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2008 
This paper focuses on the modeling of local acceleration and loss processes in the outer radiation belt. We begin by reviewing the statistical properties of waves that violate the first and second adiabatic invariants, leading to the loss and acceleration of high energy electrons in the outer radiation belt. After a brief description of the most commonly accepted methodology for computing quasilinear diffusion coefficients, we present pitchangle scattering simulations by (i) plasmaspheric hiss, (ii) a combination of plasmaspheric hiss and electromagnetic ion cyclotron (EMIC) waves, (iii) chorus waves, and (iv) a combination of chorus and EMIC waves. Simulations of the local acceleration and loss processes show that statistically, the net effect of chorus waves is acceleration at MeV energies and loss at hundreds of keV energies. The combination of threedimensional (3D) simulations of the local processes and radial transport show that the complexity of the behavior of the radiation belts is due to a number of competing processes of acceleration and loss, and depends on the dynamics of the plasmasphere, ring current, and solar wind conditions. SHPRITS, Y; SUBBOTIN, D; MEREDITH, N; ELKINGTON, S; Published by: Journal of Atmospheric and SolarTerrestrial Physics Published on: 11/2008 YEAR: 2008 DOI: 10.1016/j.jastp.2008.06.014 
2007 
The energization of relativistic electrons in the outer Van Allen radiation belt The origin and dynamics of the Van Allen radiation belts is one of the longeststanding questions of the space age, and one that is increasingly important for space applications as satellite systems become more sophisticated, smaller and more susceptible to radiation effects. The precise mechanism by which the Earth\textquoterights magnetosphere is able to accelerate electrons from thermal to ultrarelativistic energies (Edouble greater than0.5 MeV) has been particularly difficult to definitively resolve. The traditional explanation is that largescale, fluctuating electric and magnetic fields energize particles through radial diffusion1. More recent theories2, 3 and observations4, 5 have suggested that gyroresonant wave\textendashparticle interactions may be comparable to or more important than radial diffusion. Using data collected simultaneously by multiple satellites passing through the magnetosphere at different distances from the Earth, we demonstrate that the latter of these is the dominant mechanism responsible for relativistic electron acceleration. Specifically, we identify frequent and persistent peaks in equatorial electron phase space density near or inside geosynchronous orbit that provide unambiguous evidence for local wave\textendashparticle acceleration. These observations represent an important step towards a more complete physical understanding of radiation belt dynamics and to the development of spaceweather models. Chen, Yue; Reeves, Geoffrey; Friedel, Reiner; Published by: Nature Physics Published on: 09/2007 YEAR: 2007 DOI: 10.1038/nphys655 
Radiation belt electrons can interact with various modes of plasma wave in their drift orbits about the Earth, including whistlermode chorus outside the plasmasphere, and both whistlermode hiss and electromagnetic ion cyclotron waves inside the plasmasphere. Electrons undergo gyroresonant diffusion in their interactions with these waves. To determine the timescales for electron momentum diffusion and pitch angle diffusion, we develop bounceaveraged quasilinear resonant diffusion coefficients for fieldaligned electromagnetic waves in a hydrogen or multiion (H+, He+, O+) plasma. We assume that the Earth\textquoterights magnetic field is dipolar and that the wave frequency spectrum is Gaussian. Evaluation of the diffusion coefficients requires the solution of a sixthorder polynomial equation for the resonant wave frequencies in the case of a multiion (H+, He+, O+) plasma, compared to the solution of a fourthorder polynomial equation for a hydrogen plasma. In some cases, diffusion coefficients for fieldaligned waves can provide a valuable approximation for diffusion rates for oblique waves calculated using higherorder resonances. Bounceaveraged diffusion coefficients for fieldaligned waves can be evaluated generally in minimal CPU time and can therefore be profitably incorporated into comprehensive kinetic radiation belt codes. Summers, D.; Ni, Binbin; Meredith, Nigel; Published by: Journal of Geophysical Research Published on: 04/2007 YEAR: 2007 DOI: 10.1029/2006JA011801 
2006 
Phase space density analysis of the outer radiation belt energetic electron dynamics We present an analysis of the electron phase space density in the Earth\textquoterights outer radiation belt during three magnetically disturbed periods to determine the likely roles of inward radial diffusion and local acceleration in the energization of electrons to relativistic energies. During the recovery phase of the 9 October 1990 storm and the period of prolonged substorms between 11 and 16 September 1990, the relativistic electron phase space density increases substantially and peaks in the phase space density occur in the region 4.0 < L* < 5.5 for values of the first adiabatic invariant, M >= 550 MeV/G, corresponding to energies, E > \~0.8 MeV. The peaks in the phase space density are associated with prolonged substorm activity, enhanced chorus amplitudes, and predominantly low values of the ratio between the electron plasma frequency, fpe, and the electron gyrofrequency, fce (fpe/fce < \~4). The data provide further evidence for a local wave acceleration process in addition to radial diffusion operating in the heart of the outer radiation belt. During the recovery phase of the 9 October 1990 storm the peaks are more pronounced at large M (550 MeV/G) and large Kaufmann K (0.11 equation imageRE) than large M (700 MeV/G) and small K (0.025 equation imageRE), which suggests that radial diffusion is more effective below about 0.7 MeV for 5.0 < L* < 5.5 during this period. At low M (M <= 250 MeV/G), corresponding to energies, E < \~0.8 MeV, there is no evidence for a peak in phase space density and the data are more consistent with inward radial diffusion and losses to the atmosphere by pitch angle scattering. During the 26 August 1990 storm there is a net loss in the relativistic electron phase space density for 3.3 < L* < 6.0. At low M (M <= 250 MeV/G) the phase space density decreases by almost a constant factor and the gradient remains positive for all L*, but at high M (M >= 550 MeV/G) the decrease in phase space density is greater at larger L* and the gradient changes from positive to negative. The data show that it is possible to have inward radial diffusion at low energies and outward radial diffusion at higher energies, which would fill the outer radiation belt. Iles, Roger; Meredith, Nigel; Fazakerley, Andrew; Horne, Richard; Published by: Journal of Geophysical Research Published on: 03/2006 YEAR: 2006 DOI: 10.1029/2005JA011206 
2005 
Wave acceleration of electrons in the Van Allen radiation belts The Van Allen radiation belts1 are two regions encircling the Earth in which energetic charged particles are trapped inside the Earth\textquoterights magnetic field. Their properties vary according to solar activity2, 3 and they represent a hazard to satellites and humans in space4, 5. An important challenge has been to explain how the charged particles within these belts are accelerated to very high energies of several million electron volts. Here we show, on the basis of the analysis of a rare event where the outer radiation belt was depleted and then reformed closer to the Earth6, that the long established theory of acceleration by radial diffusion is inadequate; the electrons are accelerated more effectively by electromagnetic waves at frequencies of a few kilohertz. Wave acceleration can increase the electron flux by more than three orders of magnitude over the observed timescale of one to two days, more than sufficient to explain the new radiation belt. Wave acceleration could also be important for Jupiter, Saturn and other astrophysical objects with magnetic fields. Horne, Richard; Thorne, Richard; Shprits, Yuri; Meredith, Nigel; Glauert, Sarah; Smith, Andy; Kanekal, Shrikanth; Baker, Daniel; Engebretson, Mark; Posch, Jennifer; Spasojevic, Maria; Inan, Umran; Pickett, Jolene; Decreau, Pierrette; Published by: Nature Published on: 09/2005 YEAR: 2005 DOI: 10.1038/nature03939 
Techniques are presented for efficiently evaluating quasilinear diffusion coefficients for whistler mode waves propagating according to the full cold plasma index of refraction. In particular, the density ratio ωpe/Ωe can be small, which favors energy diffusion. This generalizes an approach, previously used for highdensity hiss and electromagnetic ion cyclotron waves, of identifying (and omitting) ranges of wavenormal angle θ that are incompatible with cyclotron resonant frequencies ω occurring between sharp cutoffs of the modeled wave frequency spectrum. This requires a detailed analysis of the maximum and minimum values of the refractive index as a function of ω and θ, as has previously been performed in the highdensity approximation. Sample calculations show the effect of lowdensity ratio on the pitch angle and energy diffusion coefficients modeling the effect of chorus waves on radiation belt electrons. The highdensity approximation turns out to be quite robust, especially when the upper frequency cutoff is small compared with Ωe. The techniques greatly reduce the amount of computation needed for a sample calculation, while taking into account all resonant harmonic numbers n up to \textpm$\infty$. Published by: Journal of Geophysical Research Published on: 03/2005 YEAR: 2005 DOI: 10.1029/2004JA010844 
2004 
Relativistic electrons in the outer radiation belt: Differentiating between acceleration mechanisms Many theoretical models have been developed to explain the rapid acceleration to relativistic energies of electrons that form the Earth\textquoterights radiation belts. However, after decades of research, none of these models has been unambiguously confirmed by comparison to observations. Proposed models can be separated into two types: internal and external source acceleration mechanisms. Internal source acceleration mechanisms accelerate electrons already present in the inner magnetosphere (L < 6.6), while external source acceleration mechanisms transport and accelerate a source population of electrons from the outer to the inner magnetosphere. In principle, the two types of acceleration mechanisms can be differentiated because they imply that different radial gradients of electron phase space density expressed as a function of the three adiabatic invariants will develop. Model predictions can be tested by transforming measured electron flux (given as a function of pitch angle, energy, and position) to phase space density as a function of the three invariants, μ, K, and Φ. The transformation requires adoption of a magnetic field model. Phase space density estimates have, in the past, produced contradictory results because of limited measurements and field model errors. In this study we greatly reduce the uncertainties of previous work and account for the contradictions. We use data principally from the Polar High Sensitivity Telescope energetic detector on the Polar spacecraft and the Tsyganenko and Stern [1996] field model to obtain phase space density. We show how imperfect magnetic field models produce phase space density errors and explore how those errors modify interpretations. On the basis of the analysis we conclude that the data are best explained by models that require acceleration of an internal source of electrons near L* \~ 5. We also suggest that outward radial diffusion from a phase space density peak near L* \~ 5 can explain the observed correspondence between flux enhancements at geostationary orbit and increases in ULF wave power. Published by: Journal of Geophysical Research Published on: 03/2004 YEAR: 2004 DOI: 10.1029/2003JA010153 
2003 
We examine signatures of two types of waves that may be involved in the acceleration of energetic electrons in Earth\textquoterights outer radiation belts. We have compiled a database of ULF wave power from SAMNET and IMAGE ground magnetometer stations for 1987\textendash2001. Longduration, comprehensive, in situ VLF/ELF chorus wave observations are not available, so we infer chorus wave activity from lowaltitude SAMPEX observations of MeV electron microbursts for 1996\textendash2001 since microbursts are thought to be caused by interactions between chorus and trapped electrons. We compare the ULF and microburst observations to in situ trapped electrons observed by highaltitude satellites from 1989\textendash2001. We find that electron acceleration at low L shells is closely associated with both ULF activity and MeV microbursts and thereby probably also with chorus activity. Electron flux enhancements across the outer radiation belt are, in general, related to both ULF and VLF/ELF activity. However, we suggest that electron flux peaks observed at L \~ 4.5 are likely caused by VLF/ELF wave acceleration, while ULF activity probably produces the dominant electron acceleration at geosynchronous orbit and beyond. O\textquoterightBrien, T.; Lorentzen, K.; Mann, I.; Meredith, N.; Blake, J.; Fennell, J.; Looper, M.; Milling, D.; Anderson, R.; Published by: Journal of Geophysical Research Published on: 08/2003 YEAR: 2003 DOI: 10.1029/2002JA009784 
We perform a survey of the plasma wave and particle data from the CRRES satellite during 26 geomagnetically disturbed periods to investigate the viability of a local stochastic electron acceleration mechanism to relativistic energies driven by Dopplershifted cyclotron resonant interactions with whistler mode chorus. Relativistic electron flux enhancements associated with moderate or strong storms may be seen over the whole outer zone (3 < L < 7), typically peaking in the range 4 < L < 5, whereas those associated with weak storms and intervals of prolonged substorm activity lacking a magnetic storm signature (PSALMSS) are typically observed further out in the regions 4 < L < 7 and 4.5 < L < 7, respectively. The most significant relativistic electron flux enhancements are seen outside of the plasmapause and are associated with periods of prolonged substorm activity with AE greater than 100 nT for a total integrated time greater than 2 days or greater than 300 nT for a total integrated time greater than 0.7 days. These events are also associated with enhanced fluxes of seed electrons and enhanced lowerband chorus wave power with integrated lowerband chorus wave intensities of greater than 500 pT2 day. No significant flux enhancements are seen unless the level of substorm activity is sufficiently high. These results are consistent with a local, stochastic, chorusdriven electron acceleration mechanism involving the energization of a seed population of electrons with energies of a few hundred keV to relativistic energies operating on a timescale of the order of days. Meredith, Nigel; Cain, Michelle; Horne, Richard; Thorne, Richard; Summers, D.; Anderson, Roger; Published by: Journal of Geophysical Research Published on: 06/2003 YEAR: 2003 DOI: 10.1029/2002JA009764 
1998 
Resonant diffusion curves for electron cyclotron resonance with fieldaligned electromagnetic R mode and L mode electromagnetic ion cyclotron (EMIC) waves are constructed using a fully relativistic treatment. Analytical solutions are derived for the case of a singleion plasma, and a numerical scheme is developed for the more realistic case of a multiion plasma. Diffusion curves are presented, for plasma parameters representative of the Earth\textquoterights magnetosphere at locations both inside and outside the plasmapause. The results obtained indicate minimal electron energy change along the diffusion curves for resonant interaction with L mode waves. Intense storm time EMIC waves are therefore ineffective for electron stochastic acceleration, although these waves could induce rapid pitch angle scattering for ≳ 1 MeV electrons near the duskside plasmapause. In contrast, significant energy change can occur along the diffusion curves for interaction between resonant electrons and whistler (R mode) waves. The energy change is most pronounced in regions of low plasma density. This suggests that whistler mode waves could provide a viable mechanism for electron acceleration from energies near 100 keV to above 1 MeV in the region outside the plasmapause during the recovery phase of geomagnetic storms. A model is proposed to account for the observed variations in the flux and pitch angle distribution of relativistic electrons during geomagnetic storms by combining pitch angle scattering by intense EMIC waves and energy diffusion during cyclotron resonant interaction with whistler mode chorus outside the plasmasphere. Summers, D.; Thorne, Richard; Xiao, Fuliang; Published by: Journal of Geophysical Research Published on: 09/1998 YEAR: 1998 DOI: 10.1029/98JA01740 
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