Waves which couple to energetic electrons are particularly important in space weather, as they drive rapid changes in the topology and intensity of Earth’s outer radiation belt during geomagnetic storms. This includes Ultra Low Frequency (ULF) waves that interact with electrons via radial diffusion which can lead to electron dropouts and rapid acceleration and inward transport of electrons during. In radiation belt simulations, the strength of this interaction is specified by ULF wave radial diffusion coefficients. In this paper we detail the development of new models of electric and magnetic radial diffusion coefficients derived from in-situ observations of the azimuthal electric field and compressional magnetic field. The new models use L* as it accounts for adiabatic changes due to the dynamic magnetic field coupled with an optimized set of four components of solar wind and geomagnetic activity, Bz, V, Pdyn and Sym-H, as independent variables (inputs). These independent variables are known drivers of ULF waves and offer the ability to calculate diffusion coefficients at a higher cadence then existing models based on Kp. We investigate the performance of the new models by characterizing the model residuals as a function of each independent variable and by comparing to existing radial diffusion models during a quiet geomagnetic period and through a geomagnetic storm. We find that the models developed here perform well under varying levels of activity and have a larger slope or steeper gradient as a function of L* as compared to existing models (higher radial diffusion at higher L* values).

Relativistic electrons in the radiation belts can be transported as a result of wave-particle interactions (WPI) with ultra-low frequency (ULF) waves. Such WPI are often assumed to be diffusive, parametric models for the radial diffusion coefficient often being used to assess the rates of radial transport. However, these WPI transition from initially coherent interactions to the diffusive regime over a finite time, this time depending on the ULF wave power spectral density, and local resonance conditions. Further, in the real system on the timescales of a single storm, interactions with finite discrete modes may be more realistic. Here, we use a particle-tracing model to simulate the dynamics of outer radiation belt electrons in the presence of a finite number of discrete frequency modes. We characterize the point of the onset of diffusion as a transition from separate discrete interactions in terms of wave parameters by using the “two-thirds” overlap criterion (Lichtenberg & Lieberman, 1992), a comparison between the distance between, and the widths of, the electron’s primary resonant islands in phase space. Further, we find the particle decorrelation time in our model system with typical parameters to be on the timescale of hours, which only afterwards can the system be modeled by one-dimensional radial diffusion. Direct comparison of particle transport rates in our model with previous analytic diffusion coefficient formulations show good agreement at times beyond the decorrelation time. These results are critical for determining the time periods and conditions under which ULF wave radial diffusion theory can be applied.

We present new and previously unreported in-situ observations of Hertz frequency multi-harmonic mode field line resonances detected by the Electric Field and Waves (EFW) instrument on-board the NASA Van Allen Probes during low-L perigee passes. Spectral analysis of the spin plane electric field data reveals the waves in numerous perigee passes, in sequential passes of Probes A and B, and with harmonic frequency structures from ~0.5 to 3.5 Hz which vary with L-shell, altitude, and from day to day. Comparing the observations to wave models using plasma mass density values along the field line given by empirical power laws and from the International Reference Ionosphere model (IRI), we conclude the waves are standing Alfvén field line resonances, and that only odd-mode harmonics are excited. The model eigenfrequencies are strongly controlled by the density close to the apex of the field line, suggesting a new diagnostic for equatorial ionospheric density dynamics.

This paper examines the rapid losses and acceleration of trapped relativistic and ultrarelativistic electron populations in the Van Allen radiation belt during the September 7-9, 2017, geomagnetic storm. By analyzing the dynamics of the last closed drift shell (LCDS) and the electron flux and phase space density (PSD), we show that the electron dropouts are consistent with magnetopause shadowing and outward radial diffusion to the compressed LCDS. During the recovery phase, an in-bound pass of Van Allen Probe A shows an apparent local peak in PSD. However, a fortuitous timing of a crossing of the two Van Allen Probes reveals instead how the apparent PSD peak arises from aliasing monotonic PSD profiles which are rapidly increasing due to acceleration from very fast inwards radial diffusion. In the absence of such multi-satellite conjunctions during fast acceleration events, the source might otherwise be attributed to local acceleration processes.

We examine drift phase structure in the electron radiation belt observations to differentiate radial transport mechanisms. Impulsive electrostatic or electromagnetic fields can cause radial transport and produce drift echoes (periodic drift phase structures with energy-dependent period). Narrow-band standing electromagnetic wave fields can also cause radial transport, while producing energy-independent periodic drift phase structures. Broad-band, random-phase electromagnetic wave fields can cause radial transport, but do not necessarily produce drift phase structure. We present results of three case studies showing little association between drift phase structure and ~MeV electron flux enhancements in the outer belt. We estimate the amplitude of drift phase structures expected for impulsive or narrow-band interactions to compete with broad-band, random-phase waves. We show that the observed drift phase structure is typically much smaller than would be present if either impulses or narrow-band waves were the dominant cause of radial transport. We conclude that radial transport is primarily consistent with the broad-band, random-phase, small perturbations assumed in quasilinear diffusion theory, although we cannot rule out the unlikely possibility that radial transport plays little role in radiation belt dynamics.

We present simulations of the outer radiation belt electron flux during the March 2015 and March 2013 storms using a radial diffusion model. Despite differences in Dst intensity between the two storms the response of the ultra-relativistic electrons in the outer radiation belt was remarkably similar, both showing a sudden drop in the electron flux followed by a rapid enhancement in the outer belt flux to levels over an order of magnitude higher than those observed during the pre-storm interval. Simulations of the ultra-relativistic electron flux during the March 2015 storm show that outward radial diffusion can explain the flux dropout down to L*=4. However, in order to reproduce the observed flux dropout at L*<4 requires the addition of a loss process characterised by an electron lifetime of around one hour operating below L*~3.5 during the flux dropout interval. Nonetheless, during the pre-storm and recovery phase of both storms the radial diffusion simulation reproduces the observed flux dynamics. For the March 2013 storm the flux dropout across all L-shells is reproduced by outward radial diffusion activity alone. However, during the flux enhancement interval at relativistic energies there is evidence of a growing local peak in the electron phase space density at L*~3.8, consistent with local acceleration such as by VLF chorus waves. Overall the simulation results for both storms can accurately reproduce the observed electron flux only when event specific radial diffusion coefficients are used, instead of the empirical diffusion coefficients derived from ULF wave statistics.