Fully 3-Wave Model To Study The Hard Transition To Chaotic Dynamics In Alfven Wave-Fronts.

Abstract

The derivative nonlinear Schrödinger (DNLS) equation, describing
propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is
truncated to explore the coherent, weakly nonlinear coupling of three waves near
resonance, one wave being linearly unstable and the other waves damped. No matter
how small the growth rate of the unstable wave, the four-dimensional flow for the three
wave amplitudes and a relative phase, with both resistive damping and linear Landau
damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate.
This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves,
paralleling the known fact that only LH time-harmonic solutions of the DNLS equation
are modulationally unstable. The parameter domain developing chaos is much broader
than the corresponding domain in a reduced 3-wave model that assumes equal dampings
of the daughter waves.