heal.abstract |
The relativistic motion of electrons in an intense electromagnetic wave propagating obliquely to a uniform magnetic field is studied in detail. This is done within the framework of a Fokker-Planck-Kolmogorov (FPK) analytical approach as well as numerically, by integrating the equations of motion and obtaining Poincaré's surface of section. In particular, an electron-cyclotron wave is considered. At a certain threshold value of the wave amplitude, which depends upon the angle of propagation, cyclotron resonance overlapping can lead to a diffusive acceleration to high energies. The analytically predicted diffusion rates are explicitly evaluated for various cases. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion process proceeds in stages. In the first stage the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage the ensemble-averaged square deviation of the variable involved scales quadratically with time. During the second stage, which is quite long (150ωce-1), they scale linearly with time. For much longer times (> 150ωce-1), deviation from linear scaling slowly sets in. Good agreement with the analytical model suggests that, at least for the second stage, the FPK approach is a valid approximation. © 1989 American Institute of Physics. |
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