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[1] Three-dimensional simulations of the dynamics of outer radiation belt electrons with the recently developed Versatile Electron Radiation Belt (VERB) code are presented. Simulations are preformed for an idealized storm with geomagnetic activity-dependent wave amplitudes that are parameterized as a function of the level of geomagnetic activity. Numerical experiments using the VERB code with various scattering processes (pitch angle diffusion, radial diffusion, and energy diffusion) indicate that diffusive processes are strongly coupled with each other and that they all should be included in realistic simulations of the radiation belts. We show that during storms, inward radial diffusion can produce significant accelerations to relativistic energies, while pitch angle scattering and energy diffusion produce a decrease and an increase in fluxes, respectively. We show that in the presence of high-latitude and low-latitude chorus, peaks in the radial profile of phase space density are formed between L of 4 and 6 during the recovery phase of a storm and are later smoothed by radial diffusion. Sensitivity experiments show that geomagnetic control of wave intensities plays a controlling role in the dynamics of radiation belt electrons. Numerical simulations indicate that electrons of 10-100 keV near geosynchronous orbit can reach MeV energies in the heart of the radiation belts by combined radial diffusion and in situ acceleration. We present two scenarios of acceleration of the plasma sheet electrons: (1) in the range of hundreds of keV by means of radial diffusion and (2) in the range of tens of keV by means of radial diffusion combined with local acceleration.

Relativistic electrons are hazardous for satellites and humans in space. In this study, we present a detailed description of the Versatile Electron Radiation Belt (VERB) code. The computationally efficient methods described in this report make the VERB code a useful tool for space weather forecasting and nowcasting of the relativistic electron environment. The computational efficiency of the code makes it also appropriate for future use with data assimilation tools to specify the state of the radiation environment and correct imperfect models. We also present several skill scores which can be used to quantify the state of the relativistic electron environment. Our numerical approach is based on the use of two grids: one for radial diffusion and the other for energy and pitch angle diffusion. In this paper, we describe the initial and boundary conditions, the grids and time step used for our simulations, and the tests we conduct to verify the validity of our numerical approaches. Specifically, we perform simulations with time steps ranging from 0.01 to 4 h and number of grid points ranging from 7 to 76 for each of the variables. We compare the results obtained using various spatial resolutions and time steps, giving the relative solution errors for each of the performed simulations on the basis of the developed set of skill scores. The choice of a 0.1 h time step with a grid resolution of 19 × 19 × 19 points was found to be optimal. We compare the block and split methods, showing that the split method is much faster than the block method and sufficiently accurate for time steps of half an hour or less. Additionally, we present an approximate method that simplifies simulation by using only one grid and compare it to the more accurate two‐grid method.

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Radiation in space was the first discovery of the space age. Earth's radiation belts consist of energetic particles that are trapped by the geomagnetic field and encircle the planet 1. The electron radiation belts usually form a two-zone structure with a stable inner zone and a highly variable outer zone, which forms and disappears owing to waveparticle interactions on the timescale of a day, and is strongly influenced by the very-low-frequency plasma waves. Recent observations revealed a third radiation zone at ultrarelativistic energies 2 , with the additional medium narrow belt (longlived ring) persisting for approximately 4 weeks. This new ring resulted from a combination of electron losses to the interplanetary medium and scattering by electromagnetic ion cyclotron waves to the Earth's atmosphere. Here we show that ultrarelativistic electrons can stay trapped in the outer zone and remain unaffected by the very-low-frequency plasma waves for a very long time owing to a lack of scattering into the atmosphere. The absence of scattering is explained as a result of ultrarelativistic particles being too energetic to resonantly interact with waves at low latitudes. This study shows that a different set of physical processes determines the evolution of ultrarelativistic electrons. Over half a century ago, on the basis of the observations of the first US satellite mission Explorer 1, James Van Allen and colleagues from the University of Iowa discovered the inner radiation belt 3. The inner belt is very stable and consists of electrons and protons trapped between 1.2 and 2.0 Earth radii. Later, USSR and US missions showed that the radiation belts exhibited a two-zone structure 1,4 ; there is an additional outer belt present at higher distances (∼ > 3R E). A region of relatively low electron fluxes separating the belts is usually referred to as the slot region. The outer belt consists of energetic electrons and is highly dynamic and variable. It is produced by the continuous acceleration of electrons during inward transport (second-order Fermi acceleration and betatron acceleration) 5-7 and local acceleration due to resonance with plasma waves 8-10. The energetic electrons are continuously lost to the atmosphere and also regularly depleted as a result of losses to the magnetopause (the boundary of the Earth's magnetosphere) 11-13. The two-zone structure has been observed to be altered owing to very unusual acceleration events. Observation of the so-called Halloween superstorm showed that electrons can be accelerated to relativistic energies in the slot region between the two belts. The extreme filling of the slot region in October-November 2003 was

[1] Highly energetic electrons in the Earth's radiation belts are hazardous for satellite equipment. Fluxes of relativistic electrons can vary by orders of magnitude during geomagnetic storms. The evolution of relativistic electron fluxes in the radiation belts is described by the 3-D Fokker-Planck equation in terms of the radial distance, energy, and equatorial pitch angle. To better understand the mechanisms that control radiation belt acceleration and loss and particle flux dynamics, we present a long-term radiation belt simulation for 100 days from 29 July to 6 November 1990 with the 3-D Versatile Electron Radiation Belt (VERB) code and compare the results with the electron fluxes observed by the Combined Release and Radiation Effects Satellite (CRRES). We also perform a comparison of Phase Space Density with a multisatellite reanalysis obtained by using Kalman filtering of observations from CRRES, Geosynchronous (GEO), GPS, and Akebono satellites. VERB 3-D simulations include radial, energy, and pitch angle diffusion and mixed energy and pitch angle diffusion driven by electromagnetic waves inside the magnetosphere with losses to the atmosphere. Boundary conditions account for the convective source of electrons and loss to the magnetopause. The results of the simulation that include all of the above processes show a good agreement with the data. The agreement implies that these processes are important for the radiation belt electron dynamics and therefore should be accounted for in outer radiation belt simulations. We also show that the results are very sensitive to the assumed wave model. Our simulations are driven only by the variation of the Kp index and variations of the seed electron population around geosynchronous orbit, which allows the model to be used for forecasting and nowcasting.

[1] It has been suggested that the equilibrium structure of the slot region, which separates the inner and outer radiation belts, forms as the result of a balance between inward radial diffusion and pitch angle scattering of relativistic electrons by interactions with three types of whistler mode waves: plasmaspheric hiss, lightening-generated whistlers, and ground-based Very Low Frequency (VLF) transmitters. In this study, using the time-dependent 3D Versatile Electron Radiation Belt (VERB) code, we examine how effectively the slot can be formed by a combination of radial diffusion and pitch angle diffusion, together with Coulomb scattering, and compare the simulations with the CRRES MEA 1 MeV electron observations to examine the viability of the various scattering mechanisms. The results show that the overall time evolution of the observed two-zone structure is in a good agreement with our model simulations, which suggests a balance between inward radial diffusion due to Ultra Low Frequency (ULF) electromagnetic fluctuations and pitch angle scattering due to plasmaspheric hiss and lightning-generated whistlers. However, when inward radial diffusion due to the electrostatic fluctuations is included, agreement between the observed and simulated fluxes becomes weaker, suggesting that it is important to understand and quantify the radial diffusion rates in the slot region.Citation: Kim, K.-C., Y. Shprits, D. Subbotin, and B. Ni (2011), Understanding the dynamic evolution of the relativistic electron slot region including radial and pitch angle diffusion,

[1] The evolution of relativistic electron fluxes in the radiation belts is described by the modified Fokker-Plank equation in terms of the radial distance, energy and equatorial pitch angle. In this study we present numerical solutions of the two-dimensional (2-D) and 3-D Fokker-Planck equation including mixed diffusion terms. We use finite differences method with implicit numerical scheme, which is stable for any given time step. We evaluate the importance of the mixed diffusion in 2-D and 3-D cases of the Fokker-Planck diffusion equation for radiation belts simulations. In both cases the mixed diffusion tends to inhibit local acceleration and results in lower relativistic electron fluxes, as compared to the simulation without mixed diffusion. The effect of the mixed diffusion terms is most significant at small pitch angles. The inclusion of mixed diffusion also tends to delay the formation of the peak in phase space density in the recovery phase of a storm. We also perform sensitivity simulation to the assumed wave models, which indicates that an accurate knowledge of the wave parameters is the most important factor.Citation: Subbotin, D., Y. Shprits, and B. Ni (2010), Three-dimensional VERB radiation belt simulations including mixed diffusion,