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 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.
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May 2004
Research Article|
May 01 2004
Hard transition to chaotic dynamics in Alfvén wave fronts Available to Purchase
J. R. Sanmartin;
J. R. Sanmartin
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
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O. Lopez-Rebollal;
O. Lopez-Rebollal
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
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E. del Rio;
E. del Rio
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
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S. Elaskar
S. Elaskar
Departamento de Aeronautica, Universidad Nacional de Cordoba, Cordoba, Argentina
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J. R. Sanmartin
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
O. Lopez-Rebollal
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
E. del Rio
Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Madrid, Spain
S. Elaskar
Departamento de Aeronautica, Universidad Nacional de Cordoba, Cordoba, Argentina
Phys. Plasmas 11, 2026–2035 (2004)
Article history
Received:
August 07 2003
Accepted:
February 04 2004
Citation
J. R. Sanmartin, O. Lopez-Rebollal, E. del Rio, S. Elaskar; Hard transition to chaotic dynamics in Alfvén wave fronts. Phys. Plasmas 1 May 2004; 11 (5): 2026–2035. https://doi.org/10.1063/1.1691453
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