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2021 
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 
Determining the Temporal and Spatial Coherence of Plasmaspheric Hiss Waves in the Magnetosphere Abstract Plasmaspheric hiss is one of the most important plasma waves in the Earth s magnetosphere to contribute to radiation belt dynamics by pitchangle scattering energetic electrons via waveparticle interactions. There is growing evidence that the temporal and spatial variability of waveparticle interactions are important factors in the construction of diffusionbased models of the radiation belts. Hiss amplitudes are thought to be coherent across large distances and on long timescales inside the plasmapause, which means that hiss can act on radiation belt electrons throughout their drift trajectories for many hours. In this study, we investigate both the spatial and temporal coherence of plasmaspheric hiss between the two Van Allen Probes from November 2012 to July 2019. We find ∼3,264 events where we can determine the correlation of wave amplitudes as a function of both spatial distance and time lag in order to study the spatial and temporal coherence of plasmaspheric hiss. The statistical results show that both the spatial and temporal correlation of plasmaspheric hiss decrease with increasing Lshell, and become incoherent at L > ∼4.5. Inside of L = ∼4.5, we find that hiss is coherent to within a spatial extent of up to ∼1,500 km and a time lag up to ∼10 min. We find that the spatial and temporal coherence of plasmaspheric hiss does not depend strongly on the geomagnetic index (AL*) or magnetic local time. We discuss the ramifications of our results with relevance to understanding the global characteristics of plasmaspheric hiss waves and their role in radiation belt dynamics. Zhang, Shuai; Rae, Jonathan; Watt, Clare; Degeling, Alexander; Tian, Anmin; Shi, Quanqi; Shen, XiaoChen; Smith, Andy; Wang, Mengmeng; Published by: Journal of Geophysical Research: Space Physics Published on: 02/2021 YEAR: 2021 DOI: https://doi.org/10.1029/2020JA028635 
2020 
The Implications of Temporal Variability in WaveParticle Interactions in Earth s Radiation Belts Changes in electron flux in Earth s outer radiation belt can be modeled using a diffusionbased framework. Diffusion coefficients D for such models are often constructed from statistical averages of observed inputs. Here, we use stochastic parameterization to investigate the consequences of temporal variability in D. Variability time scales are constrained using Van Allen Probe observations. Results from stochastic parameterization experiments are compared with experiments using D constructed from averaged inputs and an average of observationspecific D. We find that the evolution and final state of the numerical experiment depends upon the variability time scale of D; experiments with longer variability time scales differ from those with shorter time scales, even when the timeintegrated diffusion is the same. Short variability time scale experiments converge with solutions obtained using an averaged observationspecific D, and both exhibit greater diffusion than experiments using the averagedinput D. These experiments reveal the importance of temporal variability in radiation belt diffusion. Watt, C.; Allison, H.; Thompson, R.; Bentley, S.; Meredith, N.; Glauert, S.; Horne, R.; Rae, I.; Published by: Geophysical Research Letters Published on: 12/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2020GL089962 probabilistic methods; stochastic parameterization; Van Allen Probes 
A New Approach to Constructing Models of Electron Diffusion by EMIC Waves in the Radiation Belts Electromagnetic ion cyclotron (EMIC) waves play an important role in relativistic electron losses in the radiation belts through diffusion via resonant waveparticle interactions. We present a new approach for calculating bounce and driftaveraged EMIC electron diffusion coefficients. We calculate bounceaveraged diffusion coefficients, using quasilinear theory, for each individual Combined Release and Radiation Effects Satellite (CRRES) EMIC wave observation using fitted wave properties, the plasma density and the background magnetic field. These calculations are then combined into bounceaveraged diffusion coefficients. The resulting coefficients therefore capture the combined effects of individual spectra and plasma properties as opposed to previous approaches that use average spectral and plasma properties, resulting in diffusion over a wider range of energies and pitch angles. These calculations, and their role in radiation belt simulations, are then compared against existing diffusion models. The new diffusion coefficients are found to significantly improve the agreement between the calculated decay of relativistic electrons and Van Allen Probes data. Ross, J.; Glauert, S.; Horne, R.; Watt, C.; Meredith, N.; Woodfield, E.; Published by: Geophysical Research Letters Published on: 10/2020 YEAR: 2020 DOI: https://doi.org/10.1029/2020GL088976 Radiation belts; EMIC waves; electron diffusion; Van Allen Probes 
2019 
Variability of Quasilinear Diffusion Coefficients for Plasmaspheric Hiss In the outer radiation belt, the acceleration and loss of highenergy electrons is largely controlled by waveparticle interactions. Quasilinear diffusion coefficients are an efficient way to capture the smallscale physics of waveparticle interactions due to magnetospheric wave modes such as plasmaspheric hiss. The strength of quasilinear diffusion coefficients as a function of energy and pitch angle depends on both wave parameters and plasma parameters such as ambient magnetic field strength, plasma number density, and composition. For plasmaspheric hiss in the magnetosphere, observations indicate large variations in the wave intensity and wave normal angle, but less is known about the simultaneous variability of the magnetic field and number density. We use in situ measurements from the Van Allen Probe mission to demonstrate the variability of selected factors that control the size and shape of pitch angle diffusion coefficients: wave intensity, magnetic field strength, and electron number density. We then compare with the variability of diffusion coefficients calculated individually from colocated and simultaneous groups of measurements. We show that the distribution of the plasmaspheric hiss diffusion coefficients is highly nonGaussian with large variance and that the distributions themselves vary strongly across the three phase space bins studied. In most bins studied, the plasmaspheric hiss diffusion coefficients tend to increase with geomagnetic activity, but our results indicate that new approaches that include natural variability may yield improved parameterizations. We suggest methods like stochastic parameterization of waveparticle interactions could use variability information to improve modeling of the outer radiation belt. Watt, C.; Allison, H.; Meredith, N.; Thompson, R.; Bentley, S.; Rae, I.; Glauert, S.; Horne, R.; Published by: Journal of Geophysical Research: Space Physics Published on: 10/2019 YEAR: 2019 DOI: 10.1029/2018JA026401 empirical; Magnetosphere; parameterization; stochastic; Van Allen Probes; waveparticle interactions 
2018 
Ultralow frequency (ULF) waves play a fundamental role in the dynamics of the innermagnetosphere and outer radiation belt during geomagnetic storms. Broadband ULF wave power can transport energetic electrons via radial diffusion and discrete ULF wave power can energize electrons through a resonant interaction. Using observations from the Magnetospheric Multiscale (MMS) mission, we characterize the evolution of ULF waves during a highspeed solar wind stream (HSS) and moderate geomagnetic storm while there is an enhancement of the outer radiation belt. The Automated Flare Inference of Oscillations (AFINO) code is used to distinguish discrete ULF wave power from broadband wave power during the HSS. During periods of discrete wave power and utilizing the close separation of the MMS spacecraft, we estimate the toroidal mode ULF azimuthal wave number throughout the geomagnetic storm. We concentrate on the toroidal mode as the HSSs compresses the day side magnetosphere resulting in an asymmetric magnetic field topology where toroidal mode waves can interact with energetic electrons. Analysis of the mode structure and wave numbers demonstrates that the generation of the observed ULF waves is a combination of externally driven waves, via the KelvinHelmholtz instability, and internally driven waves, via unstable ion distributions. Further analysis of the periods and toroidal azimuthal wave numbers suggests that these waves can couple with the core electron radiation belt population via the drift resonance during the storm. The azimuthal wave number and structure of ULF wave power (broadband or discrete) have important implications for the innermagnetospheric and radiation belt dynamics. Murphy, Kyle; Inglis, Andrew; Sibeck, David; Rae, Jonathan; Watt, Clare; Silveira, Marcos; Plaschke, Ferdinand; Claudepierre, Seth; Nakamura, Rumi; Published by: Journal of Geophysical Research: Space Physics Published on: 05/2018 YEAR: 2018 DOI: 10.1029/2017JA024877 azimuthal wave number; Geomagnetic storms; mode structure; Radiation belts; ULF waves; Van Allen Probes 
The global statistical response of the outer radiation belt during geomagnetic storms Using the total radiation belt electron content calculated from Van Allen Probe phase space density (PSD), the timedependent and global response of the outer radiation belt during storms is statistically studied. Using PSD reduces the impacts of adiabatic changes in the main phase, allowing a separation of adiabatic and nonadiabatic effects, and revealing a clear modality and repeatable sequence of events in stormtime radiation belt electron dynamics. This sequence exhibits an important first adiabatic invariant (μ) dependent behaviour in the seed (150 MeV/G), relativistic (1000 MeV/G), and ultrarelativistic (4000 MeV/G) populations. The outer radiation belt statistically shows an initial phase dominated by loss followed by a second phase of rapid acceleration, whilst the seed population shows little loss and immediate enhancement. The time sequence of the transition to the acceleration is also strongly μdependent and occurs at low μ first, appearing to be repeatable from storm to storm. Murphy, Kyle; Watt, C.; Mann, Ian; Rae, Jonathan; Sibeck, David; Boyd, A.; Forsyth, C.; Turner, D.; Claudepierre, S.; Baker, D.; Spence, H.; Reeves, G.; Blake, J.; Fennell, J.; Published by: Geophysical Research Letters Published on: 04/2018 YEAR: 2018 DOI: 10.1002/2017GL076674 Geomagnetic storms; magnetospheric dynamics; Radiation belts; Solar WindMagnetosphere Coupling; statistical analysis; Van Allen Probes 
2016 
What effect do substorms have on the content of the radiation belts? Substorms are fundamental and dynamic processes in the magnetosphere, converting captured solar wind magnetic energy into plasma energy. These substorms have been suggested to be a key driver of energetic electron enhancements in the outer radiation belts. Substorms inject a keV \textquotedblleftseed\textquotedblright population into the inner magnetosphere which is subsequently energized through waveparticle interactions up to relativistic energies; however, the extent to which substorms enhance the radiation belts, either directly or indirectly, has never before been quantified. In this study, we examine increases and decreases in the total radiation belt electron content (TRBEC) following substorms and geomagnetically quiet intervals. Our results show that the radiation belts are inherently lossy, shown by a negative median change in TRBEC at all intervals following substorms and quiet intervals. However, there are up to 3 times as many increases in TRBEC following substorm intervals. There is a lag of 1\textendash3 days between the substorm or quiet intervals and their greatest effect on radiation belt content, shown in the difference between the occurrence of increases and losses in TRBEC following substorms and quiet intervals, the mean change in TRBEC following substorms or quiet intervals, and the cross correlation between SuperMAG AL (SML) and TRBEC. However, there is a statistically significant effect on the occurrence of increases and decreases in TRBEC up to a lag of 6 days. Increases in radiation belt content show a significant correlation with SML and SYMH, but decreases in the radiation belt show no apparent link with magnetospheric activity levels. Forsyth, C.; Rae, I.; Murphy, K.; Freeman, M.; Huang, C.L.; Spence, H.; Boyd, A.; Coxon, J.; Jackman, C.; Kalmoni, N.; Watt, C.; Published by: Journal of Geophysical Research: Space Physics Published on: 06/2016 YEAR: 2016 DOI: 10.1002/2016JA022620 
Cold plasma theory and parallel wave propagation are often assumed when approximating the whistler mode magnetic field wave power from electric field observations. The current study is the first to include the wave normal angle from the Electric and Magnetic Field Instrument Suite and Integrated Science package on board the Van Allen Probes in the conversion factor, thus allowing for the accuracy of these assumptions to be quantified. Results indicate that removing the assumption of parallel propagation does not significantly affect calculated plasmaspheric hiss wave powers. Hence, the assumption of parallel propagation is valid. For chorus waves, inclusion of the wave normal angle in the conversion factor leads to significant alterations in the distribution of wave power ratios (observed/ calculated); the percentage of overestimates decreases, the percentage of underestimates increases, and the spread of values is significantly reduced. Calculated plasmaspheric hiss wave powers are, on average, a good estimate of those observed, whereas calculated chorus wave powers are persistently and systematically underestimated. Investigation of wave power ratios (observed/calculated), as a function of frequency and plasma density, reveals a structure consistent with signal attenuation via the formation of a plasma sheath around the Electric Field and Waves spherical double probes instrument. A simple, densitydependent model is developed in order to quantify this effect of variable impedance between the electric field antenna and the plasma interface. This sheath impedance model is then demonstrated to be successful in significantly improving agreement between calculated and observed power spectra and wave powers. Hartley, D.; Kletzing, C.; Kurth, W.; Bounds, S.; Averkamp, T.; Hospodarsky, G.; Wygant, J.; Bonnell, J.; ik, O.; Watt, C.; Published by: Journal of Geophysical Research: Space Physics Published on: 05/2016 YEAR: 2016 DOI: 10.1002/2016JA022501 EFW; EMFISIS; Plasmaspheric Hiss; sheath impedance; Van Allen Probes; whistler mode chorus 
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