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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 
Determination of the Equatorial Electron Differential Flux From Observations at Low Earth Orbit Variations in the highenergy relativistic electron flux of the radiation belts depend on transport, acceleration, and loss processes, and importantly on the lowerenergy seed population. However, data on the seed population is limited to a few satellite missions. Here we present a new method that utilizes data from the Medium Energy Proton/Electron Detector on board the lowaltitude Polar Operational Environmental Satellites to retrieve the seed population at a pitch angle of 90\textdegree. The integral flux values measured by Medium Energy Proton/Electron Detector relate to a low equatorial pitch angle and were converted to omnidirectional flux using parameters obtained from fitting one or two urn:xwiley:jgra:media:jgra54628:jgra54628math0001 functions to pitch angle distributions given by three and a half years of Van Allen Probes data. Two methods to convert from integral to differential flux are explored. One utilizes integral and differential flux energy distributions from the AE9 model, the second employs an iterative fitting approach based on a Reverse Monte Carlo (RMC) method. The omnidirectional differential flux was converted to an equatorial pitch angle of 90\textdegree, again using statistical pitch angle distributions from Van Allen Probe data. We validate the resulting 90\textdegree flux for 100 to 600keV electrons against measurements from the Van Allen Probes and show an average agreement within a factor of 4 for L* > 3.7. The resulting data set offers a high time resolution, across multiple magnetic local time planes, and may be used to formulate eventspecific lowenergy boundary conditions for radiation belt models. Allison, Hayley; Horne, Richard; Glauert, Sarah; Del Zanna, Giulio; Published by: Journal of Geophysical Research: Space Physics Published on: 11/2018 YEAR: 2018 DOI: 10.1029/2018JA025786 electrons; integral flux; Radiation belts; seed population; Van Allen Probes 
2014 
Electron losses from the radiation belts caused by EMIC waves Electromagnetic Ion Cyclotron (EMIC) waves cause electron loss in the radiation belts by resonating with highenergy electrons at energies greater than about 500 keV. However, their effectiveness has not been fully quantified. Here we determine the effectiveness of EMIC waves by using wave data from the fluxgate magnetometer on CRRES to calculate bounceaveraged pitch angle and energy diffusion rates for L*=3.5\textendash7 for five levels of Kp between 12 and 18 MLT. To determine the electron loss, EMIC diffusion rates were included in the British Antarctic Survey Radiation Belt Model together with whistler mode chorus, plasmaspheric hiss, and radial diffusion. By simulating a 100 day period in 1990, we show that EMIC waves caused a significant reduction in the electron flux for energies greater than 2 MeV but only for pitch angles lower than about 60\textdegree. The simulations show that the distribution of electrons left behind in space looks like a pancake distribution. Since EMIC waves cannot remove electrons at all pitch angles even at 30 MeV, our results suggest that EMIC waves are unlikely to set an upper limit on the energy of the flux of radiation belt electrons. Kersten, Tobias; Horne, Richard; Glauert, Sarah; Meredith, Nigel; Fraser, Brian; Grew, Russell; Published by: Journal of Geophysical Research: Space Physics Published on: 11/2014 YEAR: 2014 DOI: 10.1002/2014JA020366 
In the Earth\textquoterights radiation belts the flux of relativistic electrons is highly variable, sometimes changing by orders of magnitude within a few hours. Since energetic electrons can damage satellites it is important to understand the processes driving these changes and, ultimately, to develop forecasts of the energetic electron population. One approach is to use threedimensional diffusion models, based on a FokkerPlanck equation. Here we describe a model where the phasespace density is set to zero at the outer L* boundary, simulating losses to the magnetopause, using recently published chorus diffusion coefficients for 1.5<=L*<=10. The value of the phasespace density on the minimumenergy boundary is determined from a recently published, solar winddependent, statistical model. Our simulations show that an outer radiation belt can be created by local acceleration of electrons from a very soft energy spectrum without the need for a source of electrons from inward radial transport. The location in L* of the peaks in flux for these steady state simulations is energy dependent and moves earthward with increasing energy. Comparisons between the model and data from the CRRES spacecraft are shown; flux dropouts are reproduced in the model by the increased outward radial diffusion that occurs during storms. Including the inward movement of the magnetopause in the model has little additional effect on the results. Finally, the location of the lowenergy boundary is shown to be important for accurate modeling of observations. Glauert, Sarah; Horne, Richard; Meredith, Nigel; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.910.1002/2014JA020092 
Threedimensional stochastic modeling of radiation belts in adiabatic invariant coordinates A 3D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of It\^o stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3D diffusion tensor, including the radiallocal cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90\textdegree is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90\textdegree, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration. Zheng, Liheng; Chan, Anthony; Albert, Jay; Elkington, Scot; Koller, Josef; Horne, Richard; Glauert, Sarah; Meredith, Nigel; Published by: Journal of Geophysical Research: Space Physics Published on: 09/2014 YEAR: 2014 DOI: 10.1002/jgra.v119.910.1002/2014JA020127 adiabatic invariant coordinates; diffusion equation; fully 3D model; Radiation belt; stochastic differential equation 
2007 
Slot region electron loss timescales due to plasmaspheric hiss and lightninggenerated whistlers [1] Energetic electrons (E > 100 keV) in the Earth\textquoterights radiation belts undergo Dopplershifted cyclotron resonant interactions with a variety of whistler mode waves leading to pitch angle scattering and subsequent loss to the atmosphere. In this study we assess the relative importance of plasmaspheric hiss and lightninggenerated whistlers in the slot region and beyond. Electron loss timescales are determined using the Pitch Angle and energy Diffusion of Ions and Electrons (PADIE) code with global models of the spectral distributions of the wave power based on CRRES observations. Our results show that plasmaspheric hiss propagating at small and intermediate wave normal angles is a significant scattering agent in the slot region and beyond. In contrast, plasmaspheric hiss propagating at large wave normal angles and lightninggenerated whistlers do not contribute significantly to radiation belt loss. The loss timescale of 2 MeV electrons due to plasmaspheric hiss propagating at small and intermediate wave normal angles in the center of the slot region (L = 2.5) lies in the range 1\textendash10 days, consistent with recent Solar Anomalous and Magnetospheric Particle Explorer (SAMPEX) observations. Wave turbulence in space, which is responsible for the generation plasmaspheric hiss, thus leads to the formation of the slot region. During active periods, losses due to plasmaspheric hiss may occur on a timescale of 1 day or less for a wide range of energies, 200 keV < E < 1 MeV, in the region 3.5 < L < 4.0. Plasmaspheric hiss may thus also be a significant loss process in the inner region of the outer radiation belt during magnetically disturbed periods. Meredith, Nigel; Horne, Richard; Glauert, Sarah; Anderson, Roger; Published by: Journal of Geophysical Research Published on: 08/2007 YEAR: 2007 DOI: 10.1029/2007JA012413 
2006 
Energetic outer zone electron loss timescales during low geomagnetic activity Following enhanced magnetic activity the fluxes of energetic electrons in the Earth\textquoterights outer radiation belt gradually decay to quiettime levels. We use CRRES observations to estimate the energetic electron loss timescales and to identify the principal loss mechanisms. Gradual loss of energetic electrons in the region 3.0 <= L <= 5.0 occurs during quiet periods (Kp < 3) following enhanced magnetic activity on timescales ranging from 1.5 to 3.5 days for 214 keV electrons to 5.5 to 6.5 days for 1.09 MeV electrons. The intervals of decay are associated with large average values of the ratio fpe/fce (>7), indicating that the decay takes place in the plasmasphere. We compute loss timescales for pitchangle scattering by plasmaspheric hiss using the PADIE code with wave properties based on CRRES observations. The resulting timescales suggest that pitch angle scattering by plasmaspheric hiss propagating at small or intermediate wave normal angles is responsible for electron loss over a wide range of energies and L shells. The region where hiss dominates loss is energydependent, ranging from 3.5 <= L <= 5.0 at 214 keV to 3.0 <= L <= 4.0 at 1.09 MeV. Plasmaspheric hiss at large wave normal angles does not contribute significantly to the loss rates. At E = 1.09 MeV the loss timescales are overestimated by a factor of \~5 for 4.5 <= L <= 5.0. We suggest that resonant waveparticle interactions with EMIC waves, which become important at MeV energies for larger L (L > \~4.5), may play a significant role in this region. Meredith, Nigel; Horne, Richard; Glauert, Sarah; Thorne, Richard; Summers, D.; Albert, Jay; Anderson, Roger; Published by: Journal of Geophysical Research Published on: 05/2006 YEAR: 2006 DOI: 10.1029/2005JA011516 
2005 
Wave acceleration of electrons in the Van Allen radiation belts The Van Allen radiation belts1 are two regions encircling the Earth in which energetic charged particles are trapped inside the Earth\textquoterights magnetic field. Their properties vary according to solar activity2, 3 and they represent a hazard to satellites and humans in space4, 5. An important challenge has been to explain how the charged particles within these belts are accelerated to very high energies of several million electron volts. Here we show, on the basis of the analysis of a rare event where the outer radiation belt was depleted and then reformed closer to the Earth6, that the long established theory of acceleration by radial diffusion is inadequate; the electrons are accelerated more effectively by electromagnetic waves at frequencies of a few kilohertz. Wave acceleration can increase the electron flux by more than three orders of magnitude over the observed timescale of one to two days, more than sufficient to explain the new radiation belt. Wave acceleration could also be important for Jupiter, Saturn and other astrophysical objects with magnetic fields. Horne, Richard; Thorne, Richard; Shprits, Yuri; Meredith, Nigel; Glauert, Sarah; Smith, Andy; Kanekal, Shrikanth; Baker, Daniel; Engebretson, Mark; Posch, Jennifer; Spasojevic, Maria; Inan, Umran; Pickett, Jolene; Decreau, Pierrette; Published by: Nature Published on: 09/2005 YEAR: 2005 DOI: 10.1038/nature03939 
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