On the Influence of Propagation Properties of Whistler-Mode Waves in the Earth’s Magnetosphere on Their Cyclotron Amplification

We study the properties of the cyclotron amplification of whistler-mode waves during their propagation in the Earth’s magnetosphere in the presence of large-scale density inhomogeneities such as the plasmapause or density ducts. Wave propagation is considered within the framework of the geometrical optics with the use of cold plasma density profiles measured onboard the Van Allen Probes satellites. Wave amplitude variation due to the cyclotron interactions with energetic electrons having an anisotropic distribution function is studied. The cyclotron growth rate is calculated along the wave trajectory taking into account the wave vector variation for a given analytical distribution function of energetic electrons. We show that in the case of guided propagation in a density duct or near the plasmapause the frequency dependences of the one-hop wave gain and the local growth rate in the equatorial region approximately coincide with each other for low initial wave normal angles (|Θ0| ≲ 30°) and relatively low energies (W0 ≲ 15 keV). The amplification band expands towards the higher frequencies for higher initial propagation angles and electron energies. In the case of nonducted propagation, the efficiency of cyclotron interactions is notably lower, and the frequency dependences of the one-hop wave gain and the equatorial growth rate differ: the waves having the initial wave angle directed towards the Earth are stronger amplified, and this asymmetry increases with increasing electron energy.