Impulsive VLF wave packets and electron beams may be formed in the magnetosphere from the superposition of Gendrin mode components defined by the condition cos &thgr;=2f/fH, where &thgr;=wave normal angle measured from the Earth's static magnetic field B¿0, 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 ≈√fHfHi=fH/43 and fHi=proton gyrofrequency. Since the group ray velocity of all Gendrin components is given by vG=c/2 fH/fN where fN=plasma frequency and is aligned with B¿0 and since the longitudinal (parallel to B¿0) component of the phase velocity is the same as vG, a Gendrin wave packet will travel in a homogeneous medium without distortion, constituting a kind of soliton. An electron whose parallel velocity v∥ is close to vG (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 vG, 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. The purpose of this letter is to show that the Gendrin mode of propagation [Gendrin, 1961> is capable of supporting a new kind of wave particle interaction involving longitudinal resonance, which we shall call the impulsive Wave Instability (IWI). Here a short duration whistler-mode wave packet (essentially an impulse) consisting of superposed Gendrin components (frequencies ranging from the lower hybrid resonance frequency fL≈ √fHfHi=fH/43, where fHi=proton gyrofrequency, to one-half the electron gyrofrequency fH/2) traps passing electrons that are close to longitudinal (i.e., Landau) resonance, where the electron parallel velocity v∥ equals the parallel component of the wave phase velocity vp∥ which is the same as the group ray velocity. For typical models of the cold plasma, it is shown that the velocity of such a wave packet is slowly reduced as it approaches the equator, causing continual trapping of electrons whose parallel velocity v∥ slightly exceeds the parallel component of the wave phase velocity vp∥.

As these trapped electrons are slowed by the wave their lost energy is transferred to the wave causing it to grow [Brice, 1960; Helliwell, EOS, 1989>, resembling the traveling wave tube where an electron beam is slowed by a slightly slower circuit wave with an axial component of electric field. This hypothesis was motivated by a proposed theory of whistler precursors [Park and Helliwell, 1977>, supported by calculations [Tkalcevic, 1982; Tkalcevic et