Dynamical Systems' approach to relativistic nonlinear wave-particle interaction in weakly collisional plasmas

摘要

In this report, we present a dynamical systems' approach to study the exactnonlinear wave-particle interaction in relativistic regime. We give aparticular attention to the effect of wave obliquity on the dynamics of theorbits by studying the specific cases of parallel ($\theta=0$) andperpendicular ($\theta=-\pi/2$) propagations in comparison to the general caseof oblique propagation $\theta=]-\pi/2, 0[$. We found that the fixed points ofthe system correspond to Landau resonance, and that the dynamics can evolvefrom trapping to surfatron acceleration for propagation angles obeying a Hopfbifurcations condition. Cyclotron-resonant particles are also studied by theconstruction of a pseudo-potential structure in the Lorentz factor $\gamma$. Wederived a condition for which Arnold diffusion results in relativisticstochastic acceleration. Hence, two general conclusions are drawn : 1) Thepropagation angle $\theta$ can significantly alter the dynamics of the orbitsat both Landau and cyclotron-resonances. 2) Considering the short-time scalesupon which the particles are accelerated, these two mechanisms for Landau andcyclotron resonant orbits could become potential candidates for problems ofparticle energization in weakly collisional space and cosmic plasmas.