Chaotic diffusion across magnetic field in electrostatic three-waves dynamical systems
An observed feature of numerical models for the diffusion across a straight magnetic field in the presence of perpendicular electrostatic turbulence with many waves is the existence of a threshold value of the turbulence amplitude for the onset of large scale stochastic motion. This paper discusses the mechanism responsible for the onset of chaos in a restricted number of waves and the conditions for the existence of a threshold, via numerical and analytical methods. It is first shown that the two dimensional guiding centre motion in the general case of two electrostatic waves, appears to be completely integrable. In this case, the Hamiltonian of this dynamical system takes the form of a generalised Kepler equation in two variables. An angle-action variables approach is explicitly given, for the determination of the exact frequencies. In the case of three-waves the time variable cannot be eliminated in general and the motion is governed by a one and a half degrees of freedom Hamiltonian. For low values of the amplitudes of the first two waves, an approximate description of the threshold of chaotic motion is derived by the mechanism of resonance overlapping. In the domain of large amplitude of the first two waves, the breaking of a resistant S-shaped curve leads to a complex permeable structure.
Bibliographic Reference: Report: EUR-EA-FC-1339 EN (1988)
Availability: Available from CEA, Département de Recherches sur la Fusion Contrôlée, Saint-Paul-lez-Durance (FR)
Record Number: 198910441 / Last updated on: 1994-12-01
Original language: en
Available languages: en