Analysis of Radiation Belt "Killer" Electron Energy Spectra. Issue 9 (12th September 2022) - Summers, Danny; Stone, Sarah
Abstract: Highly energetic (>1 MeV) electrons are typically generated in the Earth's outer radiation belt during geomagnetically disturbed times. Such "killer" electrons can be produced by electron cyclotron resonance with whistler‐mode waves. We model this process by a relativistic Fokker‐Planck diffusion equation for the electron distribution function f ( E ), where E is the normalized electron kinetic energy. The equation involves an energy diffusion coefficient D ( E ) and an advection coefficient A ( E ), which depend on the wave spectral energy density. For two types of wave energy spectrum, a Gaussian and a power law with spectral index q, we seek large‐ E steady‐state solutions for f ( E ). For lower‐band chorus, for both Gaussian and power law spectra, we find that f ∼ e − E / k fe^-E/k with k = D 0 T 0, where D 0 is a diffusion parameter and T 0 is the e‐folding timescale for electron loss. For a full‐band whistler spectrum, we find that if 2 < q < 4 then f ∼ e − 2 ( 4 − q ) E ( 4 − q ) / 2 k fe^-2(4-q)E^(4-q)/2k ; in the special case q = 4, we obtain the power law solution f ∼ E − δ, where δ = ( − 1 + 9 + 4 / k ) / 2 δ =(-1+9+4/k)/2 . We compare the analytical electron spectra obtained with the phase‐space density profiles observed by the Van Allen Probes. Key Points: Killer electron generation by chorus waves is modeled by a Fokker‐Planck diffusion equation Large‐ E asymptotic solutions for the electron energy spectra are derived We find good agreement between the asymptotic spectra and the experimental spectra from four killer electron "events"