Interaction of ring current and radiation belt protons with ducted plasmaspheric hiss: 2. Time evolution of the distribution function

The evolution of the bounce-averaged ring current/radiation belt proton distribution is simulated during resonant interactions with ducted plasmaspheric hiss. The plasmaspheric hiss is assumed to be generated by ring current electrons and to be damped by the energetic protons. Thus energy is transferred between energetic electrons and protons using the plasmaspheric hiss as a mediary. The problem is not solved self-consistently. During the simulation period, interactions with ring current electrons (not represented in the model) are assumed to maintain the wave amplitudes in the presence of damping by the energetic protons, allowing the wave spectrum to be held fixed. Diffusion coefficients in pitch angle, cross pitch angle/energy, and energy were previously calculated by Kozyra et al. (1994) and are adopted for the present study. The simulation treats the energy range, E ≥ 80 keV, within which the wave diffusion operates on a shorter timescale than other proton loss processes (i.e., Coulomb drag and charge exchange). These other loss processes are not included in the simulation. An interesting result of the simulation is that energy diffusion maximizes at moderate pitch angles near the edge of the atmospheric loss cone. Over the simulation period, diffusion in energy creates an order of magnitude enhancement in the bounce-averaged proton distribution function at moderate pitch angles. The loss cone is nearly empty because scattering of particles at small pitch angles is weak. The bounce-averaged flux distribution, mapped to ionospheric heights, results in elevated locally mirroring proton fluxes. OGO 5 observed order of magnitude enhancements in locally mirroring energetic protons at altitudes between 350 and 1300 km and invariant latitudes between 50° and 60° (Lundblad and Soraas, 1978). The proton distributions were highly anisotropic in pitch angle with nearly empty loss cones. The similarity between the observed distributions and those resulting from this simulation raises the possibility that interactions with plasmaspheric hiss play a role in forming and maintaining the characteristic zones of anisotropic proton precipitation in the subauroral ionosphere. Further assessment of the importance of this process depends on knowledge of the distribution in space and time of ducted plasmaspheric hiss in the inner magnetosphere.