The Van Allen Probes mission provides unique measurements of the most energetic radiation belt electrons at ultrarelativistic energies. Simultaneous observations of plasma waves allow for the routine inference of total plasma number density, a parameter that is very difficult to measure directly. On the basis of long-term observations in 2015, we show that the underlying plasma density has a controlling effect over acceleration to ultrarelativistic energies, which occurs only when the plasma number density drops down to very low values (~10 cm^–3). Such low density creates preferential conditions for local diffusive acceleration of electrons from hundreds of kilo–electron volts up to >7 MeV. While previous models could not reproduce the local acceleration of electrons to such high energies, here we complement the observations with a numerical model to show that the conditions of extreme cold plasma depletion result in acceleration up to >7 MeV.

Utilizing the data from the magnetometer instrument which is a part of the Electric and Magnetic Field Instrument Suite and Integrated Science instrument suite on board the Van Allen Probe A from September 2012 to April 2014, when the apogee of the satellite has passed all the magnetic local time (MLT) sectors, we obtain the statistical distribution characteristics of electromagnetic ion cyclotron (EMIC) waves in the inner magnetosphere over all magnetic local times from L = 3 to L = 6. Compared with the previous statistical results about EMIC waves, the occurrence rates of EMIC waves distribute relatively uniform in the MLT sectors in lower L shells. On the other hand, in higher L shells, there are indeed some peaks of the occurrence rate for the EMIC waves, especially in the noon, dusk, and night sectors. EMIC waves appear at lower L shells in the dawn sector than in other sectors. In the lower L shells (L < 4), the occurrence rates of EMIC waves are significant in the dawn sector. This phenomenon may result from the distribution characteristics of the plasmasphere. The location of the plasmapause is usually lower in the dawn sector than that in other sectors, and the plasmapause is considered to be the favored region for the generation of EMIC waves. In higher L shells (L > 4) the occurrence rates of EMIC waves are most significant in the dusk sector, implying the important role of the plasmapause or plasmaspheric plume in generating EMIC waves. We have also investigated the distribution characteristics of the hydrogen band and the helium band EMIC waves. Surprisingly, in the inner magnetosphere, the hydrogen band EMIC waves occur more frequently than the helium band EMIC waves. Both of them have peaks of occurrence rate in noon, dusk, and night sectors, and the hydrogen band EMIC waves have more obvious peaks than the helium band EMIC waves in the night sector, while the helium band EMIC waves are more concentrated than the hydrogen band EMIC waves in the dusk sector. Both of them occur significantly in the noon sector, which implies the important role of the solar wind dynamic pressure.

Chorus waves play an important role in the dynamic evolution of energetic electrons in the Earth's radiation belts and ring current. Using more than 5 years of Van Allen Probe data, we developed a new analytical model for upper‐band chorus (UBC; 0.5f_ce < f < f_ce) and lower‐band chorus (LBC; 0.05f_ce < f < 0.5f_ce) waves, where f_ce is the equatorial electron gyrofrequency. By applying polynomial fits to chorus wave root mean square amplitudes, we developed regression models for LBC and UBC as a function of geomagnetic activity (Kp), L, magnetic latitude (λ), and magnetic local time (MLT). Dependence on Kp is separated from the dependence on λ, L, and MLT as Kp‐scaling law to simplify the calculation of diffusion coefficients and inclusion into particle tracing codes. Frequency models for UBC and LBC are also developed, which depends on MLT and magnetic latitude. This empirical model is valid in all MLTs, magnetic latitude up to 20°, Kp ≤ 6, L‐shell range from 3.5 to 6 for LBC and from 4 to 6 for UBC. The dependence of root mean square amplitudes on L are different for different bands, which implies different energy sources for different wave bands. This analytical chorus wave model is convenient for inclusion in quasi‐linear diffusion calculations of electron scattering rates and particle simulations in the inner magnetosphere, especially for the newly developed four‐dimensional codes, which require significantly improved wave parameterizations.

Through polarization and spectra analysis of the magnetic field observed by the Van Allen Probe A, we present two typical cases of O⁺ band electromagnetic ion cyclotron (EMIC) waves in the outer plasmasphere or plasma trough. Although such O⁺ band EMIC waves are rarely observed, 18 different events of O⁺ band EMIC waves (16 events in the outer plasmasphere and two events in the plasma trough) are found from September 2012 to August 2014 with observations of the Van Allen Probe A. We find that the preferred region for the occurrence of O⁺ band EMIC waves is in L = 2–5 and magnetic local time = 03–13, 19–20, which is in accordance with the occurrence region of O⁺ ion torus. Therefore, our result suggests that the O⁺ ion torus in the outer plasmasphere during geomagnetic activities should play an important role in the generation of EMIC waves in O⁺ band.

Modeling and observations have shown that energy diffusion by chorus waves is an important source of acceleration of electrons to relativistic energies. By performing long‐term simulations using the three‐dimensional Versatile Electron Radiation Belt code, in this study, we test how the latitudinal dependence of chorus waves can affect the dynamics of the radiation belt electrons. Results show that the variability of chorus waves at high latitudes is critical for modeling of megaelectron volt (MeV) electrons. We show that, depending on the latitudinal distribution of chorus waves under different geomagnetic conditions, they cannot only produce a net acceleration but also a net loss of MeV electrons. Decrease in high‐latitude chorus waves can tip the balance between acceleration and loss toward acceleration, or alternatively, the increase in high‐latitude waves can result in a net loss of MeV electrons. Variations in high‐latitude chorus may account for some of the variability of MeV electrons.

Understanding the dynamic evolution of relativistic electrons in the Earth's radiation belts during both storm and nonstorm times is a challenging task. The U.S. National Science Foundation's Geospace Environment Modeling (GEM) focus group “Quantitative Assessment of Radiation Belt Modeling” has selected two storm time and two nonstorm time events that occurred during the second year of the Van Allen Probes mission for in‐depth study. Here, we perform simulations for these GEM challenge events using the 3D Versatile Electron Radiation Belt code. We set up the outer L^* boundary using data from the Geostationary Operational Environmental Satellites and validate the simulation results against satellite observations from both the Geostationary Operational Environmental Satellites and Van Allen Probe missions for 0.9‐MeV electrons. Our results show that the position of the plasmapause plays a significant role in the dynamic evolution of relativistic electrons. The magnetopause shadowing effect is included by using last closed drift shell, and it is shown to significantly contribute to the dropouts of relativistic electrons at high L^*. We perform simulations using four different empirical radial diffusion coefficient models for the GEM challenge events, and the results show that these simulations reproduce the general dynamic evolution of relativistic radiation belt electrons. However, in the events shown here, simulations using the radial diffusion coefficients from Brautigam and Albert (2000) produce the best agreement with satellite observations.