Nonlinear interaction of whistler waves with a modulated thin electron beam

The nonlinear theory of a thin modulated electron beam interaction with a monochromatic whistler wave is considered. The self-consistent set of differential equations describing the wave amplitude evolution and the beam particle motion has been solved by a computer code. Results issued from the numerical solution of the differential system are discussed, namely the physical features of the nonlinear beam-wave interaction (trapping, slowing down of the beam, wave damping, multiple bunching, beam focusing), as well as the influence of the physical parameters on the wave emission: beam energy and density, initial beam velocity distribution, and beam current modulation. It has been shown that the trapped particles are the source of the emission; they are decelerated in phase with the wave and remain in Cherenkov resonance with it owing to a nonlinear shift of the parallel wave number. No quasiperiodic exchange of energy between the wave and the particles has been observed. Time evolution of the wave amplitude and the particle energy has been explained by a simple model, as well as the multibunched structures appearing in the particle dynamics for certain physical parameters. (C) 1998 American Institute of Physics. [S1070-664X(98)03512-5].