Depletions of Multi-MeV Electrons and Their Association to Minima in Phase Space Density

Fast-localized electron loss, resulting from interactions with electromagnetic ion cyclotron (EMIC) waves, can produce deepening minima in phase space density (PSD) radial profiles. Here, we perform a statistical analysis of local PSD minima to quantify how readily these are associated with radiation belt depletions. The statistics of PSD minima observed over a year are compared to the Versatile Electron Radiation Belts (VERB) simulations, both including and excluding EMIC waves. The observed minima distribution can only be achieved in the simulation including EMIC waves, indicating their importance in the dynamics of the radiation belts. By analyzing electron flux depletions in conjunction with the observed PSD minima, we show that, in the heart of the outer radiation belt (L* < 5), on average, 53% of multi-MeV electron depletions are associated with PSD minima, demonstrating that fast localized loss by interactions with EMIC waves are a common and crucial process for ultra-relativistic electron populations.

Application of Wavelet Methods in the Investigation of Geospace Disturbances: A Review and an Evaluation of the Approach for Quantifying Wavelet Power

Geospace disturbances refer collectively to the variations of the geomagnetic field and the trapped particle populations in the near-Earth space. These are the result of transient and recurrent solar activity, which consequently drives the variable solar wind. They may appear in multiple timescales, from sub-seconds to days, months and years. Wavelet analysis is one of the most popular, and powerful, methods in the study of these variations, as it allows for the local decomposition of non-stationary time series in frequency (or time-scale) and time simultaneously. This article is a review of the wavelet methods used in the investigation of geomagnetic field oscillations, which underlines their advantages as spectral analysis methods and demonstrates their utilization in the interdependence of multiple time-series. Lastly, the proper methodology for the accurate estimation of the power inferred from geophysical signals, applicable in quantitative studies, is included and is publicly available at the database of the University of Athens.

From solar sneezing to killer electrons: outer radiation belt response to solar eruptions

Electrons in the outer Van Allen (radiation) belt occasionally reach relativistic energies, turning them into a potential hazard for spacecraft operating in geospace. Such electrons have secured the reputation of satellite killers and play a prominent role in space weather. The flux of these electrons can vary over time scales of years (related to the solar cycle) to minutes (related to sudden storm commencements). Electric fields and plasma waves are the main factors regulating the electron transport, acceleration and loss. Both the fields and the plasma waves are driven directly or indirectly by disturbances originating in the Sun, propagating through interplanetary space and impacting the Earth. This paper reviews our current understanding of the response of outer Van Allen belt electrons to solar eruptions and their interplanetary extensions, i.e. interplanetary coronal mass ejections and high-speed solar wind streams and the associated stream interaction regions. This article is part of the theme issue 'Solar eruptions and their space weather impact'.

Analytic Expressions for Radial Diffusion

I briefly review, compare and contrast two theoretical works that have significantly influenced radial diffusion research thus far, namely, the works of Fälthammar (1965, https://doi.org/10.1029/JZ070i011p02503) and the works of Fei et al. (2006, https://doi.org/10.1029/2005JA011211). Leveraging Fälthammar's model for magnetic field disturbances, I demonstrate that Fei et al's formulas are incorrect: they underestimate radial diffusion by a factor two in the presence of magnetic field disturbances. This underestimation comes from the erroneous assumption that radial displacements driven by magnetic field disturbances are statistically independent from radial displacements driven by induced electric fields while in fact both displacements are proportional to each other. Fei et al.'s approach is similar to Fälthammar's approach in that they both analyze radial diffusion by pieces, depending on the nature of the driver. Yet, the Fokker-Planck equation requires only one radial diffusion coefficient to characterize statistically a trapped radiation belt population cross drift shell motion. Thus, it is worth questioning the practice that consists of defining the coefficient as a sum of independent contributions. In addition, both theoretical models rely on the assumption that the background magnetic field is primarily dipolar, leading to flawed estimates. To overcome these limitations and to improve radial diffusion quantification, I use a general formulation for the variation of the third adiabatic invariant (1) to describe how to compute a radial diffusion coefficient in the most general way and (2) to highlight the assumptions that need to be questioned.

Fast Diffusion of Ultrarelativistic Electrons in the Outer Radiation Belt: 17 March 2015 Storm Event

Inward radial diffusion driven by ULF waves has long been known to be capable of accelerating radiation belt electrons to very high energies within the heart of the belts, but more recent work has shown that radial diffusion values can be highly event-specific, and mean values or empirical models may not capture the full significance of radial diffusion to acceleration events. Here we present an event of fast inward radial diffusion, occurring during a period following the geomagnetic storm of 17 March 2015. Ultrarelativistic electrons up to ∼8 MeV are accelerated in the absence of intense higher-frequency plasma waves, indicating an acceleration event in the core of the outer belt driven primarily or entirely by ULF wave-driven diffusion. We examine this fast diffusion rate along with derived radial diffusion coefficients using particle and fields instruments on the Van Allen Probes spacecraft mission.

Explaining the apparent impenetrable barrier to ultra-relativistic electrons in the outer Van Allen belt

Recent observations have shown the existence of an apparent impenetrable barrier at the inner edge of the ultra-relativistic outer electron radiation belt. This apparent impenetrable barrier has not been explained. However, recent studies have suggested that fast loss, such as associated with scattering into the atmosphere from man-made very-low frequency transmissions, is required to limit the Earthward extent of the belt. Here we show that the steep flux gradient at the implied barrier location is instead explained as a natural consequence of ultra-low frequency wave radial diffusion. Contrary to earlier claims, sharp boundaries in fast loss processes at the barrier are not needed. Moreover, we show that penetration to the barrier can occur on the timescale of days rather than years as previously reported, with the Earthward extent of the belt being limited by the finite duration of strong solar wind driving, which can encompass only a single geomagnetic storm.

The origin of the apparent impenetrable barrier in the outer Van Allen belt is still uncertain. Here, the authors report that penetration to the barrier can occur by means of ultra-low frequency wave transport, enabling ultra-relativistic electrons to reach the location of the barrier.

Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons

Van Allen radiation belts are typically two zones of energetic particles encircling the Earth separated by the slot region. How the outer radiation belt electrons are accelerated to relativistic energies remains an unanswered question. Recent studies have presented compelling evidence for the local acceleration by very-low-frequency (VLF) chorus waves. However, there has been a competing theory to the local acceleration, radial diffusion by ultra-low-frequency (ULF) waves, whose importance has not yet been determined definitively. Here we report a unique radiation belt event with intense ULF waves but no detectable VLF chorus waves. Our results demonstrate that the ULF waves moved the inner edge of the outer radiation belt earthward 0.3 Earth radii and enhanced the relativistic electron fluxes by up to one order of magnitude near the slot region within about 10 h, providing strong evidence for the radial diffusion of radiation belt relativistic electrons.

Analytic expressions for ULF wave radiation belt radial diffusion coefficients

We present analytic expressions for ULF wave-derived radiation belt radial diffusion coefficients, as a function of L and Kp, which can easily be incorporated into global radiation belt transport models. The diffusion coefficients are derived from statistical representations of ULF wave power, electric field power mapped from ground magnetometer data, and compressional magnetic field power from in situ measurements. We show that the overall electric and magnetic diffusion coefficients are to a good approximation both independent of energy. We present example 1-D radial diffusion results from simulations driven by CRRES-observed time-dependent energy spectra at the outer boundary, under the action of radial diffusion driven by the new ULF wave radial diffusion coefficients and with empirical chorus wave loss terms (as a function of energy, Kp and L). There is excellent agreement between the differential flux produced by the 1-D, Kp-driven, radial diffusion model and CRRES observations of differential electron flux at 0.976 MeV-even though the model does not include the effects of local internal acceleration sources. Our results highlight not only the importance of correct specification of radial diffusion coefficients for developing accurate models but also show significant promise for belt specification based on relatively simple models driven by solar wind parameters such as solar wind speed or geomagnetic indices such as Kp.

KEY POINTS

Analytic expressions for the radial diffusion coefficients are presentedThe coefficients do not dependent on energy or wave m valueThe electric field diffusion coefficient dominates over the magnetic.