[1] Thirty years ago Paulikas and Blake (1979) showed a remarkable correlation between geosynchronous relativistic electron fluxes and solar wind speed (Vsw). This seminal result has been a foundation of radiation belt studies, space weather forecasting, and current understanding of solar wind radiation belt coupling. We have repeated their analysis with a considerably longer-running data set from the Los Alamos National Laboratory energetic particle instruments with several surprising results. Rather than the roughly linear correlation between Vsw and log (flux), our results show a triangle-shaped distribution in which fluxes have a distinct velocity-dependent lower limit but a velocity-independent upper limit. The highest-electron fluxes can occur for any value of Vsw with no indication of a Vsw threshold. We also find a distinct solar cycle dependence with the triangle-shaped distribution evident in 2 declining phase years dominated by high-speed streams but essentially no correlation in 2 solar maximum years. For time periods that do show a triangle-shaped distribution we consider whether it can be explained by scatter due to other parameters. We examine the role of time dependence and time lag in producing the observed distribution. We also look at the same statistical relationship but at energies 1 MeV. We conclude that the relationship between radiation belt electron fluxes and solar wind velocity is substantially more complex than suggested by previous statistical studies. We find that there are important ways in which the "conventional wisdom" stating that high-velocity wind drives high-MeV electron fluxes is, in general, either misleading or unsupported.

As a response to the Geospace Environment Modeling (GEM) “Global Radiation Belt Modeling Challenge,” a 3D diffusion model is used to simulate the radiation belt electron dynamics during two intervals of the Combined Release and Radiation Effects Satellite (CRRES) mission, 15 August to 15 October 1990 and 1 February to 31 July 1991. The 3D diffusion model, developed as part of the Dynamic Radiation Environment Assimilation Model (DREAM) project, includes radial, pitch angle, and momentum diffusion and mixed pitch angle‐momentum diffusion, which are driven by dynamic wave databases from the statistical CRRES wave data, including plasmaspheric hiss, lower‐band, and upper‐band chorus. By comparing the DREAM3D model outputs to the CRRES electron phase space density (PSD) data, we find that, with a data‐driven boundary condition at Lmax = 5.5, the electron enhancements can generally be explained by radial diffusion, though additional local heating from chorus waves is required. Because the PSD reductions are included in the boundary condition at Lmax = 5.5, our model captures the fast electron dropouts over a large L range, producing better model performance compared to previous published results. Plasmaspheric hiss produces electron losses inside the plasmasphere, but the model still sometimes overestimates the PSD there. Test simulations using reduced radial diffusion coefficients or increased pitch angle diffusion coefficients inside the plasmasphere suggest that better wave models and more realistic radial diffusion coefficients, both inside and outside the plasmasphere, are needed to improve the model performance. Statistically, the results show that, with the data‐driven outer boundary condition, including radial diffusion and plasmaspheric hiss is sufficient to model the electrons during geomagnetically quiet times, but to best capture the radiation belt variations during active times, pitch angle and momentum diffusion from chorus waves are required.

The DREAM3D diffusion model is applied to Van Allen Probes observations of the fast dropout and strong enhancement of MeV electrons during the October 2012 "double-dip" storm. We show that in order to explain the very different behavior in the two "dips," diffusion in all three dimensions (energy, pitch angle, and L * ) coupled with data-driven, event-specific inputs, and boundary conditions is required.Specifically, we find that outward radial diffusion to the solar wind-driven magnetopause, an event-specific chorus wave model, and a dynamic lower-energy seed population are critical for modeling the dynamics.In contrast, models that include only a subset of processes, use statistical wave amplitudes, or rely on inward radial diffusion of a seed population, perform poorly. The results illustrate the utility of the high resolution, comprehensive set of Van Allen Probes' measurements in studying the balance between source and loss in the radiation belt, a principal goal of the mission.

We present dynamic simulations of energy‐dependent losses in the radiation belt “slot region” and the formation of the two‐belt structure for the quiet days after the 1 March storm. The simulations combine radial diffusion with a realistic scattering model, based data‐driven spatially and temporally resolved whistler‐mode hiss wave observations from the Van Allen Probes satellites. The simulations reproduce Van Allen Probes observations for all energies and L shells (2–6) including (a) the strong energy dependence to the radiation belt dynamics (b) an energy‐dependent outer boundary to the inner zone that extends to higher L shells at lower energies and (c) an “S‐shaped” energy‐dependent inner boundary to the outer zone that results from the competition between diffusive radial transport and losses. We find that the characteristic energy‐dependent structure of the radiation belts and slot region is dynamic and can be formed gradually in ~15 days, although the “S shape” can also be reproduced by assuming equilibrium conditions. The highest‐energy electrons (E > 300 keV) of the inner region of the outer belt (L ~ 4–5) also constantly decay, demonstrating that hiss wave scattering affects the outer belt during times of extended plasmasphere. Through these simulations, we explain the full structure in energy and L shell of the belts and the slot formation by hiss scattering during storm recovery. We show the power and complexity of looking dynamically at the effects over all energies and L shells and the need for using data‐driven and event‐specific conditions.

The Dynamic Radiation Environment Assimilation Model (DREAM) was developed to provide accurate, global specification of the Earth's radiation belts and to better understand the physical processes that control radiation belt structure and dynamics. DREAM is designed using a modular software approach in order to provide a computational framework that makes it easy to change components such as the global magnetic field model, radiation belt dynamics model, boundary conditions, etc. This paper provides a broad overview of the DREAM model and a summary of some of the principal results to date. We describe the structure of the DREAM model, describe the five major components, and illustrate the various options that are available for each component. We discuss how the data assimilation is performed and the data preprocessing and postprocessing that are required for producing the final DREAM outputs. We describe how we apply global magnetic field models for conversion between flux and phase space density and, in particular, the benefits of using a self‐consistent, coupled ring current–magnetic field model. We discuss some of the results from DREAM including testing of boundary condition assumptions and effects of adding a source term to radial diffusion models. We also describe some of the testing and validation of DREAM and prospects for future development.

The evolution of the radiation belts in L‐shell (L), energy (E), and equatorial pitch angle (α0) is analyzed during the calm 11‐day interval (4–15 March) following the 1 March 2013 storm. Magnetic Electron and Ion Spectrometer (MagEIS) observations from Van Allen Probes are interpreted alongside 1D and 3D Fokker‐Planck simulations combined with consistent event‐driven scattering modeling from whistler mode hiss waves. Three (L, E, α0) regions persist through 11 days of hiss wave scattering; the pitch angle‐dependent inner belt core (L ~ <2.2 and E < 700 keV), pitch angle homogeneous outer belt low‐energy core (L > ~5 and E~ < 100 keV), and a distinct pocket of electrons (L ~ [4.5, 5.5] and E ~ [0.7, 2] MeV). The pitch angle homogeneous outer belt is explained by the diffusion coefficients that are roughly constant for α0 ~ <60°, E > 100 keV, 3.5 < L < Lpp ~ 6. Thus, observed unidirectional flux decays can be used to estimate local pitch angle diffusion rates in that region. Top‐hat distributions are computed and observed at L ~ 3–3.5 and E = 100–300 keV.

Substorm injected electrons (several-100 s keV) produce whistler-mode chorus waves that are thought to have a major impact on the radiation belts by causing both energization and loss of relativistic electrons in the outer belt. High-altitude measurements, such as those from the Van Allen Probes, provide detailed wave measurements at a few points in the magnetosphere. But physics-based models of radiation-belt dynamics require knowledge of the global distribution of chorus waves. We demonstrate that time-dependent, global distributions of near-equatorial chorus wave intensities can be inferred from low-Earth-orbit (LEO) measurements of precipitating low-energy electrons. We compare in situ observations of near-equatorial chorus waves with LEO observations of precipitating electrons and derive a heuristic formula that relates, quantitatively, electron precipitation fluxes to chorus wave intensities. Finally, we demonstrate how that formula can be applied to LEO precipitation measurements and in situ Van Allen Probes wave measurements to provide global, data-driven inputs for radiation belt models.

In this study, we complement the notion of equilibrium states of the radiation belts with a discussion on the dynamics and time needed to reach equilibrium. We solve for the equilibrium states obtained using 1‐D radial diffusion with recently developed hiss and chorus lifetimes at constant values of Kp = 1, 3, and 6. We find that the equilibrium states at moderately low Kp, when plotted versus L shell (L) and energy (E), display the same interesting S shape for the inner edge of the outer belt as recently observed by the Van Allen Probes. The S shape is also produced as the radiation belts dynamically evolve toward the equilibrium state when initialized to simulate the buildup after a massive dropout or to simulate loss due to outward diffusion from a saturated state. Physically, this shape, intimately linked with the slot structure, is due to the dependence of electron loss rate (originating from wave‐particle interactions) on both energy and L shell. Equilibrium electron flux profiles are governed by the Biot number (τDiffusion/τloss), with large Biot number corresponding to low fluxes and low Biot number to large fluxes. The time it takes for the flux at a specific (L, E) to reach the value associated with the equilibrium state, starting from these different initial states, is governed by the initial state of the belts, the property of the dynamics (diffusion coefficients), and the size of the domain of computation. Its structure shows a rather complex scissor form in the (L, E) plane. The equilibrium value (phase space density or flux) is practically reachable only for selected regions in (L, E) and geomagnetic activity. Convergence to equilibrium requires hundreds of days in the inner belt for E > 300 keV and moderate Kp (≤3). It takes less time to reach equilibrium during disturbed geomagnetic conditions (Kp ≥ 3), when the system evolves faster. Restricting our interest to the slot region, below L = 4, we find that only small regions in (L, E) space can reach the equilibrium value: E ~ [200, 300] keV for L = [3.7, 4] at Kp = 1, E~[0.6, 1] MeV for L = [3, 4] at Kp = 3, and E~300 keV for L = [3.5, 4] at Kp = 6 assuming no new incoming electrons.