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2021 
Abstract Radiation belt electrons undergo frequent acceleration, transport, and loss processes under various physical mechanisms. One of the most prevalent mechanisms is radial diffusion, caused by the resonant interactions between energetic electrons and ULF waves in the Pc45 band. An indication of this resonant interaction is believed to be the appearance of periodic flux oscillations. In this study, we report longlasting, driftperiodic flux oscillations of relativistic and ultrarelativistic electrons with energies up to ∼7.7 MeV in the outer radiation belt, observed by the Van Allen Probes mission. During this March 2017 event, multiMeV electron flux oscillations at the electron drift frequency appeared coincidently with enhanced Pc5 ULF wave activity and lasted for over 10 hours in the center of the outer belt. The amplitude of such flux oscillations is well correlated with the radial gradient of electron phase space density (PSD), with almost no oscillation observed near the PSD peak. The temporal evolution of the PSD radial profile also suggests the dominant role of radial diffusion in multiMeV electron dynamics during this event. By combining these observations, we conclude that these multiMeV electron flux oscillations are caused by the resonant interactions between electrons and broadband Pc5 ULF waves and are an indicator of the ongoing radial diffusion process during this event. They contain essential information of radial diffusion and have the potential to be further used to quantify the radial diffusion effects and aid in a better understanding of this prevailing mechanism. This article is protected by copyright. All rights reserved. Zhao, Hong; Sarris, Theodore; Li, Xinlin; Weiner, Max; Huckabee, Isabela; Baker, Daniel; Jaynes, Allison; Kanekal, Shrikanth; Elkington, Scot; Barani, Mohammad; Tu, Weichao; Liu, Wenlong; Zhang, Dianjun; Hartinger, Michael; Published by: Journal of Geophysical Research: Space Physics Published on: 07/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2021JA029284 Radiation belt; multiMeV electrons; radial diffusion; ULF waves; Waveparticle interaction; Phase space density radial gradient; Van Allen Probes 
A Comparison of Radial Diffusion Coefficients in 1D and 3D LongTerm Radiation Belt Simulations AbstractRadial diffusion is one of the dominant physical mechanisms driving acceleration and loss of radiation belt electrons. A number of parameterizations for radial diffusion coefficients have been developed, each differing in the dataset used. Here, we investigate the performance of different parameterizations by Brautigam and Albert (2000), Brautigam et al. (2005), Ozeke et al. (2014), Ali et al. (2015); Ali et al. (2016); Ali (2016), and Liu et al. (2016) on longterm radiation belt modeling using the Versatile Electron Radiation Belt (VERB) code, and compare the results to Van Allen Probes observations. First, 1D radial diffusion simulations are performed, isolating the contribution of solely radial diffusion. We then take into account effects of local acceleration and loss showing additional 3D simulations, including diffusion across pitchangle, energy, and mixed diffusion. For the L* range studied, the difference between simulations with Brautigam and Albert (2000), Ozeke et al. (2014), and Liu et al. (2016) parameterizations is shown to be small, with Brautigam and Albert (2000) offering the smallest averaged (across multiple energies) absolute normalized difference with observations. Using the Ali et al. (2016) parameterization tended to result in a lower flux than both the observations and the VERB simulations using the other coefficients. We find that the 3D simulations are less sensitive to the radial diffusion coefficient chosen than the 1D simulations, suggesting that for 3D radiation belt models, a similar result is likely to be achieved, regardless of whether Brautigam and Albert (2000), Ozeke et al. (2014), and Liu et al. (2016) parameterizations are used.This article is protected by copyright. All rights reserved. Drozdov, A; Allison, H.; Shprits, Y; Elkington, S.R.; Aseev, N.A.; Published by: Journal of Geophysical Research: Space Physics Published on: 07/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2020JA028707 Radiation belts; radial diffusion; VERB code; Van Allen Probes 
The Roles of the Magnetopause and Plasmapause in StormTime ULF Wave Power Enhancements Abstract Ultra Low Frequency (ULF) waves play a crucial role in transporting and coupling energy within the magnetosphere. During geomagnetic storms, dayside magnetospheric ULF wave power is highly variable with strong enhancements that are dominated by elevated solar wind driving. However, the radial distribution of ULF wave power is complex  controlled interdependently by external solar wind driving and the internal magnetospheric structuring. We conducted a statistical analysis of observed stormtime ULF wave power from the Van Allen Probes spacecraft within 2012  2016. Focusing on the dayside (06 < Magnetic Local Time ≤ 15), we observe large enhancements across 3 < L < 6 and a steep L dependence during the main phase. We consider how accounting for concurrent magnetopause and plasmapause locations may reduce statistical variability and improve parameterisation of spatial trends over and above using the L value. Ordering storm time ULF wave power by L provides the weakest dependences from those considered, whereas ordering by distance from the magnetopause is more effective. We also explore dependences on local plasma density and find that spatially localised ULF wave power enhancements are confined within high density patches in the afternoon sector (likely plasmaspheric plumes). The results have critical implications for empirical models of ULF wave power and radial diffusion coefficients. We highlight the necessity of improved characterisation of the highly distorted stormtime cold plasma density distribution, in order to more accurately predict ULF wave power. Sandhu, J.; Rae, I.; Staples, F.; Hartley, D.; Walach, M.T.; Elsden, T.; Murphy, K.; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2021JA029337 ULF waves; Geomagnetic storms; Van Allen Probes; radial diffusion; inner magnetosphere; plasmasphere 
Modeling the Dynamics of Radiation Belt Electrons with Source and Loss Driven by the Solar Wind Abstract A radial diffusion model directly driven by the solar wind is developed to reproduce MeV electron variations between L=212 (L is L* in this study) from October 2012 to April 2015. The radial diffusion coefficient, internal source rate, quick loss due to EMIC waves, and slow loss due to hiss waves are all expressed in terms of the solar wind speed, dynamic pressure, and interplanetary magnetic field (IMF). The model achieves a prediction efficiency (PE) of 0.45 at L=5 and 0.51 at L=4 after converting the electron phase space densities to differential fluxes and comparing with Van Allen Probes measurements of 2 MeV and 3 MeV electrons at L=5 and L=4, respectively. Machine learning techniques are used to tune parameters to get higher PE. By tuning parameters for every 60day period, the model obtains PE values of 0.58 and 0.82 at L=5 and L=4, respectively. Inspired by these results, we divide the solar wind activity into three categories based on the condition of solar wind speed, IMF Bz, and dynamic pressure, and then tune these three sets of parameters to obtain the highest PE. This experiment confirms that the solar wind speed has the greatest influence on the electron flux variations, particularly at higher L, while the dynamic pressure has more influence at lower L. Also, the PE at L=4 is mostly higher than those at L=5, suggesting that the electron loss due to the magnetopause shadowing combined with the outward radial diffusion is not well captured in the model. This article is protected by copyright. All rights reserved. Xiang, Zheng; Li, Xinlin; Kapali, Sudha; Gannon, Jennifer; Ni, Binbin; Zhao, Hong; Zhang, Kun; Khoo, Leng; Published by: Journal of Geophysical Research: Space Physics Published on: 05/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2020JA028988 Radiation belt; Solar wind; flux prediction; radial diffusion; magnetopause shadowing; waveparticle interactions; Van Allen Probes 
Abstract The impact of radial diffusion in storm time radiation belt dynamics is welldebated. In this study we quantify the changes and variability in radial diffusion coefficients during geomagnetic storms. A statistical analysis of Van Allen Probes data (2012 − 2019) is conducted to obtain measurements of the magnetic and electric power spectral densities for Ultra Low Frequency (ULF) waves, and corresponding radial diffusion coefficients. The results show global wave power enhancements occur during the storm main phase, and continue into the recovery phase. Local time asymmetries show sources of wave power are both external solar wind driving and internal sources from coupling with ring current ions and substorms. Wave power enhancements are also observed at low L values (L < 4). The accessibility of wave power to low L is attributed to a depression of the Alfvén continuum. The increased wave power drives enhancements in both the magnetic and electric field diffusion coefficients by more than an order of magnitude. Significant variability in diffusion coefficients is observed, with values ranging over several orders of magnitude. A comparison to the Kp parameterised empirical model of Ozeke et al. (2014) is conducted and indicates important differences during storm times. Although the electric field diffusion coefficient is relatively well described by the empirical model, the magnetic field diffusion coefficient is approximately ∼ 10 times larger than predicted. We discuss how differences could be attributed to dataset limitations and assumptions. Alternative stormtime radial diffusion coefficients are provided as a function of L* and storm phase. Sandhu, J.; Rae, I.; Wygant, J.; Breneman, A.; Tian, S.; Watt, C.; Horne, R.; Ozeke, L.; Georgiou, M.; Walach, M.T.; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2020JA029024 ULF waves; radial diffusion; outer radiation belt; Van Allen Probes; Geomagnetic storms 
2020 
Simulations of Electron Flux Oscillations as Observed by MagEIS in Response to Broadband ULF Waves Coherent electron flux oscillations of hundreds of keV are often observed by the Van Allen Probes in the magnetosphere during quiet times in association with ultralow frequency (ULF) waves. They are observed in the form of periodic flux fluctuations, with a drift frequency that is energy dependent, but are not associated with drift echoes following storm or substormrelated energetic particle injections. Instead, they are associated with the resonant interaction of electrons with ULF waves and are an indication of ongoing electron radial diffusion. To investigate details of such flux oscillations, particletracing simulations are conducted under the effect of realistic, broadband ULF electric and consistent magnetic fluctuations. Virtual detectors are simulated along spacecraft orbits and the results are compared to measurements. Through a parametric study, it is found that the width of electron energy channels is a critical parameter affecting the observed amplitude of flux oscillations, with narrower energy channel widths enabling the observation of higheramplitude flux oscillations; this potentially explains why such features were not observed regularly before the Van Allen Probes era, as previous spacecraft generally had lower energy resolution, which only enabled the observation of largeamplitude drift echoes following a storm or substorm. Results are confirmed using the Magnetic Electron Ion Spectrometer (MagEIS) ultrahigh energy resolution data. Energy width effects are quantified through a parametric simulation study that matches flux oscillation observations during a period that is characterized by extremely quiet conditions, where the Van Allen Probes observed flux oscillations over multiple days. Sarris, Theodore; Li, Xinlin; Temerin, Michael; Zhao, Hong; Khoo, Leng; Turner, Drew; Liu, Wenlong; Claudepierre, Seth; Published by: Journal of Geophysical Research: Space Physics Published on: 05/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2020JA027798 electron flux oscillations; ULF waves; Magnetosphere; Radiation belts; radial diffusion; particle tracing simulations; Van Allen Probes 
Bayesian Inference of QuasiLinear Radial Diffusion Parameters using Van Allen Probes Abstract The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is derived from a quasilinear approach with prescribed inner and outer boundary conditions. The 1D diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which is typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (e.g., Kp). These terms are typically empirically derived, not directly measurable, and hence are not known precisely, due to the inherent nonlinearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the empirical parameterization employed in the literature. Sarma, Rakesh; Chandorkar, Mandar; Zhelavskaya, Irina; Shprits, Yuri; Drozdov, Alexander; Camporeale, Enrico; Published by: Journal of Geophysical Research: Space Physics Published on: 04/2020 YEAR: 2020 DOI: 10.1029/2019JA027618 radial diffusion; Magnetosphere; Bayesian inference; Van Allen radiation belt; Van Allen Probes 
Bayesian Inference of QuasiLinear Radial Diffusion Parameters using Van Allen Probes The Van Allen radiation belts in the magnetosphere have been extensively studied using models based on radial diffusion theory, which is derived from a quasilinear approach with prescribed inner and outer boundary conditions. The 1D diffusion model requires the knowledge of a diffusion coefficient and an electron loss timescale, which is typically parameterized in terms of various quantities such as the spatial (L) coordinate or a geomagnetic index (e.g., Kp). These terms are typically empirically derived, not directly measurable, and hence are not known precisely, due to the inherent nonlinearity of the process and the variable boundary conditions. In this work, we demonstrate a probabilistic approach by inferring the values of the diffusion and loss term parameters, along with their uncertainty, in a Bayesian framework, where identification is obtained using the Van Allen Probe measurements. Our results show that the probabilistic approach statistically improves the performance of the model, compared to the empirical parameterization employed in the literature. Sarma, Rakesh; Chandorkar, Mandar; Zhelavskaya, Irina; Shprits, Yuri; Drozdov, Alexander; Camporeale, Enrico; Published by: Journal of Geophysical Research: Space Physics Published on: 04/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2019JA027618 radial diffusion; Magnetosphere; Bayesian inference; Van Allen radiation belt; Van Allen Probes 
2019 
Variability of the Proton Radiation Belt Significant steady but slow variability of radiation belt proton intensity, in the energy range \~19\textendash200 MeV and for L<2.4, has been observed in an empirical model derived from data taken by Van Allen Probes during 2013\textendash2019. It is compared to predictions of a theoretical model based on measured initial and boundary conditions. Two aspects of the variability are considered in detail and require adjustments to model parameters. Observed inward transport of proton intensity maxima near L=1.9 and associated increasing intensity are caused in the model by inward radial diffusion from an external source while conserving the first two adiabatic invariants. The diffusion coefficient is constrained by these observations and is required to have increased near the start of 2015 by a factor \~2. Observed decay of proton intensity at L<1.6 can be caused only in part by energy loss to free and bound electrons in the local plasma and neutral atmosphere. Another, unknown loss mechanism is required to match observed proton decay rates as a function of energy. Accounting for the expected influence of slow radial diffusion at low L, the additional loss should have a mean lifetime near 22 years, independent of L and energy in the range \~19\textendash70 MeV. Several candidate loss mechanisms are considered\textemdashadded plasma or neutral density, elastic Coulomb scattering, plasma wave scattering, fieldline curvature scattering, and collision with orbital debris\textemdashbut none are found viable. Published by: Journal of Geophysical Research: Space Physics Published on: 07/2019 YEAR: 2019 DOI: 10.1029/2019JA026754 
We present the temporal evolution of electron Phase Space Density (PSD) in the outer radiation belt during the intense March 2015 geomagnetic storm. Comparing observed PSD profiles as a function of L* at fixed first, M, and second, K, adiabatic invariants with those produced by simulations is critical for determining the physical processes responsible for the outer radiation belt dynamics. Here we show that the bulk of the accelerated and enhanced outer radiation belt population consists of electrons with K < 0.17 G1/2Re. For these electrons, the observed PSD versus L* profiles during the recovery phase of the storm have a positive radial gradient. We compare the observed temporal evolution of the PSD profiles during the recovery phase with those produced by radial diffusion simulations driven by observed Ultralow Frequency wave power as measured on the ground. Our results indicate that the dominant flux enhancement, inside L* < 5, in the heart of the outer radiation belt during the March 2015 geomagnetic storm is consistent with that produced by fast inward radial diffusion of electrons from a dynamic outer boundary driven by enhanced Ultralow Frequency wave power. Ozeke, L.; Mann, I.; Claudepierre, S.; Henderson, M.; Morley, S.; Murphy, K.; Olifer, L.; Spence, H.; Baker, D.; Published by: Journal of Geophysical Research: Space Physics Published on: 01/2019 YEAR: 2019 DOI: 10.1029/2018JA026326 Local Acceleration; March 2015 storm; Phase space density; radial diffusion; Radiation belt; ULF waves; Van Allen Probes 
2018 
Inward radial diffusion driven by ULF waves has long been known to be capable of accelerating radiation belt electrons to very high energies within the heart of the belts, but more recent work has shown that radial diffusion values can be highly eventspecific and mean values or empirical models may not capture the full significance of radial diffusion to acceleration events. Here we present an event of fast inward radial diffusion, occurring during a period following the geomagnetic storm of 17 March 2015. Ultrarelativistic electrons up to \~8 MeV are accelerated in the absence of intense higherfrequency plasma waves, indicating an acceleration event in the core of the outer belt driven primarily or entirely by ULF wavedriven diffusion. We examine this fast diffusion rate along with derived radial diffusion coefficients using particle and fields instruments on the Van Allen Probes spacecraft mission. Jaynes, A.; Ali, A.; Elkington, S.; Malaspina, D.; Baker, D.; Li, X.; Kanekal, S.; Henderson, M.; Kletzing, C.; Wygant, J.; Published by: Geophysical Research Letters Published on: 09/2018 YEAR: 2018 DOI: 10.1029/2018GL079786 Magnetosphere; radial diffusion; Radiation belts; ULF waves; Van Allen Probes 
A Statistical Survey of Radiation Belt Dropouts Observed by Van Allen Probes A statistical analysis on the radiation belt dropouts is performed based on 4 years of electron phase space density data from the Van Allen Probes. The μ, K, and L* dependence of dropouts and their driving mechanisms and geomagnetic and solar wind conditions are investigated using electron phase space density data sets for the first time. Our results suggest that electronmagnetic ion cyclotron (EMIC) wave scattering is the dominant dropout mechanism at low L* region, which requires the most active geomagnetic and solar wind conditions. In contrast, dropouts at high L* have a higher occurrence and are due to a combination of EMIC wave scattering and outward radial diffusion associated with magnetopause shadowing. In addition, outward radial diffusion at high L* is found to cause larger dropouts than EMIC wave scattering and is accompanied with active geomagnetic and solar wind drivers. Xiang, Zheng; Tu, Weichao; Ni, Binbin; Henderson, M.; Cao, Xing; Published by: Geophysical Research Letters Published on: 08/2018 YEAR: 2018 DOI: 10.1029/2018GL078907 EMIC wave; magnetopause shadowing; Phase space density; radial diffusion; radiation belt dropout; Van Allen Probes; wave particle interaction 
We simulate the radiation belt electron flux enhancements during selected Geospace Environment Modeling (GEM) challenge events to quantitatively compare the major processes involved in relativistic electron acceleration under different conditions. Van Allen Probes observed significant electron flux enhancement during both the storm time of 17\textendash18 March 2013 and non\textendashstorm time of 19\textendash20 September 2013, but the distributions of plasma waves and energetic electrons for the two events were dramatically different. During 17\textendash18 March 2013, the SYMH minimum reached 130 nT, intense chorus waves (peak Bw ~140 pT) occurred at 3.5 < L < 5.5, and several hundred keV to several MeV electron fluxes increased by ~2 orders of magnitude mostly at 3.5 < L < 5.5. During 19\textendash20 September 2013, the SYMH remained higher than 30 nT, modestly intense chorus waves (peak Bw ~80 pT) occurred at L > 5.5, and electron fluxes at energies up to 3 MeV increased by a factor of ~5 at L > 5.5. The two electron flux enhancement events were simulated using the available wave distribution and diffusion coefficients from the GEM focus group Quantitative Assessment of Radiation Belt Modeling. By comparing the individual roles of local electron heating and radial transport, our simulation indicates that resonant interaction with chorus waves is the dominant process that accounts for the electron flux enhancement during the storm time event particularly near the flux peak locations, while radial diffusion by ultralowfrequency waves plays a dominant role in the enhancement during the non\textendashstorm time event. Incorporation of both processes reasonably reproduces the observed location and magnitude of electron flux enhancement. Ma, Q.; Li, W.; Bortnik, J.; Thorne, R.; Chu, X.; Ozeke, L.; Reeves, G.; Kletzing, C.; Kurth, W.; Hospodarsky, G.; Engebretson, M.; Spence, H.; Baker, D.; Blake, J.; Fennell, J.; Claudepierre, S.; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2018 YEAR: 2018 DOI: 10.1002/2017JA025114 electron accelerationl whistler mode waves; radial diffusion; radiation belt simulation; Van Allen Probes; Van Allen Probes observation 
Previous studies have revealed a typical picture that seed electrons are transported inward under the drive of radial diffusion and then accelerated via chorus to relativistic energies. Here we show a potentially different process during the 2\textendash3 October 2013 storm when Van Allen Probes observed extremely rapid (by about 50 times in 2 h) flux enhancements of relativistic (1.8\textendash3.4 MeV) electrons but without distinct chorus at lower Lshells. Meanwhile, Time History of Events and Macroscale Interactions during Substorms satellites simultaneously measured enhanced chorus and fluxes of energetic (\~100\textendash300 keV) seed electrons at higher Lshells. Numerical calculations show that chorus can efficiently accelerate seed electrons at L \~ 8.3. Then radial diffusion further increased the phase space density of relativistic electrons throughout the outer radiation belts, with a remarkable agreement with the observation in magnitude and timescale. The current results provide a different physical scenario on the interplay between radial diffusion and local acceleration in outer radiation belt. Liu, Si; Yan, Qi; Yang, Chang; Zhou, Qinghua; He, Zhaoguo; He, Yihua; Gao, Zhonglei; Xiao, Fuliang; Published by: Geophysical Research Letters Published on: 02/2018 YEAR: 2018 DOI: 10.1002/grl.v45.310.1002/2017GL076513 chorusdriven acceleration; radial diffusion; Radiation belt; THEMIS; Van Allen Probes 
2017 
Rapid loss of radiation belt relativistic electrons by EMIC waves How relativistic electrons are lost is an important question surrounding the complex dynamics of the Earth\textquoterights outer radiation belt. Radial loss to the magnetopause and local loss to the atmosphere are two main competing paradigms. Here, on the basis of the analysis of a radiation belt storm event on 27 February 2014, we present new evidence for the EMIC wavedriven local precipitation loss of relativistic electrons in the heart of the outer radiation belt. During the main phase of this storm, the radial profile of relativistic electron phase space density was quasimonotonic, qualitatively inconsistent with the prediction of radial loss theory. The local loss at low Lshells was required to prevent the development of phase space density peak resulting from the radial loss process at high Lshells. The rapid loss of relativistic electrons in the heart of outer radiation belt was observed as a dip structure of the electron flux temporal profile closely related to intense EMIC waves. Our simulations further confirm that the observed EMIC waves within a quite limited longitudinal region was able to reduce the offequatorially mirroring relativistic electron fluxes by up to 2 orders of magnitude within about 1.5 h. Su, Zhenpeng; Gao, Zhonglei; Zheng, Huinan; Wang, Yuming; Wang, Shui; Spence, H.; Reeves, G.; Baker, D.; Wygant, J.; Published by: Journal of Geophysical Research: Space Physics Published on: 08/2017 YEAR: 2017 DOI: 10.1002/2017JA024169 electron loss; EMIC waves; pitch angle scattering; radial diffusion; Radiation belts; Van Allen Probes; Waveparticle interaction 
On the Relationship Between Electron Flux Oscillations and ULF WaveDriven Radial Transport The objective of this study is to investigate the relationship between the levels of electron flux oscillations and radial diffusion for different Phase Space Density (PSD) gradients, through observation and particle tracing simulations under the effect of model Ultra Low Frequency (ULF) fluctuations. This investigation aims to demonstrate that electron flux oscillation is associated with and could be used as an indicator of ongoing radial diffusion. To this direction, flux oscillations are observed through the Van Allen Probes\textquoteright MagEIS energetic particle detector; subsequently, flux oscillations are produced in a particle tracing model that simulates radial diffusion by using model magnetic and electric field fluctuations that are approximating measured magnetic and electric field fluctuations as recorded by the Van Allen Probes\textquoteright EMFISIS and EFW instruments, respectively. The flux oscillation amplitudes are then correlated with Phase Space Density gradients in the magnetosphere and with the ongoing radial diffusion process. Sarris, Theodore; Li, Xinlin; Temerin, Michael; Zhao, Hong; Califf, Sam; Liu, Wenlong; Ergun, Robert; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2017 YEAR: 2017 DOI: 10.1002/2016JA023741 Flux Oscillations; MAGEis; EMFISIS; EFW; Phase space density; radial diffusion; Radiation belts; Van Allen Probes 
The 17 March 2015 St. Patrick\textquoterights Day Storm is the largest geomagnetic storm to date of Solar Cycle 24, with a Dst of 223 nT. The magnetopause moved inside geosynchronous orbit under high solar wind dynamic pressure and strong southward IMF Bz causing loss, however a subsequent drop in pressure allowed for rapid rebuilding of the radiation belts. The 17 March 2013 storm also shows similar effects on outer zone electrons: first a rapid dropout due to inward motion of the magnetopause followed by rapid increase in flux above the prestorm level early in the recovery phase and a slow increase over the next 12 days. These phases can be seen in temporal evolution of the electron phase space density measured by the ECT instruments on Van Allen Probes. Using the LyonFedderMobarry global MHD model driven by upstream solar wind measurements, we simulated both St. Patrick\textquoterights Day 2013 and 2015 events, analyzing LFM electric and magnetic fields to calculate radial diffusion coefficients. These coefficients have been implemented in a radial diffusion code, using the measured electron phase space density following the local heating as the initial radial profile and outer boundary condition for subsequent temporal evolution over the next 12 days, beginning 18 March. Agreement with electron phase space density at 1000 MeV/G measured by the MagEIS component of the ECT instrument suite on Van Allen Probes was much improved using radial diffusion coefficients from the MHD simulations relative to coefficients parametrized by a global geomagnetic activity index. Li, Zhao; Hudson, Mary; Patel, Maulik; Wiltberger, Michael; Boyd, Alex; Turner, Drew; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2017 YEAR: 2017 DOI: 10.1002/2016JA023846 March 2013; March 2015; radial diffusion; Radiation belt; Van Allen Probes 
In September 2014 an unusually longlasting (≳10 days) ultrarelativistic electron flux depletion occurred in the outer radiation belt despite ongoing solar wind forcing. We simulate this period using a ULF wave radial diffusion model, driven by observed ULF wave power coupled to flux variations at the outer boundary at L* = 5, including empirical electron loss models due to chorus and hiss wave scattering. Our results show that unexplained rapid main phase loss, that depletes the belt within hours, is essential to explain the observations. Such ultrarelativistic electron extinction decouples the prestorm and poststorm fluxes, revealing the subsequent belt dynamics to be surprisingly independent of prestorm flux. However, once this extinction is included, ULF wave transport and coupling to the outer boundary explain the extended depletion event and also the eventual flux recovery. Neither local acceleration nor ongoing losses from hiss or chorus wave scattering to the atmosphere are required. Ozeke, Louis; Mann, Ian; Murphy, Kyle; Sibeck, David; Baker, Daniel; Published by: Geophysical Research Letters Published on: 03/2017 YEAR: 2017 DOI: 10.1002/2017GL072811 radial diffusion; Radiation belt; ULF waves; ultrarelativistic; Van Allen Probes; waveparticle interactions 
Radial diffusion is one of the dominant physical mechanisms that drives acceleration and loss of the radiation belt electrons, which makes it very important for nowcasting and forecasting space weather models. We investigate the sensitivity of the two parameterizations of the radial diffusion of Brautigam and Albert (2000) and Ozeke et al. (2014) on longterm radiation belt modeling using the Versatile Electron Radiation Belt (VERB). Following Brautigam and Albert (2000) and Ozeke et al. (2014), we first perform 1D radial diffusion simulations. Comparison of the simulation results with observations shows that the difference between simulations with either radial diffusion parameterization is small. To take into account effects of local acceleration and loss, we perform 3D simulations, including pitch angle, energy, and mixed diffusion. We found that the results of 3D simulations are even less sensitive to the choice of parameterization of radial diffusion rates than the results of 1D simulations at various energies (from 0.59 to 1.80 MeV). This result demonstrates that the inclusion of local acceleration and pitch angle diffusion can provide a negative feedback effect, such that the result is largely indistinguishable simulations conducted with different radial diffusion parameterizations. We also perform a number of sensitivity tests by multiplying radial diffusion rates by constant factors and show that such an approach leads to unrealistic predictions of radiation belt dynamics. Drozdov, A; Shprits, Y; Aseev, N.; Kellerman, A.; Reeves, G.; Published by: Space Weather Published on: 01/2017 YEAR: 2017 DOI: 10.1002/swe.v15.110.1002/2016SW001426 radial diffusion; Radiation belts; Van Allen Probes; VERB code 
2016 
Electric and Magnetic Radial Diffusion Coefficients Using the Van Allen Probes Data ULF waves are a common occurrence in the inner magnetosphere and they contribute to particle motion, significantly, at times. We used the magnetic and the electric field data from the EMFISIS and the EFW instruments on board the Van Allen Probes to estimate the ULF wave power in the compressional component of the magnetic field and the azimuthal component of the electric field, respectively. Using L*, Kp, and MLT as parameters, we conclude that the noon sector contains higher ULF Pc5 wave power compared with the other MLT sectors. The dawn, dusk, and midnight sectors have no statistically significant difference between them. The driftaveraged power spectral densities are used to derive the magnetic and the electric component of the radial diffusion coefficient. Both components exhibit little to no energy dependence, resulting in simple analytic models for both components. More importantly, the electric component is larger than the magnetic component by one to two orders of magnitude for almost all L* and Kp; thus, the electric field perturbations are more effective in driving radial diffusion of charged particles in the inner magnetosphere. We also present a comparison of the Van Allen Probes radial diffusion coefficients, including the error estimates, with some of the previous published results. This allows us to gauge the large amount of uncertainty present in such estimates. Ali, Ashar; Malaspina, David; Elkington, Scot; Jaynes, Allison; Chan, Anthony; Wygant, John; Kletzing, Craig; Published by: Journal of Geophysical Research: Space Physics Published on: 08/2016 YEAR: 2016 DOI: 10.1002/2016JA023002 Electric and Magnetic Components; radial diffusion; RBSP; Van Allen Probes 
The 17\textendash18 March 2015 storm is the largest geomagnetic storm in the Van Allen Probes era to date. The LyonFedderMobarry global MHD model has been run for this event using ARTEMIS data as solar wind input. The ULF wave power spectral density of the azimuthal electric field and compressional magnetic field is analyzed in the 0.5\textendash8.3 mHz range. The lowest three azimuthal modes account for 70\% of the total power during quiet times. However, during high activity, they are not exclusively dominant. The calculation of the radial diffusion coefficient is presented. We conclude that the electric field radial diffusion coefficient is dominant over the magnetic field coefficient by one to two orders of magnitude. This result contrasts with the dominant magnetic field diffusion coefficient used in most 3D diffusion models. Li, Zhao; Hudson, Mary; Paral, Jan; Wiltberger, Michael; Turner, Drew; Published by: Journal of Geophysical Research: Space Physics Published on: 07/2016 YEAR: 2016 DOI: 10.1002/2016JA022508 March 2015; radial diffusion; radial diffusion coefficient; Radiation belt; ULF waves; Van Allen Probes 
Inner zone and slot electron radial diffusion revisited Using recent data from NASA\textquoterights Van Allen Probes, we estimate the quiet time radial diffusion coefficients for electrons in the inner radiation belt (L < 3) with energies from ~50 to 750 keV. The observations are consistent with dynamics dominated by pitch angle scattering and radial diffusion. We use a coordinate system in which these two modes of diffusion are separable. Then we integrate phase space density over pitch angle to obtain a \textquotedblleftbundle content\textquotedblright that is invariant to pitch angle scattering, except for atmospheric loss. We estimate the effective radial diffusion coefficient from the temporal and radial variation of the bundle content. We show that our diffusion coefficients agree well with previously determined values obtained in the 1960s and 1970s and follow the form one expects for radial diffusion caused by exponentially decaying impulses in the largescale electrostatic potential. O\textquoterightBrien, T.; Claudepierre, S.; Guild, T.; Fennell, J.; Turner, D.; Blake, J.; Clemmons, J.; Roeder, J.; Published by: Geophysical Research Letters Published on: 07/2016 YEAR: 2016 DOI: 10.1002/2016GL069749 Inner zone; radial diffusion; Radiation belt; Van Allen Probes 
Various physical processes are known to cause acceleration, loss, and transport of energetic electrons in the Earth\textquoterights radiation belts, but their quantitative roles in different time and space need further investigation. During the largest storm over the past decade (17 March 2015), relativistic electrons experienced fairly rapid acceleration up to ~7 MeV within 2 days after an initial substantial dropout, as observed by Van Allen Probes. In the present paper, we evaluate the relative roles of various physical processes during the recovery phase of this large storm using a 3D diffusion simulation. By quantitatively comparing the observed and simulated electron evolution, we found that chorus plays a critical role in accelerating electrons up to several MeV near the developing peak location and produces characteristic flattop pitch angle distributions. By only including radial diffusion, the simulation underestimates the observed electron acceleration, while radial diffusion plays an important role in redistributing electrons and potentially accelerates them to even higher energies. Moreover, plasmaspheric hiss is found to provide efficient pitch angle scattering losses for hundreds of keV electrons, while its scattering effect on > 1 MeV electrons is relatively slow. Although an additional loss process is required to fully explain the overestimated electron fluxes at multiMeV, the combined physical processes of radial diffusion and pitch angle and energy diffusion by chorus and hiss reproduce the observed electron dynamics remarkably well, suggesting that quasilinear diffusion theory is reasonable to evaluate radiation belt electron dynamics during this big storm. Li, W.; Ma, Q.; Thorne, R.; Bortnik, J.; Zhang, X.J.; Li, J.; Baker, D.; Reeves, G.; Spence, H.; Kletzing, C.; Kurth, W.; Hospodarsky, G.; Blake, J.; Fennell, J.; Kanekal, S.; Angelopoulos, V.; Green, J.; Goldstein, J.; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2016 YEAR: 2016 DOI: 10.1002/jgra.v121.610.1002/2016JA022400 chorusdriven local acceleration; Electron acceleration; radial diffusion; Van Allen Probes 
The radial and local diffusion processes induced by various plasma waves govern the highly energetic electron dynamics in the Earth\textquoterights radiation belts, causing distinct characteristics in electron distributions at various energies. In this study, we present our simulation results of the energetic electron evolution during a geomagnetic storm using the University of California, Los Angeles 3D diffusion code. Following the plasma sheet electron injections, the electrons at different energy bands detected by the Magnetic Electron Ion Spectrometer (MagEIS) and Relativistic Electron Proton Telescope (REPT) instruments on board the Van Allen Probes exhibit a rapid enhancement followed by a slow diffusive movement in differential energy fluxes, and the radial extent to which electrons can penetrate into depends on energy with closer penetration toward the Earth at lower energies than higher energies. We incorporate radial diffusion, local acceleration, and loss processes due to whistler mode wave observations to perform a 3D diffusion simulation. Our simulation results demonstrate that chorus waves cause electron flux increase by more than 1 order of magnitude during the first 18 h, and the subsequent radial extents of the energetic electrons during the storm recovery phase are determined by the coupled radial diffusion and the pitch angle scattering by EMIC waves and plasmaspheric hiss. The radial diffusion caused by ULF waves and local plasma wave scattering are energy dependent, which lead to the observed electron flux variations with energy dependences. This study suggests that plasma wave distributions in the inner magnetosphere are crucial for the energydependent intrusions of several hundred keV to several MeV electrons. Ma, Q.; Li, W.; Thorne, R.; Nishimura, Y.; Zhang, X.J.; Reeves, G.; Kletzing, C.; Kurth, W.; Hospodarsky, G.; Henderson, M.; Spence, H.; Baker, D.; Blake, J.; Fennell, J.; Angelopoulos, V.; Published by: Journal of Geophysical Research: Space Physics Published on: 05/2016 YEAR: 2016 DOI: 10.1002/2016JA022507 electron acceleration and loss; energydependent diffusion; radial diffusion; radiation belt simulation; Van Allen Probes 
Inward diffusion and loss of radiation belt protons Radiation belt protons in the kinetic energy range 24 to 76 MeV are being measured by the Relativistic Electron Proton Telescope on each of the two Van Allen Probes. Data have been processed for the purpose of studying variability in the trapped proton intensity during October 2013 to August 2015. For the lower energies (≲32 MeV), equatorial proton intensity near L = 2 showed a steady increase that is consistent with inward diffusion of trapped solar protons, as shown by positive radial gradients in phase space density at fixed values of the first two adiabatic invariants. It is postulated that these protons were trapped with enhanced efficiency during the 7 March 2012 solar proton event. A model that includes radial diffusion, along with known trapped proton source and loss processes, shows that the observed average rate of increase near L = 2 is predicted by the same model diffusion coefficient that is required to form the entire proton radiation belt, down to low L, over an extended (\~103 year) interval. A slower intensity decrease for lower energies near L = 1.5 may also be caused by inward diffusion, though it is faster than predicted by the model. Higherenergy (≳40 MeV) protons near the L = 1.5 intensity maximum are from cosmic ray albedo neutron decay. Their observed intensity is lower than expected by a factor \~2, but the discrepancy is resolved by adding an unspecified loss process to the model with a mean lifetime \~120 years. Selesnick, R.; Baker, D.; Jaynes, A.; Li, X.; Kanekal, S.; Hudson, M.; Kress, B.; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2016 YEAR: 2016 DOI: 10.1002/2015JA022154 
2015 
We used the fluxgate magnetometer data from Combined Release and Radiation Effects Satellite (CRRES) to estimate the power spectral density (PSD) of the compressional component of the geomagnetic field in the \~1 mHz to \~8 mHz range. We conclude that magnetic wave power is generally higher in the noon sector for quiet times with no significant difference between the dawn, dusk, and the midnight sectors. However, during high Kp activity, the noon sector is not necessarily dominant anymore. The magnetic PSDs have a very distinct dependence on Kp. In addition, the PSDs appear to have a weak dependence on McIlwain parameter L with power slightly increasing as L increases. The magnetic wave PSDs are used along with the Fei et al. (2006) formulation to compute inline image as a function of L and Kp. The L dependence of inline image is systematically studied and is shown to depend on Kp. More significantly, we conclude that inline imageis the dominant term driving radial diffusion, typically exceeding inline image by 1\textendash2 orders of magnitude. Ali, Ashar; Elkington, Scot; Tu, Weichao; Ozeke, Louis; Chan, Anthony; Friedel, Reiner; Published by: Journal of Geophysical Research: Space Physics Published on: 02/2015 YEAR: 2015 DOI: 10.1002/2014JA020419 
2014 
Radial diffusion simulations of the 20 September 2007 radiation belt dropout This is a study of a dropout of radiation belt electrons, associated with an isolated solar wind density pulse on 20 September 2007, as seen by the solidstate telescopes (SST) detectors on THEMIS (Time History of Events and Macroscale Interactions during Substorms). Omnidirectional fluxes were converted to phase space density at constant invariants M = 700 MeV G1 and K = 0.014 RE G1/2, with the assumption of local pitch angle α ≈ 80\textdegree and using the T04 magnetic field model. The last closed drift shell, which was calculated throughout the time interval, never came within the simulation outer boundary of L* = 6. It is found, using several different models for diffusion rates, that radial diffusion alone only allows the datadriven, timedependent boundary values at Lmax = 6 and Lmin = 3.7 to propagate a few tenths of an RE during the simulation; far too slow to account for the dropout observed over the broad range of L* = 4\textendash5.5. Pitch angle diffusion via resonant interactions with several types of waves (chorus, electromagnetic ion cyclotron waves, and plasmaspheric and plume hiss) also seems problematic, for several reasons which are discussed. Published by: Annales Geophysicae Published on: 11/2014 YEAR: 2014 DOI: 10.5194/angeo329252014 
A ULF wave driver of ring current energization ULF wave radial diffusion plays an important role in the transport of energetic electrons in the outer radiation belt, yet similar ring current transport is seldom considered even though ions satisfy a nearly identical drift resonance condition albeit without the relativistic correction. By examining the correlation between ULF wave power and the response of the ring current, characterized by Dst, we demonstrate a definite correlation between ULF wave power and Dst. Significantly, the lagged correlation peaks such that ULF waves precede the response of the ring current and Dst. We suggest that this correlation is the result of enhanced radial transport and energization of ring current ions through drift resonance and ULF wave radial diffusion of ring current ions. An analysis and comparison of the ion and electron diffusion coefficients further support this conclusion, ULF waves providing an important missing physical transport process explaining Dst underestimation in ring current models. Murphy, Kyle; Mann, Ian; Ozeke, Louis; Published by: Geophysical Research Letters Published on: 10/2014 YEAR: 2014 DOI: 10.1002/grl.v41.1910.1002/2014GL061253 Dst; radial diffusion; ring current dynamics; ULF waves; wave particle interactions 
March 2013 provided the first equinoctial period when all of the instruments on the Van Allen Probes spacecraft were fully operational. This interval was characterized by disturbances of outer zone electrons with two timescales of variation, diffusive and rapid dropout and restoration [Baker et al., 2014]. A radial diffusion model was applied to the monthlong interval to confirm that electron phase space density is well described by radial diffusion for the whole month at low first invariant <=400 MeV/G, but peaks in phase space density observed by the ECT instrument suite at higher first invariant are not reproduced by radial transport from a source at higher L. The model does well for much of the monthlong interval, capturing three of four enhancements in phase space density which emerge from the outer boundary, while the strong enhancement following dropout on 1718 March requires local acceleration at higher first invariant (M = 1000 MeV/G vs. 200 MeV/G) not included in our model. We have incorporated phase space density from ECT measurement at the outer boundary and plasmapause determination from the EFW instrument to separate hiss and chorus loss models. Li, Zhao; Hudson, Mary; Jaynes, Allison; Boyd, Alexander; Malaspina, David; Thaller, Scott; Wygant, John; Henderson, Michael; Published by: Journal of Geophysical Research: Space Physics Published on: 10/2014 YEAR: 2014 DOI: 10.1002/2014JA020359 
Estimates of the power per mode number of broadband ULF waves at geosynchronous orbit In studies of radial diffusion processes in the magnetosphere it is well known that ultralow frequency (ULF) waves of frequency mωd can resonantly interact with particles of drift frequency ωd, where m is the waves\textquoteright azimuthal mode number. Due to difficulties in estimating m, an oversimplifying assumption is often made in simulations, namely that all ULF wave power is located at a single mode number. In this paper a technique is presented for extracting information on the distribution of ULF power in a range of azimuthal mode numbers. As a first step, the cross power and phase differences between time series from azimuthally aligned magnetometers are calculated. Subsequently, through integrating the ULF power at particular ranges of phase differences that correspond to particular mode numbers, estimates of the fraction of the total power at each phase difference range or mode number are provided. Albeit entwined with many ambiguities, this technique offers critical information that is currently missing when estimating radial diffusion of energetic particles. As proofofconcept, the technique is first tested successfully for a wellstudied case of narrowband ULF Field Line Resonances (FLR) for which the mode number was calculated simultaneously through groundbased and space measurements. Subsequently, the technique is demonstrated for the broadband ULF waves that accompanied the 2003 \textquotedblleftHalloween\textquotedblright magnetospheric storms. The temporal evolution of power at each mode number gives insight into the evolution of ULF waves during a storm as well as more accurate characterization of broadband ULF waves that can be used in radial diffusion simulations. Published by: Journal of Geophysical Research: Space Physics Published on: 07/2014 YEAR: 2014 DOI: 10.1002/2013JA019238 Magnetosphere; mode number; radial diffusion; Radiation belts; ULF waves; ultralow frequency 
Radial diffusion comparing a THEMIS statistical model with geosynchronous measurements as input The outer boundary energetic electron flux is used as a driver in radial diffusion calculations, and its precise determination is critical to the solution. A new model was proposed recently based on Time History of Events and Macroscale Interactions during Substorms (THEMIS) measurements to express the boundary flux as three fit functions of solar wind parameters in a response window that depend on energy and which solar wind parameter is used: speed, density, or both. The Dartmouth radial diffusion model has been run using Los Alamos National Laboratory (LANL) geosynchronous satellite measurements as the constraint for a onemonth interval in July to August 2004, and the calculated phase space density (PSD) is compared with GPS measurements, at magnetic equatorial plane crossings, as a test of the model. We also used the PSD generated from the Shin and Lee model as constraint and examined it by computing the error relative to the LANL geosynchronous spacecraft datadriven run. The calculation shows that there is overestimation and underestimation at different times; however, the direct insertion of the statistical model can be used to drive the radial diffusion model generally, producing the phase space density dropout and increase during a storm. Having this model based on a solar wind parameterized data set, we can run the radial diffusion model for storms when particle measurements are not available as input. We chose the Whole Heliosphere Interval as an example and compared the result with MHD/testparticle simulations, obtaining better agreement with GPS measurement using the diffusion model, which incorporates atmospheric losses and an initial equilibrium radial profile. Li, Zhao; Hudson, Mary; Chen, Yue; Published by: Journal of Geophysical Research: Space Physics Published on: 03/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.310.1002/2013JA019320 outer boundary; radial diffusion; Radiation belt; Van Allen Probes 
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