science Data Center (Saturnian rings fact feet) have provided the values for the radial extension, thickness, and optical depth of the C, B, Cassini division, A, and F rings. The G ring has a thickness of 10 3 km and an optical depth equal to 10 6 ; and both the thickness and optical depth of the E ring are described by a power-law dependence on radial distance [Showalter et al., 1991]. Dust particles are assumed to be icy grains with densities described by n(a > a 0 )=n(a 0 )[a/a 0 ] q with a being the radius of the dust particle [e.g., Showalter et al., 1984; Zebker et al., 1985]. [13] The transport of particles within the inner magnetosphere of Saturn has been modeled using a standard D LL = D o L n parametric form (given a diffusion term in the transport equation). D o and n are free parameters constrained by spacecraft data. The best fit value for n determined between 1 10 range values was close to 3. This is in agreement with the theoretical value of n = 3 estimated by Brice and McDonough [1973] when they assume transport generated by ionospheric perturbations. Fixing n = 3 imposes D 0 to be equal to 10 8 s 1 for the electron transport and 10 9 s 1 for the proton transport. [14] For Saturn s radiation-belt model, the resolution of the Fokker-Plank equation uses a derivation of the Runge- Kutta numerical method [Dahlquist and Björck, 1974]. Dirichlet boundary conditions fix the value of the phase space density [Beutier, 1993]. The particle source is reduced in our case to a boundary condition at 6 Rs that allows for the inner Saturnian magnetosphere to be filled by the particle transport process. At this boundary (L = 6), particle flux observations from the Low Energy Charged Particle (LECP) experiment during Voyager flybys in the 1980s are combined to build energy and pitch-angle spectra [Krimigis et al., 1983]. 3. Results and Discussions [15] In order to evaluate the importance of each physical process, we have plotted the different terms of the transport equation as a function of the equatorial radial distance. Figure 1 displays the relative importance of each process for 310 kev electrons and 350 kev protons and for 80 pitchangle, represented by the associated time scales (inverse of the lifetimes). The choice of these two energies is somewhat arbitrary, but reasonably representative of the dynamics of radiation-belt particles in the sense that particles with these energies are consistent with most of the physical processes. Furthermore, the selected energies coincide with LECP channels. Results from Figure 1 show that effects induced by plasma are neglected compared to those engendering by any other process and their contributions to shape particle distributions are insignificant in the inner magnetosphere. [16] For 310 kev energy electrons, absorption by ring particles dominates all other processes throughout the extent of the main rings (<2.3 Rs). Outside of this region, radiation belts dynamics is dominated by radial transport (curve 1); except for a strong effect of the moons limited to their specific locations (curve 2). Between the moons locations, rings and neutral clouds moderately contribute to the dynamics of the electron belt.

3 SANTOS-COSTA ET AL.: MODELING THE RADIATION BELTS OF SATURN SSC 6-3 Figure 1. Importance of the physical processes occurring in the inner magnetosphere of Saturn evaluated by plotting the time scales of each process (in s 1 units) for the radiation-belt electrons (left panel) and protons (right panel). Curve (1) plots the radial diffusion coefficient; curves (2) the moons sweeping effect, curves (3a, b, c) the rings effects ( a for absorption, b for energy degradation, c for pitch angle diffusion); curves (4a, b, c) the effects operating within plasma and neutral clouds ( a for absorption, b for energy degradation, c for pitch angle diffusion); finally, curves indexed by (5b, d) represent the degradation terms engendered during the synchrotron emission of electrons ( b for energy degradation, d for pitch-angle degradation). [17] Let us now compare this with the behavior of 350 kev protons, as evidenced by the right-hand panel of Figure 1. Inside the outer edge of the main rings (<2.3 Rs), ring absorption is dominant just as in the case of electrons. Outside of it, absorption by the moons strongly dominates at their respective L-shell locations, while radial diffusion transport and interactions with neutral clouds (more peculiarly charge exchanges inducing absorption) are of comparable importance and dominate all other processes between the moon s locations. Interaction of trapped protons with neutrals is then the source of an intense emission of energetic neutral atoms (curve 4a), which dominates the contribution of the E-ring particle interactions to this same energetic neutral atoms production (curve 3a). [18] As a complement to this description, Figures 2 and 3 display the fluxes of 310 kev electrons and of 350 kev protons in a meridian plane. Figures 2 and 3 confirm the conclusion highlighted in Figure 1: trapped particle absorption by ring and dust particles produces a strong decrease of the equatorial and non-equatorial radiation-belt particle fluxes in the innermost part of the magnetosphere of Saturn. Moons orbiting in the [2.1; 2.5] Rs region reinforce this effect by being an "absorbent barrier for the trapped particle transport in the internal magnetosphere. Beyond 2.5 Rs, moons sweeping effects are clearly visible on the trapped electron and proton population (particularly for Enceladus near 4 Rs). The charge exchange process strongly and rather uniformly affects the trapped protons in the outer part of the inner magnetosphere. From Figures 2 and 3, note that charged particle distribution is more confined towards the equator for the protons and more extended in latitudes for the electrons. This is the direct consequence of the pitchangle distribution assumed at the outer boundary (6 Rs) and of its nearly adiabatic transport into Saturn s inner magnetosphere, which is only weakly perturbed by pitchangle diffusion or degradation mechanisms. Note that the off Figure 2. Omni-directional differential electron flux in a meridian plane (310 kev energy particle) from simulation. The dark curve represents the meridional view of the Voyager-2 trajectory. Figure 3. Omni-directional differential proton flux in a meridian plane (350 kev energy particle) from simulation. The dark curve represents the meridional view of the Voyager-2 trajectory.

4 SSC 6-4 SANTOS-COSTA ET AL.: MODELING THE RADIATION BELTS OF SATURN equatorial peaks in Figure 2 are formed by losses at the equator during the electron transport. [19] The study of energy and pitch-angle dependence on the particle distributions brings out the same conclusions deduced from that of 330 kev trapped particle distribution (electrons and protons): rings contribute to absorb most of the radiation-belts particles (equatorial and non-equatorial particles) in the innermost part of the magnetosphere of Saturn while moons effect shapes locally the trapped particle populations in the outer region of the inner magnetosphere. Synchrotron emission causes low electron loss rates which confirm the weakness of this radiation for Saturn. Pitch-angle dependence is coming from the pitchangle spectrum at the outer boundary. [20] Comparisons between theoretical results and spacecraft data set are presented on Figures 4 and 5. In this paper, only comparisons with Voyager-2 measurements are displayed for 47, 310 and 3240 kev energy electrons and for 37, 107 and 350 kev energy protons. From Figures 4 and 5, one can note that simulation results reproduce the observations (fluctuation and intensity) along the trajectory of the spacecraft. This result means that the model computes right flux levels by including realistic dynamics of Saturn s radiation belts. Nonetheless, discrepancies between observations and simulations can be pointed out at some particular energies and in peculiar regions of the inner magnetosphere of Saturn. The differences are peculiarly notable in the [2.5; 3.5] Rs region (during the equator crossing of the spacecraft) and indicate that too much trapped particles are transported and confined near the magnetic equator. Further modeling work and Cassini observations will permit to explain these discrepancies. 4. Conclusion [21] Results of a physical model for energetic electrons and protons trapped in the inner magnetosphere of Saturn are presented in this paper. The radiation-belt particle spatial Figure 5. Unidirectional differential proton flux comparisons for three energies (1: 37 kev; 2: 107 kev; 3: 350 kev) between Voyager-2 observations (black curves) and our proton radiation belts model (light curves) during the spacecraft s flyby within the inner magnetosphere of Saturn. distribution has been determined by modeling the trapped particle interactions with the different components of the Saturn system: moons, dust rings, neutral clouds, plasma and magnetic field. Our results suggest some explanations on the dynamics of the radiation belts of Saturn. [22] Absorption by ring particles is dominant in the [1; 2.3] Rs region (inducing low trapped electron and ion populations) while moons local losses act as the prominent physical process in the outer part of the inner magnetosphere ([2.3; 6] Rs). At the present time, wave-particle interaction effects have not been introduced in our model. Knowing this importance in the dynamics of the Earth s radiation belt [Dungey, 1963], this will have to be done in the future. Concerning the proton radiation belts model, beyond 2.3 Rs, moons effect and interactions with neutrals are the prominent processes occurring in the outer part of the inner magnetosphere. Our simulations predict a strong production of energetic neutral hydrogen atoms, but it predicts also a very weak synchrotron emission confirming the weakness of this radiation for Saturn [Van Allen and Grosskreutz, 1989]. Synchrotron emission and energetic neutral atoms produced by the radiation-belt particles of Saturn will be studied and analyzed in depth in a subsequent study. [23] Acknowledgments. This work was supported by the Centre National d Etudes Spatiales (CNES) through a postdoctoral grant. Figure 4. Unidirectional differential electron flux comparisons for three energies (1: 47 kev; 2: 310 kev; 3: 3240 kev) between Voyager-2 observations (black curves) and our electron radiation belts model (light curves) during the spacecraft s flyby within the inner magnetosphere of Saturn. References Beutier, T., Modélisation tridimensionnelle pour l étude de la dynamique des ceintures de radiation, Thesis report, ENSAE, Beutier, T., and D. Boscher, A three-dimensional analysis of the electron radiation belt by the Salammbô code, J. Geophys. Res., 100(A8), 14,853 14,861, Beutier, T., D. Boscher, and M. France, Salammbô: A three-dimensional simulation of the proton radiation belt, J. Geophys. Res., 100(A9), 17,181 17,188, Brice, N., and T. R. McDonough, Jupiter s radiation belts, Icarus, 18, , Dahlquist, G., and A. Björck, Differential Equations, in Numerical Methods, Prentice-Hall, Inc., , 1974.

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