Chaotic diffusion across magnetic field in electrostatic three-waves dynamical systems

Numerical and analytical methods are applied to study the mechanism responsible for the onset of chaos in a restricted number of waves. The integrability of the two-dimensional guiding center motion (for two electrostatic waves) and the addition of a third wave of small amplitude, leading to a chaotic motion, is shown. The guiding center system in three waves is proven to be cahotic, by taking into account the case of equal frequencies with particular orientations and reducing the motion equations to a unique time-dependent second order differential equation in one variable. For low values of the amplitudes of the first two waves an approximative description of the threshold of cahotic motion is derived, using the standard mechanism of resonance overlapping. For larger values of the third perturbation wave amplitude, the mechanism leading to large-scale stochasticity in phase space is studied, as the result of the collapse of two hyperbolic points, occurring when the amplitude of the perturbation reaches that of the two first waves. Concerning to large amplitudes of the two first waves, the breaking of a resistent S- shaped curve, leading to a complex permeable structure is observed