Modeling the radiation belts: what are the important physical processes to be taken into account in models?

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Adv. Space Res. Vol. 28, No. 12, pp. 1739-1746,200l 0 2001 COSPAR. Published bv Elsevier Science Ltd. All riehts reserved Printed in “GreatBritain 0273-1177101$20.00 + 0.00 PII: SO273-1177(01)00540-3

MODELING THE RADIATION BELTS : WHAT ARE THE IMPORTANT PHYSICAL PROCESSES TO BE TAKEN INTO ACCOUNT IN MODELS ? D. Boscher, S. Bourdarie ONERADESP,

2. Avenue Edouard Belin, BP 4025, 31055 Toulouse Cedex 4, France

ABSTRACT During active periods, physical processes acting on particle dynamics are well known to have several origins and can play a role at different times, different locations, and with different time scales. As their effects can be opposite, it is necessary to identify them and their relative importance: - the particle sources (plasmasheet or direct solar wind entry) - the particle losses (precipitation or drift loss) - the particle transport and acceleration (convection access, magnetic or electric pulse or variation and recirculation). The various phenomena are explained and results are presented. In particular, we demonstrate that classical diffusion models like the Salammbo code can account for all these phenomena. 0 2001 COSPAR. Published by Elsevier Science Ltd. All rights reserved.

INTRODUCTION In the Sixties and Seventies, great efforts were made to understand the sources, losses and transport of radiation belt particles (Hess, 1968, Roederer, 1970, Schulz and Lanzerotti, 1974). All the main processes to shape the radiation belt were studied, and good orders of magnitude of both proton and electron flux were found using the classical Fokker-Planck diffusion equation. Nevertheless, some uncertainties remain at the end of this period on the ultimate source of the low energy (ring current) protons and energetic electrons. Moreover, the dynamical behavior of the radiation belts was not well understood at that times. With the results of the NASA/DOD CRRES (Combined Release and Radiation Effects Satellite) satellite in the beginning of the Nineties (Vampola, 1992), the vision of this dynamics was completely renewed. In particular, new survey plots (color coded flux in a L versus time plot) show very clearly the effect of the storms on trapped particles (Brautigham et al., 1992, Friedel and Korth, 1995, Gussenhoven et al., 1996). Moreover, this mission had the chance to record the effects of the March 1991 great storm which creates a second proton and a third electron belt. In parallel, modeling efforts were made in the Nineties and great advances attempted to solve remaining questions. Most of the physical processes acting on these particles have now been identified, even during magnetic active periods. We want here to review the present knowledge about the sources, the losses and the particle transport in the Earth radiation belts.

THE SOURCES From the radiation belt point of view, particles have different origins. Three sources are now clearly identified: plasmasheet injections, CRAND process and solar wind direct entry. They all affect different

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energy range and L values. The main source of the radiation belt particles is in the plasmasheet (see Figure 1). During substorms, these particles are injected in the night side at the outer edge of the radiation belt (outside the plasmapause) either by increased convection or induced electric field (dipolarisation). This source is highly dynamic as the number of substorms depends strongly on the magnetic activity. By radial transport across drift shells, these particles can accelerate easily up to around 1 MeV in the inner belt region (L c 3), either for protons or electrons, but not more. So the source of high energy particles must be found elsewhere. For protons, another phenomenon, which creates the very high energy population is the Cosmic Ray Albedo Neutron Decay (CRAND). Neutrons are created at the top of the atmosphere by interaction between the cosmic rays and atmosphere neutrals. They can fly to very large distances inside (and outside) the magnetosphere, decaying in a proton and an electron. With this process, very high energy protons (up to hundreds of MeVs) are created everywhere in the magnetosphere, those trapped by the Earth magnetic field being stable for years. This process cannot create electrons with energies higher than a MeV and it is negligible compared to accelerated particles from plasmasheet injections. Sources of particles can also be found directly in the solar wind (in the magnetosheath). Solar Energetic Particles have access to the inner magnetosphere, principally due to the opening of drift shells at the magnetopause. High energy protons (and ions) have access to inner regions of the magnetosphere due to their large Larmor radii, the limit depending on the particle energy. This limit, denoted as 1 on Figure 1, is known as the geomagnetic cut-off, which acts as a shield for cosmic ray as well as Solar Energetic Particle (magnetospheric shielding). Usually, these particles just cross the magnetosphere, but when a magnetic storm is present at the same time, they can be trapped and then become a source of high energy particles, especially in the 10 MeV range. These particles are accelerated inside the magnetosphere and create a second proton belt around 30 MeV and a third electron belt at around 15 MeV (MeV electrons being highly relativistic). E (MeV) 100 10 1 0.1

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Fig. 1. Sources of the radiation belts (left panel: protons, right panel: electrons)

THE

TRANSPORT The main transport in the radiation belt region is related to any electric field or perturbations of the magnetic field. If it is not sure that electric fields (convection) exist in the magnetosphere, magnetic field perturbations are nearly always present, inducing electric fields. These perturbations are related to any magnetospheric current changes, but to have an impact on the radiation belts, they must be asymmetric (Fahhammar,1965). It is the case for perturbations due to magnetopause, tail or asymmetric ring currents, plus the crossing of shock waves in the magnetosphere. While it was demonstrated by Falthammar (1965) that magnetopause current variations produce radial transport, and by Hudson et al. (1997) that the crossing of a shock wave create a second belt in March 1991, other sources of radial transport were not

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extensively studied (it is now sure that ULF waves are also a principal actor in the radial diffusion, see Liu et al., 1999). The global effect of these perturbations is a particle diffusion across drift shells (see Figure 2). Particles can be displaced inward or outward depending on their location on the drift shell during the perturbation. In fact, the resulting diffusion is mainly inward due to the main field configuration. So particles diffuse principally from outer regions to inner ones. Most of these perturbations being relatively slow to cross the magnetosphere, particles usually conserve their first (relativistic magnetic moment) and second invariants. Therefore, they are more and more accelerated as they go to lower L values (in the E versus L plot, non relativistic particles follow E = l/L’ curves, while highly relativistic ones follow E 0~ In?‘*, see Figure 2).

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Fig. 2. Radial transport of radiation belt particles(left panel: protons, right panel: electrons).

A second major transport process, very efficient in the internal magnetosphere for electrons, is the pitch angle diffusion by resonant interaction between gyrating particles and waves, Particle pitch angle is modified, which means that it can lower or enlarge. Nevertheless, as the main electron source (the plasmasheet) is located in the magnetic equator region, the global effect is the filling of all the magnetic latitudes (see Figure 3a). This effect is very efficient inside the plasmasphere (the mean plasmapause location is around L = 4.5). E (MeV)

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Fig, 3. Transport including pitch angle diffusion for electrons : a) pitch angle diffusion, b) acceleration including recirculation (in black).

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Moreover, the combination of radial diffusion and pitch angle diffusion can be the source of an extra acceleration, creating 1 MeV electrons inside the magnetosphere (see Figure 3b). In this process, particles are gradually accelerated and decelerated along small loops (Boscher et al., 2000a). In fact, they are diffused in energy by this process, but due to the particle spectrum, this diffusion corresponds to a net particle acceleration and a source of energetic electrons. Other processes, like interactions with chorus waves, or electric field direct acceleration, are also possible acceleration processes for energetic electrons. In fact, all these processes induce electron energy diffusion and MeV electron. Pitch angle diffusion can also be due to interaction between electrons and free and bounded electrons from neutrals (Coulomb interactions). Finally, friction by free and bounded electrons from neutrals produce deceleration of protons as well as electrons. But unless particles bounce near the Earth, these transport processes are less effective than the first two ones (radial and wave pitch angle diffusion). THE LOSSES Radiation belt particles are mainly lost at the top of the atmosphere (near 100 km altitude). This loss is associated to the different transport processes. The main loss is due to radial transport (see Figure 4). As radial transport is done using conservation of the first two adiabatic invariants, the particle pitch angle is only weakly modified during this process. Particles transported inward are bouncing nearer and nearer the Earth and this transport is not too far from purely radial, as shown on Figure 4. Particles with low pitch angle are precipitated into the loss cone when they move to lower L shells. This process is very important at high L shells where the loss cone is strongly modified from one L shell to another. The second loss, only valid for electrons, is related to the pitch angle diffusion by wave particle interaction. As the particle pitch angle is scattered, it can lower into the loss cone and particles are precipitated. Finally, two other transport processes are acting to lose particles, the first one is due to diffusion by Coulomb collisions (similar to the diffusion by wave particle interaction), and the second one is due to friction with bound and free electrons (particles can be so decelerated that they participate to the plasma population which is globally neutral and are lost from the radiation belt point of view).

use

shell

Fig. 4. Precipitation

by radial transport.

Another loss is related to the opening al., 2000). Particles can be trapped during shells. But following a pressure increase Earth and outer closed drift shells become

Fig. 5. Particle loss by opening of drift shells.

of drift shells to the magnetopause (see Figure 5) (Desorgher et long periods of quiet magnetic activity on different closed drift in the solar wind, the magnetopause is compressed toward the open drift shells (like the one referred as 2 on the figure). This

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drift shell opening can also occur in the case of magnetosphere depression, as during ring current increases. This loss process depends very much on magnetic activity. During intense storms like March 1991, losses were recorded down to L = 3, while it seems they act at L = 1.8 and above during the March 1989 storm. E (MeV) 100 10 1 0.1 0.01 b

0.001 1

23456789L

Fig. 6. Regions of long term trapping for the radiation belts (left panel: protons, right panel: electrons).

Other losses also exist like the well known charge exchange or nuclear inelastic interactions (INIs) but they are restricted to protons. The global effect of losses can be seen on Figure 6. The gray portion of the E versus L plane is the region where particles can be trapped for long duration. In particular, the two electron belts are clearly visible on this figure in the 100 keV range. We must also notice that it is very difficult for particles in the 10 MeV range to be transported down to L values lower than 2. Two limits are variable with magnetic activity, the one referred as drift loss on the figure, and the other corresponding to the wave-particle diffusion area because wave frequency, amplitude, location and direction are highly variable. MODELING THE PROTON BELT Using a classical Fokker-Planck equation, it is possible to take all these processes into account and we want to show only two results obtained by such a model: Salammb6. The first one is related to protons while the second one gives results for electrons. In the first example (Vacaresse et al., 1999), 1.5 MeV and 36 MeV protons are shown on Figure 8. This figure is plotted like a survey plot, showing gray scale coded unidirectional equatorial flux in a L versus time plot. The modeling was here made to reproduce in the L range [ 1:7] the flux as seen on CRRES. At low energy (1.5 MeV, top panel), injections are clearly seen at L = 7, but depending on the magnetic activity, drift losses frequently remove all the particles during short time intervals. As the March 1991 event (in the middle of the figure) was very strong, it removes particles down to L = 2.2 in the simulation. Then new particles seems to be created near L = 3.5 but this effect is due to particle acceleration from plasmasheet by radial diffusion. As radial diffusion goes down with L, these two combined processes (loss and radial diffusion) create two proton belts. From the same run, higher energy particles (36 MeV) can be deduced as shown on the bottom survey plot of Figure 8. Here the dynamics is different. It corresponds at high L values to the variations of the Solar Energetic Proton flux. These protons move with constant energy and flux down to L values around 3.5. Then, they can be stopped at the magnetic cut-off or penetrate in the radiation belt region, depending on the magnetic activity. When they are transported inside the trapping region, they produce (or enhance) a second belt which is clearly seen twice on the figure: - one at the beginning of the period, near L = 3.5. This second belt was created by the August 1, 1990 little storm and the coincident SEPE (see Hudson et al., 1999). It disappears suddenly during the August 14, 1990 little storm, due to drift loss,

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D. Boscherand S. Bourdarie MMeV.cm2.s.sr L

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Figure 7: Salammbo proton results during the CRRES life: unidirectional (top panel) and 36 MeV (bottom panel).

equatorial fluxes for 1.5 MeV

- one after the March 1991 storm, at lower L values (L = 2.3) because of the higher intensity of the storm. In the absence of a new very strong storm, efficient to produce losses at so low L values, this second belt stays there for months. All these processes can be modeled in a classical diffusion code, as it is made in Salammbo. Nevertheless, the quantitative parameters are not exactly well known (the real location of the cut-off, which depends on magnetic activity, the radial diffusion coefficients,...), so it seems impossible to reproduce the dynamics of the radiation belts in great details.

MODELING THE ELECTRON BELT The Figure 9 shows Salammbo electron results during an active period in September-October 1991 (survey plots for three different energies, from bottom to the top 100, 410, 1600 keV, and the magnetic activity index Kp) (Boscher et al., 1998, Boscher et al., 2000b). Here the injections (low energy flux at L = 7) are deduced from synchronous measurements. The lower energy panel (a) shows essentially the enhanced particle transport during magnetic active periods. But due to the pitch angle diffusion by waves, particles are lost at the same time in the slot region (between L = 2.8 and 4.5). Then the flux is varying during all the period, though globally it increases by a factor of 10 and more in this region. The middle energy (around 400 keV, panel b) shows typically the same phenomenon (enhanced radial diffusion), but due to the particle inertia, only increases are recorded. The two periods of high activity are clearly visible. The first storm “creates” particles in the L = 4 region (in fact, it is only a global acceleration of lower energy particles by radial diffusion), and the second storm pushes these

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particles inward by the same process. Here the slot region is not filled with particles, though it can appear in the case of a more intense storm. At higher energy (1.6 MeV, panel c), the plot shows the acceleration of energetic electrons in the outer belt, mainly by the recirculation process. Drift losses were not taken into account in this simulation. In this case, they could explain some differences between those results and measurements. The global dynamics of the electron belt is well reproduced in this simulation (Boscher and Bourdarie, 1998). Nevertheless, key parameters are not enough well known to quantitatively reproduce the dynamics of the electron belt.

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Figure 8: Salammb6 electron results during an active period in September-October 1991: Kp (bottom panel), omnidirectional equatorial flux for 100 keV (a), 410 keV (b) and 1.6 MeV (c).

CONCLUSION Though the main processes governing the creation and dynamics of the radiation belts are well understood, the importance of the different parameters acting during active periods is not completely elucidated. In particular, efforts must be made in the radial diffusion process, which is the most important one in the core of the belts. In order to reduce the uncertainties, these efforts must be made on both protons and electrons, as the same processes act on both particles. Nevertheless, it is not obvious to improve our knowledge on radial diffusion, as other processes take place during magnetic active periods in the same region (particularly losses), and the equation with time dependent diffusion is highly non linear. Moreover, other processes are acting during the same periods of time, which make the analysis

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difficult, in particular the adiabatic transport of particles and the shell splitting, which are both related to the magnetic field. The modeling of this magnetic field in particular during active periods is a key point to reach complete understanding of the radiation belt dynamics. Unless good models of the magnetic field exist in the inner region, more accurate mappings of the radiation belt will not be possible at all. References

Boscher, D., S. Bourdarie, Physical modeling of the outer belt high energy electrons, in “Workshop on Space Weather”, ESA WPP-155,411, Noordwijk (Netherlands), Nov 1998. Boscher, D., S. Bourdarie, R. Thorne, B. Abel, Influence of the wave characteristics on the electron radiation belt distribution, Adv. Space Res., 26, 163,200Oa. Boscher, D., S. Bourdarie, R. M. Thome, B. Abel, Toward nowcasting of the electron belt, submitted AGU monograph, Feb 2000b. Brautigham, D.H., M.S. Gussenhoven, E.G. Mullen, Quasi-static model of outer zone electrons, IEEE Trans. Nucl. Sci., 39, 1797, 1992. Desorgher, L., P. Btihler, A. Zehnder, E. 0. Fhickiger, Simulation of the outer radiation belt electron flux decrease during the March 26, 1995, magnetic storm, .I. Geophys. Res., 105,21211,2000. F~tharnmar, C.G., Effects of time-dependent electric fields on geomagnetically trapped radiation, .I. Geophys. Res., 70,2503, 1965. Friedel, R.H.W., A. Korth, Long-term observations of keV ion and electron variability in the outer radiation belt from CRRES, Geophys. Res. Z&t., 22, 1853, 1995. Gussenhoven, M.S., E.G. Mullen, D.H. Brautigham, Improved understanding of the Earth’s radiation belts from the CRRES satellite, IEEE Trans. Nucl. Sci., 43,353, 1996. Hess, W. N., The radiation belt and mametosnhere, ed. Blaisdell Publishing Co, Waltham, USA, 1968 Hudson, M., S. Elkington, J. Lyon, V. Marcher&o, I. Roth, M. Temerin, J. Blake, M. Gussenhoven, J. Wygant, Simulations of radiation belt formation during storm sudden commencements, J. Geophys. Res., 102, 14087, 1997. Liu, W. W., G. Rostoker, D. Baker, Internal acceleration of relativistic electrons by large-amplitude ULF pulsations, .I. Geophys. Res., 104, 17391, 1999. Roederer, J.G., Dvnamics of geomagnetically tranued radiation, ed. Springer-Verlag, Berlin, Germany, 1970. Schulz, M., L.J. Lanzerotti, Particle diffusion in the radiation belts, ed. Springer-Verlag, Berlin, Germany, 1974. Vacaresse, A., D. Boscher, S. Bourdarie, M. Blanc, J.-A. Sauvaud, Modeling the high energy proton belt, J. Geophys. Res., 104,28601, 1999. Vampola, A.L., Combined Release and Radiation Effects Satellite, J. Spacecraft, 29,555, 1992.