Hard transition to chaotic dynamics in Alfvén wave fronts

Abstract

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfvén waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting 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, with damping less than about (unstable wave frequency)2/4×ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model (different dampings of daughter waves, four-dimensional flow); both models differ in significant phase-space features but keep common features essential for the transition.