Frequency bands and gaps of magnetospheric chorus waves generated by resonant beam/plateau electrons

In this paper, the modifications of the whistler dispersion characteristics are investigated which arise if resonant electrons are taken into account. The following chain of processes is emphasized: Generation of whistler waves propagating at different angles to the magnetic field and their nonlinear interaction with resonant electrons result in the appearance of modulated electron beams in the background plasma. As a result, the dispersion characteristics of waves in this new plasma might be significantly changed. By analysing the modified dispersion characteristics these changes are discussed. Supported by particle simulations and space observations, it is assumed that in the electron distribution function at the resonance velocity a plateau-like beam is formed. Because of the weakness of the beam, the term “beam/plateau population (b/p)” is used. By solving the kinetic dispersion relation of whistler waves in electron plasmas with b/p populations, the associated modifications of the whistler dispersion characteristics are presented in diagrams showing, in particular, the frequency versus propagation angle dependence of the excited waves. It is important to point out the two functions of the b/p populations. Because of the bi-directional excitation of whistler waves by temperature anisotropy, one has to distinguish between up- and downstream populations and accordingly between two b/p modes. The interaction of the beam-shifted cyclotron mode ω = Ωe + k⋅Vb (V bVb is the b/p velocity, Ωe: electron cyclotron frequency) with the whistler mode leads to enhanced damping at the ω-k point where they intersect. This is the origin of the frequency gap at half the electron cyclotron frequency (ω~Ωe/2) for quasi-parallel waves which are driven by temperature anisotropy. Furthermore, it is shown that the upstream b/p electrons alone (in the absence of temperature anisotropy) can excite (very) oblique whistler waves near the resonance cone. The governing instability results from the interaction of the beam/plateau mode ω = k⋅Vb (Vb > 0) with the whistler mode. As a further remarkable effect, another frequency gap at ω~Ωe/2 in the range of large propagation angles may arise. It happens at the triple point where both b/p modes and the whistler mode intersect. Our investigation shows that the consideration of resonant electrons in form of beam/plateau populations leads to significant modifications of the spectrum of magnetospheric whistler waves which are originally driven by temperature anisotropy. Relations to recent and former space observations are discussed.