Guiding-center chaotic motion in three electrostatic waves

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Abstract
The dynamics of guiding centers in a general configuration of three electrostatic plane waves is studied in the plane (x,y) perpendicular to a strong magnetic field. The associated Hamiltonian is nonautonomous with 11/2 degrees of freedom, and the conjugated variables are the coordinates (x,y). This is the simplest system that exhibits the onset of chaotic motion in electrostatic plasma turbulence. An explicit analytical solution is obtained for the unperturbed integrable system consisting of two low-amplitude waves, by solving a generalized Kepler equation. Chaotic diffusion of guiding centers becomes possible due to the existence of a third wave. As the amplitude of the perturbation increases, chaotic motion is first localized, then extended over a network spread over the whole phase space along separatrices, and finally densely covers the full space.