Limit on stably trapped particle fluxes

TLDR

Whistler mode noise causes electron pitch‑angle diffusion, while ion cyclotron noise similarly couples to ions. Since excessive wave growth leads to rapid diffusion and particle loss, limiting the growth rate to the rate at which wave energy is depleted by propagation yields an upper bound on the trapped equatorial particle flux. This diffusion precipitates particles into the ionosphere and produces a pitch‑angle distribution of trapped particles that is unstable to further wave growth. Electron fluxes >40 keV and proton fluxes >120 keV observed on Explorers 14 and 12 obey the predicted limit, with fluxes just below the limit beyond L = 4 suggesting an acceleration source that keeps particles near the precipitation threshold; the roughly equal limiting proton and electron fluxes help explain the higher densities of high‑energy protons, and the observed pitch‑angle profiles and required whistler‑mode noise intensity are consistent with the diffusion coefficient and lifetimes.

Abstract

Whistler mode noise leads to electron pitch angle diffusion. Similarly, ion cyclotron noise couples to ions. This diffusion results in particle precipitation into the ionosphere and creates a pitch angle distributon of trapped particles that is unstable to further wave growth. Since excessive wave growth leads to rapid diffusion and particle loss, the requirement that the growth rate be limited to the rate at which wave energy is depleted by wave propagation permits an estimate of an upper limit to the trapped equatorial particle flux. Electron fluxes >40 kev and proton fluxes >120 kev observed on Explorers 14 and 12, respectively, obey this limit with occasional exceptions. Beyond L = 4, the fluxes are just below their limit, indicating that an unspecified acceleration source, sufficient to keep the trapped particles near their precipitation limit, exists. Limiting proton and electron fluxes are roughly equal, suggesting a partial explanation for the existence of larger densities of high-energy protons than of electrons. Observed electron pitch angle profiles correspond to a diffusion coefficient in agreement with observed lifetimes. The required equatorial whistler mode wide band noise intensity, 10−2γ, is not obviously inconsistent with observations and is consistent with the lifetime and with limiting trapped particle intensity.