Whistler mode waves below lower hybrid resonance frequency: generation and spectral features

Equatorial noise in the frequency range below the lower hybrid resonance frequency, whose structure is shaped by high proton cyclotron harmonics, has been observed by the Cluster spacecraft. We develop a model of this wave phenomenon which assumes (as, in general, has been suggested long ago) that the observed spectrum is excited due to loss-cone instability of energetic ions in the equatorial region of the magnetosphere. The wave field is represented as a sum of constant frequency wave packets which cross a number of cyclotron resonances while propagating in a highly oblique mode along quite specific trajectories. The growth (damping) rate of these wave packets varies both in sign and magnitude along the ray path, making the wave net amplification, but not the growth rate, the main characteristic of the wave generation process. The growth rates and the wave amplitudes along the ray paths, determined by the equations of geometrical optics, have been calculated for a 3D set of wave packets with various frequencies, initial L-shells, and initial wave normal angles at the equator. It is shown that the dynamical spectrum resulting from the proposed model qualitatively matches observations.