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2020 
In this study we focus on the radiation belt dynamics driven by the geomagnetic storms during September 2017. Besides the longlasting threebelt structures of ultrarelativistic electrons (>2 MeV, existing for tens of days), which has been studied intensively during the Van Allen Probe era, it is found that magnetospheric electrons of hundreds of keVs can also have threebelt structures at similar L extent during storm time. Measurements of 500–800 keV electrons from MagEIS instrument onboard Van Allen Probes show doublepeaked (L = 3.5 and 4.5, respectively) fluxversusLshell profile in the outer belt, which lasted for 2–3 days. During the time interval of such transient threebelt structure, the energyversusL spectrogram shows novel distributions differing from both “Sshaped” and “Vshaped” spectrograms reported previously. Such peculiar distribution also illustrates the energydependent occurrence of the threebelt profile. The gradual formation of “reversed energy spectrum” at L ∼ 3.5 also indicates that hiss scattering inside the plasmapause contributed to the fast decay of subMeV remnant belt. Hao, Y.; Zong, Q.G.; Zhou, X.Z.; Zou, H.; Rankin, R.; Sun, Y.; Chen, X.; Liu, Y.; Fu, S; Baker, D.; Spence, H.; Blake, J.; Reeves, G.; Claudepierre, S.; Published by: Journal of Geophysical Research: Space Physics Published on: 07/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2020JA028031 storage ring; threebelt structure; hiss wave; electron lifetime; Radial Transport; Van Allen Probes 
Evolutions of equatorial ring current ions during a magnetic storm In this paper, we present evolutions of the phase space density (PSD) spectra of ring current (RC) ions based on observations made by Van Allen Probe B during a geomagnetic storm on 23–24 August 2016. By analyzing PSD spectra ratios from the initial phase to the main phase of the storm, we find that during the main phase, RC ions with low magnetic moment μ values can penetrate deeper into the magnetosphere than can those with high μ values, and that the μ range of PSD enhancement meets the relationship: S(O+) > S(He+) > S(H+). Based on simultaneously observed ULF waves, theoretical calculation suggests that the radial transport of RC ions into the deep inner magnetosphere is caused by driftbounce resonance interactions, and the efficiency of these resonance interactions satisfies the relationship: η(O+) > η(He+) > η(H+), leading to the differences in μ range of PSD enhancement for different RC ions. In the recovery phase, the observed decay rates for different RC ions meet the relationship: R(O+) > R(He+) > R(H+), in accordance with previous theoretical calculations, i.e., the charge exchange lifetime of O+ is shorter than those of H+ and He+. Huang, Zheng; Yuan, Zhigang; Yu, Xiongdong; Published by: Earth and Planetary Physics Published on: 03/2020 YEAR: 2020 DOI: 10.26464/epp2020019 ULF waves; ring current; waveparticle interactions; Radial Transport; Geomagnetic storm; Decay rates; Van Allen Probes 
2018 
During geomagnetic storms the intensities of the outer radiation belt electron population can exhibit dramatic variability. Deep depletions in intensity during the main phase are followed by increases during the recovery phase, often to levels that significantly exceed their prestorm values. To study these processes, we simulate the evolution of the outer radiation belt during the 17 March 2013 geomagnetic storm using our newlydeveloped radiation belt model (CHIMP) based on test particle and coupled 3D ring current and global MHD simulations, and driven solely with solar wind and F10.7 flux data. Our approach differs from previous work in that we use MHD information to identify regions of strong, bursty, and azimuthally localized Earthward convection in the magnetotail where test particles are then seeded. We validate our model using in situ Van Allen Probe electron intensities over a multiday period and show that our model is able to reproduce meaningful qualitative and quantitative agreement. Analysis of our model enables us to study the processes that govern the transition from the pre to poststorm outer belt. Our analysis demonstrates that during the early main phase of the storm the preexisting outer belt is largely wiped out via magnetopause losses and subsequently a new outer belt is created during a handful of discrete, mesoscale injections. Finally, we demonstrate the potential importance of magnetic gradient trapping in the transport and energization of outer belt electrons using a controlled numerical experiment. Sorathia, K.; Ukhorskiy, A; Merkin, V.; Fennell, J.; Claudepierre, S.; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2018 YEAR: 2018 DOI: 10.1029/2018JA025506 dropout; Geomagnetic storms; magnetopause loss; Radial Transport; Radiation belt; Van Allen Probes 
Observations during the main phase of geomagnetic storms reveal an anticorrelation between the occurrence of broadband low frequency electromagnetic waves and outer radiation belt electron flux. We show that the driftbounce motion of electrons in the magnetic field of these waves leads to rapid electron transport. For observed spectral energy densities it is demonstrated that the wave magnetic field can drive radial diffusion via driftbounce resonance on timescales less than a drift orbit. This process may provide outward transport sufficient to account for electron \textquotedblleftdropouts\textquotedblright during storm main phase and more generally modulate the outer radiation belt during geomagnetic storms. Chaston, C.; Bonnell, J.; Wygant, J.; Reeves, G.; Baker, D.; Melrose, D.; Published by: Geophysical Research Letters Published on: 02/2018 YEAR: 2018 DOI: 10.1002/2017GL076362 Alfven waves; Geomagnetic storms; Radial Transport; Radiation belts; Van Allen Probes 
2015 
Global StormTime Depletion of the Outer Electron Belt The outer radiation belt consists of relativistic (>0.5 MeV) electrons trapped on closed trajectories around Earth where the magnetic field is nearly dipolar. During increased geomagnetic activity, electron intensities in the belt can vary by ordersof magnitude at different spatial and temporal scale. The main phase of geomagnetic storms often produces deep depletions of electron intensities over broad regions of the outer belt. Previous studies identified three possible processes that can contribute to the mainphase depletions: adiabatic inflation of electron drift orbits caused by the ring current growth, electron loss into the atmosphere, and electron escape through the magnetopause boundary. In this paper we investigate the relative importance of the adiabatic effect and magnetopause loss to the rapid depletion of the outer belt observed at the Van Allen Probes spacecraft during the main phase of March 17, 2013 storm. The intensities of >1 MeV electrons were depleted by more than an order of magnitude over the entire radial extent of the belt in less than 6 hours after the sudden storm commencement. For the analysis we used threedimensional testparticle simulations of global evolution of the outer belt in the TsyganenkoSitnov (TS07D) magnetic field model with an inductive electric field. Comparison of the simulation results with electron measurements from the MagEIS experiment shows that magnetopause loss accounts for most of the observed depletion at L>5, while at lower L shells the depletion is adiabatic. Both magnetopause loss and the adiabatic effect are controlled by the change in global configuration of the magnetic field due to stormtime development of the ring current; a simulation of electron evolution without a ring current produces a much weaker depletion. Ukhorskiy, A; Sitnov, M.; Millan, R.; Kress, B.; Fennell, J.; Claudepierre, S.; Barnes, R.; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2015 YEAR: 2015 DOI: 10.1002/2014JA020645 dropout; Geomagnetic storms; magnetopause loss; Radial Transport; Radiation belt; ring current; Van Allen Probes 
2008 
Radial transport in the outer radiation belt due to global magnetospheric compressions Earth\textquoterights outer radiation belt is populated by relativistic electrons that produce a complex dynamical response to varying geomagnetic activity. One fundamental process defining global state of the belt is radial transport of electrons across their drift shells. Radial transport is induced by resonant interaction of electron drift motion with ULF oscillations of electric and magnetic fields and is commonly believed to be a diffusive process. The goal of this paper is the analysis of radial transport due to typical ULF fluctuations in the inner magnetospheric fields. For this purpose a testparticle approach is used in the guiding center approximation. In particular we consider ULF oscillations due to global magnetospheric compressions. It is shown that typical pressure variations induce largescale fluctuations in magnetic and inductive electric fields that produce a substantial impact on relativistic electrons. Electron motion becomes stochastic due to overlap of electron populations trapped in the vicinities of drift resonances with adjacent harmonics of the field spectrum. It is shown that in spite of the underlying stochasticity the radial diffusion limit is not fully attainable in the outer radiation belt. This is attributed to the fact that phase correlations in electron motion do not have time to decay due to finite size of the system. As a result collective motion of the outer belt electrons can exhibit large deviations from radial diffusion. Solution of the full Liouville\textquoterights equation is required for accurate description of radial transport in the belt. Published by: Journal of Atmospheric and SolarTerrestrial Physics Published on: 11/2008 YEAR: 2008 DOI: 10.1016/j.jastp.2008.07.018 
In this paper, we focus on the modeling of radial transport in the Earth\textquoterights outer radiation belt. A historical overview of the first observations of the radiation belts is presented, followed by a brief description of radial diffusion. We describe how resonant interactions with poloidal and toroidal components of the ULF waves can change the electron\textquoterights energy and provide radial displacements. We also present radial diffusion and guiding center simulations that show the importance of radial transport in redistributing relativistic electron fluxes and also in accelerating and decelerating radiation belt electrons. We conclude by presenting guiding center simulations of the coupled particle tracing and magnetohydrodynamic (MHD) codes and by discussing the origin of relativistic electrons at geosynchronous orbit. Local acceleration and losses and 3D simulations of the dynamics of the radiation belt fluxes are discussed in the companion paper [Shprits, Y.Y., Subbotin, D.A., Meredith, N.P., Elkington, S.R., 2008. Review of modeling of losses and sources of relativistic electrons in the outer radiation belt II: Local acceleration and loss. Journal of Atmospheric and SolarTerrestrial Physics, this issue. doi:10.1016/j.jastp.2008.06.014]. SHPRITS, Y; ELKINGTON, S; MEREDITH, N; SUBBOTIN, D; Published by: Journal of Atmospheric and SolarTerrestrial Physics Published on: 11/2008 YEAR: 2008 DOI: 10.1016/j.jastp.2008.06.008 
[1] The interaction between relativistic, equatorially mirroring electrons and Pc5 Ultra Low Frequency (ULF) waves in the magnetosphere is investigated using a numerical MagnetoHydroDynamic (MHD) model for waves and a testkinetic model for electron phase space density (PSD). The temporal and spatial characteristics of a ULF wave packet are constrained using groundbased observations of narrowband ULF activity following a geomagnetic storm on 24 March 1991, which occurred from 1200 to 1340 Universal Time (UT). A salient feature of the ULF waves during this interval was the apparent localization of the ULF wave power to the dayside of the magnetosphere and the antisunward propagation of ULF wave phase in the morning and afternoon sectors. This is interpreted to imply a localized source of ULF wave power close to noon Magnetic Local Time (MLT) at the magnetopause. The expected electron dynamics are investigated using model wavefields to predict the observable characteristics of the interaction in satellite electron flux data. The wave and kinetic models show that the localized radial motion of magnetic field lines associated with MHD fast waves propagating from the ULF source region acts to periodically inject electrons from high L to lower L within the magnetosphere. This action becomes resonant when the drift period of the electrons matches a multiple of the ULF wave period and leads to an enhancement in radial transport. Published by: Journal of Geophysical Research Published on: 10/2008 YEAR: 2008 DOI: 10.1029/2008JA013254 
2007 
The effect of ULF compressional modes and field line resonances on relativistic electron dynamics The adiabatic, driftresonant interaction between relativistic, equatorially mirroring electrons and a ULF compressional wave that couples to a field line resonance (FLR) is modelled. Investigations are focussed on the effect of azimuthal localisation in wave amplitude on the electron dynamics. The ULF wave fields on the equatorial plane (r , φ ) are modelled using a box model [Zhu, X., Kivelson, M.G., 1988. Analytic formulation and quantitative solutions of the coupled ULF wave problem. J. Geophys. Res. 93(A8), 8602\textendash8612], and azimuthal variations are introduced by adding a discrete spectrum of azimuthal modes. Electron trajectories are calculated using drift equations assuming constant magnetic moment M , and the evolution of the distribution function f(r,φ,M,t) from an assumed initial condition is calculated by assuming f remains constant along electron trajectories. The azimuthal variation in ULF wave structure is shown to have a profound effect on the electron dynamics once a threshold in azimuthal variation is exceeded. Electron energy changes occur that are significantly larger than the trapping width corresponding to the maximum wave amplitude. We show how this can be explained in terms of the overlap of multiple resonance islands, produced by the introduction of azimuthal amplitude variation. This anomalous energisation is characterised by performing parameter scans in the modulation amplitude ε and the wave electric field. A simple parametric model for the threshold is shown to give reasonable agreement with the threshold observed in the electron dynamics model. Above the threshold, the radial transport averaged over φ is shown to become diffusive in nature over a timescale of about 25 wave periods. The anomalous energisation described in this paper occurs over the first 15 wave periods, indicating the importance of convective transport in this process. Degeling, A.; Rankin, R.; Kabin, K.; Marchand, R.; Mann, I.R.; Published by: Planetary and Space Science Published on: 04/2007 YEAR: 2007 DOI: 10.1016/j.pss.2006.04.039 
2006 
In an MHD particle simulation of the September 1998 magnetic storm the evolution of the radiation belt electron radial flux profile appears to be diffusive, and diffusion caused by ULF waves has been invoked as the probable mechanism. In order to separate adiabatic and nonadiabatic effects and to investigate the radial diffusion mechanism during this storm, in this work we solve a radial diffusion equation with ULF wave diffusion coefficients and a timedependent outer boundary condition, and the results are compared with the phase space density of the MHD particle simulation. The diffusion coefficients include contributions from both symmetric resonance modes (ω ≈ mωd, where ω is the wave frequency, m is the azimuthal wave number, and ωd is the bounceaveraged drift frequency) and asymmetric resonance modes (ω ≈ (m \textpm 1)ωd). ULF wave power spectral densities are obtained from a Fourier analysis of the electric and magnetic fields of the MHD simulation and are used in calculating the radial diffusion coefficients. The asymmetric diffusion coefficients are proportional to the magnetic field asymmetry, which is also calculated from the MHD field. The resulting diffusion coefficients vary with the radial coordinate L (the Roederer Lvalue) and with time during different phases of the storm. The last closed drift shell defines the location of the outer boundary. Both the location of the outer boundary and the value of the phase space density at the outer boundary are timevarying. The diffusion calculation simulates a 42hour period during the 24\textendash26 September 1998 magnetic storm, starting just before the storm sudden commencement and ending in the late recovery phase. The differential flux calculated in the MHD particle simulation is converted to phase space density. Phase space densities in both simulations (diffusion and MHD particle) are functions of Roederer Lvalue for fixed first and second adiabatic invariants. The Roederer Lvalue is calculated using drift shell tracing in the MHD magnetic field, and particles have zero second invariant. The radial diffusion calculation reproduces the main features of the MHD particle simulation quite well. The symmetric resonance modes dominate the radial diffusion, especially in the inner and middle L region, while the asymmetric resonances are more important in the outer region. Using both symmetric and asymmetric terms gives a better result than using only one or the other and is better than using a simple power law diffusion coefficient. We find that it is important to specify the value of the phase space density on the outer boundary dynamically in order to get better agreement between the radial diffusion simulation and the MHD particle simulation. Fei, Yue; Chan, Anthony; Elkington, Scot; Wiltberger, Michael; Published by: Journal of Geophysical Research Published on: 12/2006 YEAR: 2006 DOI: 10.1029/2005JA011211 
In the present work, a test particle simulation is performed in a model of analytic Ultra Low Frequency, ULF, perturbations in the electric and magnetic fields of the Earth\textquoterights magnetosphere. The goal of this work is to examine if the radial transport of energetic particles in quiettime ULF magnetospheric perturbations of various azimuthal mode numbers can be described as a diffusive process and be approximated by theoretically derived radial diffusion coefficients. In the model realistic compressional electromagnetic field perturbations are constructed by a superposition of a large number of propagating electric and consistent magnetic pulses. The diffusion rates of the electrons under the effect of the fluctuating fields are calculated numerically through the testparticle simulation as a function of the radial coordinate L in a dipolar magnetosphere; these calculations are then compared to the symmetric, electromagnetic radial diffusion coefficients for compressional, poloidal perturbations in the Earth\textquoterights magnetosphere. In the model the amplitude of the perturbation fields can be adjusted to represent realistic states of magnetospheric activity. Similarly, the azimuthal modulation of the fields can be adjusted to represent different azimuthal modes of fluctuations and the contribution to radial diffusion from each mode can be quantified. Two simulations of quiettime magnetospheric variability are performed: in the first simulation, diffusion due to poloidal perturbations of mode number m=1 is calculated; in the second, the diffusion rates from multiplemode (m=0 to m=8) perturbations are calculated. The numerical calculations of the diffusion coefficients derived from the particle orbits are found to agree with the corresponding theoretical estimates of the diffusion coefficient within a factor of two. Sarris, T.; Li, X.; Temerin, M.; Published by: Annales Geophysicae Published on: 10/2006 YEAR: 2006 DOI: 10.5194/angeo2425832006 
A review of ULF interactions with radiation belt electrons Energetic particle fluxes in the outer zone radiation belts can vary over orders of magnitude on a variety of timescales. Power at ULF frequencies, on the order of a few millihertz, have been associated with changes in flux levels among relativis tic electrons comprising the outer zone of the radiation belts. Power in this part of the spectrum may occur as a result of a number of processes, including internally generated waves induced by plasma instabilities, and externally generated processes such as shear instabilities at the flanks or compressive variations in the solar wind. Changes in the largescale convective motion of the magnetosphere are another important class of externally driven variations with power at ULF wavelengths. The mechanism for interaction between ULF variations and the radiation belts may result in (or require) pitch angle scattering, or may conserve the first two adiabatic invariants of particle motion. Of the latter class of interactions, radial diffusion describes the result when ULF variations lead to stochastic motion among the particle populations, and has been studied extensively as a description of radial transport within the belts. Rates of radial diffusion depend strongly on the characteristics of the driving ULF waves. This work is intended as a non exhaustive review of radiation belt interactions with ULF waves, outlining the cur rent theories and methods in studying the interaction, and describing pertinent wave properties Published by: Published on: YEAR: 2006 DOI: 10.1029/169GM12 
2005 
Impact of toroidal ULF waves on the outer radiation belt electrons Relativistic electron fluxes in the outer radiation belt exhibit highly variable complex behavior. Previous studies have established a strong correlation of electron fluxes and the inner magnetospheric ULF waves in the Pc 3\textendash5 frequency range. Resonant interaction of ULF waves with the drift motion of radiation belt electrons violates their third adiabatic invariant and consequently leads to their radial transport. If the waveparticle interaction has a stochastic character, then the electron transport is diffusive. The goal of this paper is to analyze the impact of toroidal ULF waves on radiation belt electrons. The study is based on direct measurements of ULF electric fields on the CRRES spacecraft. We show that the electric fields of inner magnetospheric toroidal ULF waves exhibit high asymmetry in magnetic local time and have narrowband frequency spectra. Such narrowband waves can induce radial diffusion of energetic electrons, if an extrinsic stochasticity is introduced in the system. The quasiperiodic variations in the solar wind dynamic pressure are identified as a possible source of extrinsic stochasticity. In the asymmetric magnetic field, drifting electrons can interact with both azimuthal and radial electric field components. We derive analytically and then calculate numerically the diffusion rates associated with azimuthal and radial electric field components of the waves. It is shown that even under highly disturbed geomagnetic conditions, when the background field asymmetry is large, the diffusion rates due to the radial field component are small. At the same time, the resonant scattering of energetic electrons by the azimuthal electric field of the waves provides an efficient form of radial diffusion and therefore can play an important role in the dynamics of the outer radiation belt. Ukhorskiy, A; Takahashi, K; Anderson, B.; Korth, H.; Published by: Journal of Geophysical Research Published on: 10/2005 YEAR: 2005 DOI: 10.1029/2005JA011017 
The influence of ultralow frequency (ULF) waves in the Pc5 frequency range on radiation belt electrons in a compressed dipole magnetic field is examined. This is the first analysis in three dimensions utilizing model ULF wave electric and magnetic fields on the guiding center trajectories of relativistic electrons. A model is developed, describing magnetic and electric fields associated with poloidal mode Pc5 ULF waves. The frequency and L dependence of the ULF wave power are included in this model by incorporating published groundbased magnetometer data. It is demonstrated here that realistic spectral characteristics play a significant role in the rate of diffusion of relativistic electrons via drift resonance with poloidal mode ULF waves. Radial diffusion rates including bounce motion show a weak pitch angle dependence for αeq >= 50\textdegree (λ <= 20\textdegree) for a power spectral density which is Lindependent. The databased model for greater power at higher L values yields stronger diffusion at αeq = 90\textdegree. The L6 dependence of the diffusion coefficient which is obtained for a power spectral density which is Lindependent is amplified by power spectral density which increases with L. During geomagnetic storms when ULF wave power is increased, ULF waves are a significant driver of increased fluxes of relativistic electrons inside geosynchronous orbit. Diffusion timescales obtained here, when frequency and L dependence comparable to observations of ULF wave power are included, support this conclusion. Perry, K.; Hudson, M.; Elkington, S.; Published by: Journal of Geophysical Research Published on: 03/2005 YEAR: 2005 DOI: 10.1029/2004JA010760 
2004 
Time dependent radial diffusion modeling of relativistic electrons with realistic loss rates Model simulations are compared to the typically observed evolution of MeV electron fluxes during geomagnetic storms to investigate whether radial diffusion alone can account for the observed variability and to estimate the effect of electron lifetimes. We demonstrate that knowledge of lifetimes is crucial for understanding the radial structure of the stormtime radiation belts and their temporal evolution. Our model results suggest that outer zone lifetimes at 1 MeV are on the order of few days during quitetimes and less than a day during stormtime conditions. Losses outside plasmasphere should be included in the modeling of electron fluxes since effective lifetimes are much shorter than that of plasmaspheric losses. Simulations with variable outer boundary conditions show that the depletion of the main phase relativistic electron fluxes at L <= 4 can not be explained only by variations in fluxes near geosynchronous orbit and require local lifetimes as short as 0.5 day. Radial diffusion alone is unable to account for either the gradual build up of relativistic electron fluxes or the maxima in phase space density near L = 4  5 observed during the recovery phase of many storms, which suggests that an additional local acceleration source is also required. Published by: Geophysical Research Letters Published on: 04/2004 YEAR: 2004 DOI: 10.1029/2004GL019591 
2003 
Using the data from the NOAA and ExosD satellites during the 3 November 1993 magnetic storm, the dynamic behavior of electrons with energies from a few tens of kiloelectronvolts to a few and its relation to plasma waves were examined. After the late main phase, relativistic electron flux started to recover from the heart of the outer radiation belt, where the cold plasma density was extremely low, and intense whistler mode chorus emissions were detected. The phase space density showed a peak in the outer belt, and the peak increased gradually. The simulation of the inward radial diffusion process could not reproduce the observed energy spectrum and phase space density variation. On the other hand, the simulated energy diffusion due to the gyroresonant electronwhistler mode wave interactions, under the assumption of the Kolmogorov turbulence spectrum, could generate the relativistic electrons without the flux transport from the outer region. The present study suggested that the seed population of relativistic electrons, which appeared in the heart of the outer radiation belt during the late main phase, was the ring current electrons injected from the plasma sheet, and that the acceleration by whistler mode chorus via gyroresonant wave\textendashparticle interactions outside the plasmapause could play an important role to generate the relativistic electrons. Published by: Journal of Geophysical Research Published on: 03/2003 YEAR: 2003 DOI: 10.1029/2001JA007542 
Resonant acceleration and diffusion of outer zone electrons in an asymmetric geomagnetic field [1] The outer zone radiation belt consists of energetic electrons drifting in closed orbits encircling the Earth between \~3 and 7 RE. Electron fluxes in the outer belt show a strong correlation with solar and magnetospheric activity, generally increasing during geomagnetic storms with associated high solar wind speeds, and increasing in the presence of magnetospheric ULF waves in the Pc5 frequency range. In this paper, we examine the influence of Pc5 ULF waves on energetic electrons drifting in an asymmetric, compressed dipole and find that such particles may be efficiently accelerated through a driftresonant interaction with the waves. We find that the efficiency of this acceleration increases with increasing magnetospheric distortion (such as may be attributed to increased solar wind pressure associated with high solar wind speeds) and with increasing ULF wave activity. A preponderance of ULF power in the dawn and dusk flanks is shown to be consistent with the proposed acceleration mechanism. Under a continuum of wave modes and frequencies, we find that the drift resonant acceleration process leads to additional modes of radial diffusion in the outer belts, with timescales that may be appropriate to those observed during geomagnetic storms. Published by: Journal of Geophysical Research Published on: 03/2003 YEAR: 2003 DOI: 10.1029/2001JA009202 
2000 
The response of outer radiation belt relativistic electrons to the October 9, 1990, magnetic storm is analyzed in detail using a radial diffusion model and data from the Combined Release and Radiation Effects Satellite (CRRES) and the Los Alamos National Laboratory (LANL) geosynchronous satellite 1989046. Electron measurements are expressed in terms of phase space density as a function of the three adiabatic invariants determined from CRRES magnetic field data and the Tsyganenko 1989 Kpdependent magnetic field model. The radial diffusion model is implemented with a timedependent radial diffusion coefficient parameterized by Kp, and a timedependent outer boundary condition scaled by geosynchronous electron data. The results show that radial diffusion propagates outer boundary variations into the heart of the outer radiation belt, accounting for both significant decreases and increases in the <1 MeV electron flux throughout that region. It is further shown that the gradual increase throughout the recovery phase of the >1 MeV electrons is inconsistent with the radial diffusion model given the parameter regime chosen for this study. Greatly enhanced whistler chorus waves observed by CRRES throughout the recovery phase suggest that a possible explanation for the inconsistency may be electron acceleration via waveparticle interaction. Published by: Journal of Geophysical Research Published on: 01/2000 YEAR: 2000 DOI: 10.1029/1999JA900344 
1999 
There has been increasing evidence that Pc5 ULF oscillations play a fundamental role in the dynamics of outer zone electrons. In this work we examine the adiabatic response of electrons to toroidalmode Pc5 field line resonances using a simplified magnetic field model. We find that electrons can be adiabatically accelerated through a driftresonant interaction with the waves, and present expressions describing the resonance condition and halfwidth for resonant interaction. The presence of magnetospheric convection electric fields is seen to increase the rate of resonant energization, and allow bulk acceleration of radiation belt electrons. Conditions leading to the greatest rate of acceleration in the proposed mechanism, a nonaxisymmetric magnetic field, superimposed toroidal oscillations, and strong convection electric fields, are likely to prevail during storms associated with high solar wind speeds. Elkington, Scot; Hudson, M.; Chan, Anthony; Published by: Geophysical Research Letters Published on: 11/1999 YEAR: 1999 DOI: 10.1029/1999GL003659 
1988 
Simultaneous Radial and Pitch Angle Diffusion in the Outer Electron Radiation Belt A solution of the bimodal (radial and pitch angle) diffusion equation for the radiation belts is developed with special regard for the requirements of satellite radiation belt data analysis. In this paper, we use this solution to test the bimodal theory of outer electron belt diffusion by confronting it with satellite data. Satellite observations, usually over finite volumes of (L, t) space, are seldom sufficient in spacetime duration to cover the relaxation to equilibrium of the entire radiation belt. Since time scales of continuous data coverage are often comparable to that of radiation belt disturbances, it is therefore inappropriate to apply impulsive semiinfinite time response solutions of diffusion theory to interpret data from a finite window of (L, t) space. Observational limitations indicate that appropriate solutions for the interpretation of satellite data are general solutions for a finitevolume boundary value problem in bimodal diffusion. Here we test such a solution as the prime candidate for comprehensive radiation belt dynamic modeling by applying the solution and developing a method of analysis to radiation belt electron data obtained by the SCATHA satellite at moderate geomagnetic activity. The results and the generality of our solution indicate its promise as a new approach to dynamic modeling of the radiation belts. Chiu, Y.; Nightingale, R.; Rinaldi, M.; Published by: Journal of Geophysical Research Published on: 04/1988 YEAR: 1988 DOI: 10.1029/JA093iA04p02619 
1981 
An account is given of measurements of electrons made by the LLNL magnetic electron spectrometer (60\textendash3000 keV in seven differential energy channels) on the Ogo 5 satellite in the earth\textquoterights outerbelt regions during 1968 and early 1969. The data were analyzed to identify those features dominated by pitch angle and radial diffusion; in doing so all aspects of phase space covered by the data were studied, including pitch angle distributions and spectral features, as well as decay rates. The pitch angle distributions are reported elsewhere. The spectra observed in the weeks after a storm at L \~3\textendash4.5 show the evolution of a peak at \~1.5 MeV and pronounced minima at \~0.5 MeV. The observed pitch angle diffusion lifetimes are identified as being the shortest decays observed and are found to be highly energy and L dependent with minimum lifetimes of \~1\textendash2 days occurring at L \~3\textendash4.5. Two contiguous periods of decay, following the intense storm injection on October 31 and November 1, were analyzed in terms of radial diffusion. Significant differences were found between the derived values of DLL for the two periods; also significant energy dependence shows in the results. Although the values of DLL vary by about a factor of 10, representative values are 0.3 day1 at L=6, 0.06 at L=4, 0.015 at L=3, and 0.001 at L=2.5. Despite the wide variation of many prior results in the literature, there is a family of results in approximate agreement with the present results. By noting the variations in DLL, as a function of the invariant quantities, we are able to order a fair body of previous results with our new results. West, H.; Buck, R.; Davidson, G.; Published by: Journal of Geophysical Research Published on: 04/1981 YEAR: 1981 DOI: 10.1029/JA086iA04p02111 
1979 
Direct Evaluation of the Radial Diffusion Coefficient near L = 6 Due to Electric Field Fluctuations The radial diffusion coefficient for radiation belt particles near L=6 has been calculated from the measured electric field fluctuations. Simultaneous balloon flights in August 1974 from six auroral zone sites ranging 180\textdegree in magnetic longitude produced the electric field data. The large scale slowly varying ionospheric electric fields from these flights have been mapped to the equator during the quiet magnetic conditions of this campaign. These mapped equatorial electric fields were then Fourier transformed in space and time to produce power spectra of the first two terms of the global azimuthal electric field. From these power spectra the radial diffusion coefficient has been calculated. Published by: Journal of Geophysical Research Published on: 06/1979 YEAR: 1979 DOI: 10.1029/JA084iA06p02559 
1973 
Measurements at conjugate points on the ground near L = 4 of the power spectra of magneticfield fluctuations in the frequency range 0.5 to 20 mHz are used as a means of estimating daily values for the relativisticelectron radialdiffusion coefficient DLL for two periods in December 1971 and January 1972. The values deduced for L10 DLL show a strong variation with magnetic activity, as measured by the Fredricksburg magnetic index KFR. The radialdiffusion coefficient typically increases by a factor of \~10 for a unit increase in KFR. When KFR ≲ 2, it is generally found that DLL ≲ 2 \texttimes 109 L10 day1 for equatorially mirroring electrons having a first invariant M = 750 Mev/gauss; a value of DLL \~4 \texttimes 107 L10 day1 is deduced for one day on which the mean KFR was 4.5. The quantity L10 DLL theoretically depends on energy and L as (L/M)(s2)/2 for relativistic particles, where s is the logarithmic slope of the powerlaw spectrum of magnetic fluctuations observed on the ground. For the time period analyzed, s typically had values between 1 and 3. Lanzerotti, L.; Morgan, Caroline; Published by: Journal of Geophysical Research Published on: 08/1973 YEAR: 1973 DOI: 10.1029/JA078i022p04600 
1972 
InnerZone EnergeticElectron Repopulation by Radial Diffusion A quantitative study of the intrusion of natural electrons into the inner radiation zone during and after the geomagnetic storm of September 2, 1966, shows that the transport is consistent with a radialdiffusion mechanism in which the first two invariants are conserved. Except for the 3day period of the storm main phase when data were missing, the radialdiffusion coefficient is D = 2.7 \texttimes 105 L7.9 μ0.5 day1 in the range 1.7 <= L <= 2.6 and 13.3 <= μ <= 27.4 Mev gauss1. This value could be produced by variation of a largescale electric field across the magnetosphere having an amplitude of 0.28 mv / m and a period of 1600 sec. Electric fields having approximately these characteristics have been inferred from previous observations of the motion of whistler ducts within the plasmapause. If fields of this amplitude and period exist throughout the magnetosphere, the radial diffusion of all geomagnetically trapped particles except the highenergy innerzone protons is strongly influenced by electricfield variations. A comprehensive review of previously reported radialdiffusion coefficients shows reasonable agreement for L less than about 3.0, but serious discrepancies among reported values exist for determinations made in the outer zone. These discrepancies cannot be explained by the simple theory of radial diffusion due to variation of largescale electric or magnetic fields. Tomassian, Albert; Farley, Thomas; Vampola, Alfred; Published by: Journal of Geophysical Research Published on: 07/1972 YEAR: 1972 DOI: 10.1029/JA077i019p03441 
1970 
Radial Diffusion of OuterZone Electrons: An Empirical Approach to ThirdInvariant Violation The nearequatorial fluxes of outerzone electrons (E>0.5 Mev and E>1.9 Mev) measured by an instrument on the satellite Explorer 15 following the geomagnetic storm of December 17\textendash18, 1962, are used to determine the electron radial diffusion coefficients and electron lifetimes as functions of L for selected values of the conserved first invariant \textmu. For each value of \textmu, the diffusion coefficient is assumed to be timeindependent and representable in the form D = DnLn. The diffusion coefficients and lifetimes are then simultaneously obtained by requiring that the Ldependent reciprocal electron lifetime, as determined from the FokkerPlanck equation, deviate minimally from a constant in time. Applied to the data, these few assumptions yield a value of D that is smaller by approximately a factor of 10 than the value recently found by Newkirk and Walt in a separate analysis of 1.6Mev electron data obtained during the same time period on another satellite. The electron lifetimes are found to be strong functions of L, with 4 to 6day lifetimes observed at the higher L values (4.6\textendash4.8). Lanzerotti, L.; Maclennan, C.; Schulz, Michael; Published by: Journal of Geophysical Research Published on: 10/1970 YEAR: 1970 DOI: 10.1029/JA075i028p05351 
1969 
Radial Diffusion of Starfish Electrons A study of the change in electron intensities in the Starfish electron belt from January 1, 1963, to November 3, 1965, indicates that radial diffusion, both inward and outward from L of 1.40, was a significant loss mechanism for these electrons during this period. For L values of 1.20 and below, the indicated steepening of the pitchangle distributions during this period has been interpreted as the result of a radial diffusion source for each L shell concentrated near the geomagnetic equator. Since pitchangle diffusion lifetimes are not well known for 1.20 < L < 1.65, a definitive radial diffusion coefficient cannot be computed from these data. A maximum reasonable diffusion coefficient (mean square displacement per unit time) computed for this range of L for this period has a minimum at L of 1.31, and a value of 4.4 \texttimes 105 RE\texttwosuperior/day at that point. This maximum coefficient, representing an average over a 3year period, is more than an order of magnitude too small to account for the apparent radial diffusion of natural electrons into this region that took place in September 1966. The results are, however, consistent with population of the inner zone by radial electron diffusion occurring during relatively short periods during which the diffusion coefficient is enhanced by two or three orders of magnitude. Published by: Journal of Geophysical Research Published on: 07/1969 YEAR: 1969 DOI: 10.1029/JA074i014p03591 
Convection Electric Fields and the Diffusion of Trapped Magnetospheric Radiation We explore here the possible importance of timedependent convection electric fields as an agent for diffusing trapped magnetospheric radiation inward toward the earth. By using a formalism (Birmingham, Northrop, and Fälthammar, 1967) based on first principles, and by adopting a simple model for the magnetosphere and its electric field, we succeed in deriving a onedimensional diffusion equation to describe statistically the lossfree motion of mirroring particles with arbitrary but conserved values of the first two adiabatic invariants M and J. Solution of this equation bears out the fact that reasonable electric field strengths, correlated in time for no longer than the azimuthal drift period of an average particle, move particles toward the earth at a rate at least an order of magnitude faster than electric fields whose source is a fluctuating current on the magnetopause. Published by: Journal of Geophysical Research Published on: 05/1969 YEAR: 1969 DOI: 10.1029/JA074i009p02169 
Diffusion of Equatorial Particles in the Outer Radiation Zone Expansions and contractions of the permanently compressed magnetosphere lead to the diffusion of equatorially trapped particles across drift shells. A general technique for obtaining the electric fields induced by these expansions and contractions is described and applied to the Mead geomagnetic field model. The resulting electric drifts are calculated and are superimposed upon the gradient drift executed by a particle that conserves its first (μ) and second (J = 0) adiabatic invariants. The noonmidnight asymmetry of the unperturbed drift trajectory (resulting from gradient drift alone) is approximated by means of a simple model. In this model the angular drift frequency is found to be the geometric mean of a particle\textquoterights angular drift velocities at noon and midnight. The radial diffusion coefficient D = (\textonehalf) (ΔL)\texttwosuperior/time is calculated as a function of the McIlwain parameter L and in terms of the spectral density of fluctuations in the standoff distance of the magnetosphere boundary. Because the unperturbed drift trajectories are asymmetric, driftresonant diffusion of particles is produced by spectral components at all harmonics of the drift frequency, although the first (fundamental) harmonic is the major contributor. Schulz, Michael; Eviatar, Aharon; Published by: Journal of Geophysical Research Published on: 05/1969 YEAR: 1969 DOI: 10.1029/JA074i009p02182 
Particle fluxes in the outer geomagnetic field The outer geomagnetic field comprises the outer radiation belt, consisting of electrons with energies of 104\textendash107 ev, and the unstable radiation zone. The outer radiation belt is bounded on its inner side by a gap, which is at various times located at a distance of 2.2\textendash3.5 RE and in which a considerable precipitation of electrons from radiation belts occurs, possibly owing to a high intensity of electromagnetic waves. The boundary separating the outer radiation belt from the unstable radiation zone is at λ \~ 71\textdegree and \~9 RE in the equatorial plane on the sunlit side, and at 7\textendash8 RE in the equatorial plane on the nightside. Beyond this, the unstable radiation zone extends out to the magnetosphere boundary and up to λ \~ 77\textdegree on the sunlit side, and out to 14\textendash15 RE on the nightside. The relatively rapid electron intensity variations with periods of 1\textendash7 days are essentially absent at distances less than that of the outer belt but are distinctly seen in the outer belt. In the unstable radiation zone the intensity of electrons with energies of the order of 105 ev changes by several times, and good correlation is observed with the increase in Kp. Analysis of the outer belt data shows that this belt is formed partly by electron diffusion into the magnetosphere (like the belt of protons with energies of 105\textendash107 ev) and partly by the simultaneous acceleration of electrons at various distances from the earth. A comparison of electron intensity changes with the solar activity cycle shows little or no correlation for electrons with Ee > 40 kev. The intensity of electrons with Ee > 500 kev has changed significantly; in 1964 it was 30 times lower than in 1959. The absence of significant dependence of the diffusion coefficients for electrons with E \~ 104\textendash105 ev on the phase of the solar activity cycle shows that the relatively weak magnetic disturbances that do not change with the phase of the cycle are of major importance in diffusion. This suggests that these magnetic disturbances appear at great distances from the sun because of the instabilities of plasma itself and, therefore, that they depend little on solar activity. Vernov, S.; Gorchakov, E.; Kuznetsov, S.; Logachev, Yu.; Sosnovets, E.; Stolpovsky, V.; Published by: Reviews of Geophysics Published on: 02/1969 YEAR: 1969 DOI: 10.1029/RG007i001p00257 
1968 
Radial Diffusion Coefficient for Electrons at 1.76 < L < 5 Radial diffusion by nonconservation of the third adiabatic invariant of particle motion is assumed in analyzing experiments in which electrons appeared to move across field lines. Timedependent solutions of the FokkerPlanck diffusion equation are obtained numerically and fitted to the experimental results by adjusting the diffusion coefficient. Values deduced for the diffusion coefficient vary from 1.3 \texttimes 105 RE\texttwosuperior/day at L = 1.76 to 0.10 RE\texttwosuperior/day at L = 5. In the interval 2.6 < L < 5, the coefficient varies as L10\textpm1. Assuming a constant electron source of arbitrary magnitude at L = 6 and the above diffusion coefficients, the equatorial equilibrium distribution is calculated for electrons with energies above 1.6 Mev. The calculation yields an outer belt of electrons whose radial distribution is in good agreement with the observed belt. The calculated distribution also exhibits an inner belt at L ≈ 1.5. However, the calculated intensity of the inner belt relative to the outer belt is several orders of magnitude smaller than the experimental ratio. Published by: Journal of Geophysical Research Published on: 12/1968 YEAR: 1968 DOI: 10.1029/JA073i023p07231 
Radial Diffusion Coefficient for Electrons at Low L Values An empirical evaluation of the diffusion coefficient for trapped electrons diffusing across low L shells is obtained by adjusting the coefficient to account for the observed radial profile and the longterm decay rate of the trapped electron flux. The diffusion mechanism is not identified, but it is assumed that the adiabatic invariants \textmu and J are conserved. The average value of the coefficient for electrons > 1.6 Mev energy is found to decrease monotonically from \~4 \texttimes 106 RE\texttwosuperior/day at L = 1.16 to \~2 \texttimes 107 RE\texttwosuperior/day at L = 1.20. Published by: Journal of Geophysical Research Published on: 02/1968 YEAR: 1968 DOI: 10.1029/JA073i003p01013 
1965 
Effects of timedependent electric fields on geomagnetically trapped radiation. Largescale electric potential fields in the magnetosphere are generally invoked in theories of the aurora. It is shown in the present article that irregular fluctuations of such fields cause a random radial motion of trapped energetic particles by violating the third adiabatic invariant. When the first and second invariants are conserved, any radial motion of the particles is associated with a corresponding energy change. Some particles move outward and others inward; but, if there is a source in the outer magnetosphere and a sink farther in, there will be a net inward transport and an associated net energy gain. This mechanism supplements that of particle transport by magnetic disturbances, which has already been discussed in the literature. The transport and acceleration of energetic particles by fluctuating electric potential fields have a formal similarity to the socalled stochastic mode of acceleration in synchrocyclotrons. In the magnetosphere, the rate of displacement of trapped particles is found to depend on the spectral power density of the fluctuating electric fields at the azimuthal drift frequency and its harmonics. Which of these frequencies is most important depends on the spatial structure of the fluctuations. The observational data needed for numerical evaluation of the rate of transport are still lacking, but the formulas derived serve the purpose of indicating what properties of the fields are important and ought to be measured experimentally. The effects of magnetic time variations, which have been discussed in the literature under special assumptions, are considered in a more general way. A firstorder result is given, which applies not only to initial phases of magnetic storms but also to other types of magnetic time variations. Published by: Journal of Geophysical Research Published on: 06/1965 YEAR: 1965 DOI: 10.1029/JZ070i011p02503 
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