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

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 (similar to 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.