| As a magnetoplasma, the earth's magnetosphere can support a variety of electromagnetic wave modes in a wide range of frequencies. An important example is the right-hand elliptically polarized whistler mode wave that propagates at frequencies below the electron gyrofrequency. The whistler mode waves can interact through doppler-shifted resonance with energetic electrons trapped in the geomagnetic field. Due to these interactions, the waves can be amplified and the distribution of the energetic electrons can be disturbed. In this work we consider one important class of wave-particle interactions in the inner magnetosphere, namely, the cyclotron resonance interaction between coherent VLF waves and radiation belt electrons. One consequence of such interactions is the pitch angle scattering of the electrons and the resultant precipitation of these electrons into the ionosphere where they can cause ionization and conductivity enhancements, heating and the emission of X rays and light.;We employ a test particle simulation method to study the wave-induced perturbations of electron trajectories. To include the quasi-relativistic electron energies up to at least hundreds of keV, the well-known equations of motion for the cyclotron resonance wave-particle interaction are rewritten by taking into account relativistic effects. Based on these equations and the test particle scheme, a computer model is developed for determining the transient evolution of the energy flux into the ionosphere of electrons precipitated due to interactions with VLF wave packets propagating longitudinally along the geomagnetic field lines. By taking account of the group travel times of wave components of different frequency as well as the wave amplitude variations resulting from the signal dispersion, the transient precipitation model is applied to the cases of variable frequency VLF signals, such as whistlers, chorus emissions and triggered emissions. We have compared the predictions of our model, i.e., the precipitation flux level, pulse shape and associated time relationships, with ground based observations of the ionospheric effects of VLF wave-induced particle precipitation. The results demonstrate that our model can be used to interpret the observed experimental results and to diagnose some features of the energetic electron distributions in the magnetosphere. |
