W. Horton and Y-H. Ichikawa
World Scientific, 1996
ISBN 981-02-236-5
Chaos and Structures in Nonlinear Plasmas develops the subject of nonlinear plasma physics from a general physics perspective. The development, largely self-contained, is appropriate for the advanced undergraduate and beginning graduate students.
The book begins with a description of nonlinear oscillations, the parametric instability, the pendulum, and the nonlinear island overlap criterion. The Kolomogorov-Arnold-Moser (KAM) theory is analyzed. Laboratory visualizations of the KAM theory are presented for experiments in toroidal plasma confinement systems and rotating fluids. The presentation of the subject of nonlinear maps shows how maps are related to nonlinear dynamics in plasma physics.
The subjects of transport in E X B flows in plasmas and geostrophic flows in fluids are developed in parallel, with emphasis placed on the generality of the Charney-Hasegawa-Mima equation.
Coherent structures in laboratory and space plasmas are described in terms of the soliton concept, with the Alfven soliton used to illustrate the principal approach. Inverse scattering theory is presented in detail with several examples given.
Numerous space plasma and fusion physics examples are developed throughout the book. The dual nature of wave turbulence and vortex dynamics is emphasized for plasmas and geophysical flows. The final chapter deals with turbulence theory, renormalized mode coupling equations, and Kolomogorov-type spectra as modified for anisotropic plasmas and geostrophic flows.