A Natural Limit to the Spectral Hardness of Worst Case Electron Radiation in the Terrestrial Van Allen Belt

Abstract

The flux of relativistic electrons in the terrestrial Van Allen radiation belt can vary by orders of magnitude during a geomagnetic storm. The response is typically assumed to be controlled by an often delicate balance between acceleration and loss processes. Here we analyze all 133 magnetic storms from the NASA Van Allen Probes era. We show how the belts demonstrate a repeatable response which limits not only the worst case flux, but also controls and delivers a limit to the severity of the spectral hardness, consistent with the theory of Kennel and Petschek first developed over 50 years ago. When this theory is extended to relativistic energies, the observed electron flux is seen to reach a naturally limited worst case with a clear energy dependence. Here we show how the Kennel‐Petschek theory can explain the evolution and hardening of the electron spectrum during geomagnetic storms. It also introduces an energy‐dependent maximum flux limit. This limit is never reached during the Van Allen Probes era at energies above 2.6 MeV, meanwhile, it is reached within hours at lower energies (∼100 keV) in almost every storm. No current radiation belt models include this effect; without it, they cannot accurately predict the consequent radiation dynamics. Overall, our results demonstrate how this creates a remarkable absolute natural limit to both the spectral hardness and the severity of extreme electron space radiation.

Upper Limit on Outer Radiation Belt Electron Flux Based on Dynamical Equilibrium

“…We adopt a simple but realistic lower boundary condition, such that F(E min , t) is given by Equation 14with D EE = 0, equivalent to a condition ∂f/∂E = ∂ 2 f/∂E 2 = 0 there. This lower boundary condition corresponds to injections maintaining a relatively flat electron PSD in the vicinity of E min ≈ 0.1 MeV, as during several observations (Baker et al, 1979;Olifer et al, 2022). This allows a rapid increase of F(E min , t) as long as F(E min , t)/τ L < F S (E min )/τ S .…”

“…For sustained electron injections lasting up to t ≈ 12−72 hr (Agapitov et al., 2018; Hua, Bortnik, & Ma, 2022; Mourenas, Artemyev, et al., 2022; Turner et al., 2015), Equation gives E max ≈ 0.8–2 MeV. The weak variation of E max with parameters in Equation , and the much smaller electron flux above ∼1.5 MeV during intense injections (Hua, Bortnik, & Ma, 2022; Mourenas, Artemyev, et al., 2022; Olifer et al., 2022), lend credence to this first‐order estimate.…”

“…We use level-2 spin-averaged omnidirectional electron fluxes measured by the Magnetic Electron Ion Spectrometer (MagEIS) (Claudepierre et al, 2021) of the Energetic Particle, Composition, and Thermal Plasma (ECT) Suite (Spence et al, 2013) on board the Van Allen Probes. During the three periods examined in Figures 4a-4c, Olifer et al (2022) have shown that the electron flux roughly reached the Kennel-Petschek flux limit J KP (E) at ∼0.1-0.3 MeV. During the fourth event displayed in Figure 4d, a growing peak of PSD of 2-4 MeV electrons, recorded by the Van Allen Probes at L* ≃ 4.5, was not reproduced by simulations of ULF wave-driven electron inward radial diffusion without chorus-driven acceleration, suggesting a key role of chorus wave-driven energization during this storm (Hudson et al, 2021;.…”

Unraveling the Critical Geomagnetic Conditions Controlling the Upper Limit of Electron Fluxes in the Earth's Outer Radiation Belt

“…The follow‐up study of Olifer et al. (2022) further found that the relativistic electrons below ∼2.6 MeV can only reach the KP limit during the strongest enhancement events. They concluded that the higher energy fluxes stayed below KP limit during the Van Allen Probes era, resulting in a sharper energy gradient.…”

“…Both studies revealed the consistency between the observed maximum fluxes over ∼100 keV-∼1 MeV and confirmed predictions from the Kennel & Petschek (KP) theory (Kennel & Petschel, 1966), while the upper limit of multi-MeV electron fluxes was not well captured by KP theory. The follow-up study of Olifer et al (2022) further found that the relativistic electrons below ∼2.6 MeV can only reach the KP limit during the strongest enhancement events. They concluded that the higher energy fluxes stayed below KP limit during the Van Allen Probes era, resulting in a sharper energy gradient.…”