Hard transition to chaotic dynamics in Alfvén wave fronts

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!/43ion 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. © 2004 American Institute of Physics. @DOI: 10.1063/1.1691453#