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

In this report, we present a dynamical systems' approach to study the exact nonlinear wave-particle interaction in relativistic regime. We give a particular attention to the effect of wave obliquity on the dynamics of the orbits by studying the specific cases of parallel ($θ=0$) and perpendicular ($θ=-π/2$) propagations in comparison to the general case of oblique propagation $θ=]-π/2, 0[$. We found that the fixed points of the system correspond to Landau resonance, and that the dynamics can evolve from trapping to surfatron acceleration for propagation angles obeying a Hopf bifurcations condition. Cyclotron-resonant particles are also studied by the construction of a pseudo-potential structure in the Lorentz factor $γ$. We derived a condition for which Arnold diffusion results in relativistic stochastic acceleration. Hence, two general conclusions are drawn : 1) The propagation angle $θ$ can significantly alter the dynamics of the orbits at both Landau and cyclotron-resonances. 2) Considering the short-time scales upon which the particles are accelerated, these two mechanisms for Landau and cyclotron resonant orbits could become potential candidates for problems of particle energization in weakly collisional space and cosmic plasmas.