Non-linear theory of particle dynamics in cosmic electromagnetic fields. I - Regular motion in a simple Alfven wave

Astronomy and Astrophysics – Astrophysics

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Cosmic Plasma, Cosmic Rays, Magnetohydrodynamic Waves, Nonlinear Equations, Particle Diffusion, Plasma-Electromagnetic Interaction, Electromagnetic Fields, Particle Motion, Perturbation Theory, Plasma Resonance

Scientific paper

A study of the nonlinear dynamics of the nonthermal component of the cosmic environment is presented. The problem of a test particle propagating in a sinusoidal Alfven wave is of basic importance in the perturbation theory of cosmic ray dynamics. In fact, it is assumed that the character of the motion is diffusive because of resonant pitch angle scattering off fluctuations of the cosmic magnetic field. The nonlinear theory of this problem shows a richer behavior. An approximate invariant of the motion, which accurately describes the dynamics in the vicinity of resonances is found. This invariant shows that particles can be locked in a resonant configuration, instead of being scattered. Only one resonance is admitted between a particle and an individual harmonic of the magnetic fluctuations, by the well known cyclotron resonance condition of quasi-linear theory. A nonlinear resonance condition yielding an infinite number of resonances in the motion of a particle in a purely sinusoidal wave, parallel to the mean magnetic field is found.

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