An Empirical Model of Radiation Belt Electron Pitch Angle Distributions Based On Van Allen Probes Measurements

Abstract

Based on over 4 years of Van Allen Probes measurements, an empirical model of radiation belt electron equatorial pitch angle distribution (PAD) is constructed. The model, developed by fitting electron PADs with Legendre polynomials, provides the statistical PADs as a function of L-shell (L = 1-6), magnetic local time, electron energy (~30 keV to 5.2 MeV), and geomagnetic activity (represented by the Dst index) and is also the first empirical PAD model in the inner belt and slot region. For megaelectron volt electrons, model results show more significant day-night PAD asymmetry of electrons with higher energies and during disturbed times, which is caused by geomagnetic field configuration and flux radial gradient changes. Steeper PADs with higher fluxes around 90°pitch angle and lower fluxes at lower pitch angles for higherenergy electrons and during active times are also present, which could be due to electromagnetic ion cyclotron wave scattering. For hundreds of kiloelectron volt electrons, cap PADs are generally present in the slot region during quiet times and their energy-dependent features are consistent with hiss wave scattering, while during active times, cap PADs are less significant especially at outer part of slot region, which could be due to the complex energizing and transport processes. The 90°-minimum PADs are persistently present in the inner belt and appear in the slot region during active times, and minima at 90°pitch angle are more significant for electrons with higher energies, which could be a critical evidence in identifying the underlying physical processes responsible for the formation of 90°-minimum PADs.

Evolution of Pitch Angle‐Distributed Megaelectron Volt Electrons During Each Phase of the Geomagnetic Storm

“…Pancake PADs are highly anisotropic electron velocity distribution, peaked at 90 • to the magnetic field and were first detected by Wrenn et al (1979). However, we note that there exist few more types of electron PADs like cigar cap as explained in Figure 1 of Zhao et al (2018). Butterfly PADs have a minimum flux around 90 • pitch angle (PA) and peaks at around 45 • and 125 • indicating magnetopause shadowing, drift shell splitting, or wave-particle interactions (e.g., West et al, 1973).…”

“…The sin n ( eq ) function with a negative value of n yielded a reasonable fit to the observations. Recently, Zhao et al (2018) constructed an empirical radiation belt model that provides a statistical picture of electron PAD in the inner belt and slot region. Applying the full set of trigonometric functions entails more fitting coefficients, and they are difficult to handle and interpret.…”

Evolution of Radiation Belt Electron Pitch Angle Distribution Due to Combined Scattering by Plasmaspheric Hiss and Magnetosonic Waves

“…Wave‐particle interactions in the Earth radiation belt play an important role in both energy exchange between plasma waves and electrons and altering electron pitch angle distributions (PADs; e.g., Thorne et al, ). There are four typical categories of electron PADs: pancake (or 90 ° ‐peaked), top‐hat, flat‐top, and butterfly distributions (e.g., Baker et al, ; Gu et al, ; Zhao, Li, Blake, Fennell, Claudepierre, Baker, Jaynes, Malaspina, & Kanekal, , Zhao, Li, Blake, Fennell, Claudepierre, Baker, Jaynes, & Malaspina, , Zhao et al, , ). The pancake PADs are characterized by the flux peak at 90 ° pitch angle and smooth decrease toward the field‐aligned directions, possibly resulting from wave‐particle interactions or the inward radial diffusion (e.g., Schulz & Lanzerotti, ).…”

Storm-time depletions of multi-MeV radiation belt electrons observed at different pitch angles

“…Other physical processes can result in various shapes of PADs, such as pancake, flat top, cigar, cap, and 90°-minimum (Zhao et al, 2018). The pancake PAD is commonly observed and it is believed to be a result of pitch angle scattering due to wave-particle interactions accompanied by a loss to the atmosphere (e.g.…”

“…Although, previous studies discuss the potential effect of the EMIC waves on PAD of multi-MeV electrons (e.g. Usanova et al, 2014, Zhao et al, 2018, understanding of the role of EMIC waves in depletion of the electrons during storms remains incomplete. The EMIC waves are commonly present during geomagnetic storms (Fraser et al, 2010;Halford et al, 2010;Keika et al, 2013;Saikin et al, 2016;Wang et al, 2016), however the effect of the narrowing of PAD and depletions of multi-MeV elections flux driven by EMIC waves was only studied during specific storms or short intervals (e.g.…”