Hard transition to chaotic dynamics in Alfvén wave-fronts

SANMARTÍN, JUAN; LOPEZ-REBOLLAL, OSCAR; DEL RIO, EZEQUIEL; ELASKAR, SERGIO

PHYSICS OF PLASMAS

American Institute of Physics

Año: 2004 vol. 15 p. 2026 - 2035

1070-664X

The derivative nonlinear Schro¨dinger DNLS equation, describing propagation of circularly polarized Alfve´n 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 frequency2/4ion 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.DNLS equation, describing propagation of circularly polarized Alfve´n 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 frequency2/4ion 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.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 frequency2/4ion 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.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 frequency2/4ion 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.unstable wave frequency2/4ion 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.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.