Cyclotron-resonance amplification of VLF and ULF whistlers

Abstract

Electromagnetic signals that propagate through the magnetosphere exchange energy with nonthermal charged particles by the cyclotron-resonance mechanism. The interaction is due to a Doppler shift of the propagation frequency ω to the cyclotron frequency ωc of the charged particle that allows the particle to resonate with the electromagnetic fields. The dominant exchange is between electrons around 1 kev and VLF whistlers that propagate in the right-hand mode and between protons around 1 kev and ULF whistlers (Pc 1 geomagnetic micropulsations) that propagate in the left-hand mode. The complex wave number k(ω) = kr + iki for propagation in a hot uniform plasma parallel to a static magnetic field is assumed to describe whistler properties locally in the magnetosphere. The power transfer function A(ω), which relates the input and output power spectrums, is determined by the path integral of ki along a geomagnetic flux tube. Spectrums of A for both VLF and ULF whistlers have been evaluated for a variety of energy and pitch-angle distributions of the form E−n sinm α. In general, A has an amplification maximum just below a sharp absorption cutoff, which is consistent with observations. The detailed input-output spectrums of whistlers that are necessary to test the theory are not available yet. When these spectrums are measured, this interaction may provide a possible method for mapping the phase space distribution of nonthermal particles in the magnetosphere.