Limit on Stably Trapped Particle Fluxes

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.