SUDDEN TRANSITION TO CHAOS IN PLASMA-WAVE INTERACTIONS

The coherent three-wave interaction, with linear growth in the higher frequency wave and damping in the two other waves, is reconsidered; fo r equal dampings, the resulting three-dimensional (3-D) flow of a rela tive phase and just two amplitudes behaved chaotically, no matter how small the growth of the unstable wave. The general case of different d ampings is studied here to test whether, and how, that hard scenario f or chaos is preserved in passing from 3-D to four-dimensional flows. I t is found that the wave with higher damping is partially slaved to th e other damped wave; this retains a feature of the original problem (a n invariant surface that meets an unstable fixed point, at zero growth rate) that gave rise to the chaotic attractor and determined its stru cture, and suggests that the sudden transition to chaos should appear in more complex wave interactions. (C) 1998 American Institute of Phys ics.