The role of the Gendrin mode of VLF propagation in the generation of magnetospheric emissions

Impulsive VLF wave packets and electron beams may be formed in the magnetosphere from the superposition of Gendrin mode components defined by the condition cosθ=2ffH where θ=wave normal angle measured from the Earth's static magnetic field B¯o ,f=frequency of the wave component and fH = electron gyrofrequency. The frequency range of the Gendrin mode spectrum is defined by fL < f < fH/2, where fL = lower hybrid resonance frequency ≈ =fH/43and fHi = proton gyrofrequency. Since the group ray velocity of all Gendrin components is given by υG=c2fHfN where fN = plasma frequency, and is aligned with B¯o and since the longitudinal (parallel to B¯o) component of the phase velocity is the same as υG, a Gendrin wave packet will travel in a homogeneous medium without distortion, constituting a kind of soliton. An electron whose parallel velocity υ∥ is close to υG (i.e., near longitudinal resonance) may become trapped by the E∥ of the Gendrin wave packet, giving up energy to the packet as it propagates in a region of decreasing υG, such as a typical field line path approaching the magnetic equator. As the packet grows E∥ increases causing more trapping and accordingly more wave growth, giving rise to an “Impulsive Wave Instability” (IWI). Wave packet growth is limited by wave loss due to drift away from the main packet of previously generated components that no longer satisfy the Gendrin condition. As the packet leaves the equator growth ceases, the packet collapses and the previously trapped electrons become transient electron beams that may themselves trigger more emissions. It is suggested that the impulsive VLF emissions observed by DE1 and other satellites may be caused by the IWI mechanism.