Chaos and complexity in the dynamics of nonlinear Alfven waves in a magnetoplasma

The nonlinear dynamics of circularly polarized dispersive Alfven wave (AW) envelopes coupled to the driven ion-sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number of harmonic modes, a low-dimensional dynamical model is proposed to describe the nonlinear wave-wave interactions. It is found that two subintervals of the wave number of modulation k of AW envelope exist, namely, (3/4)k(c) < k < k(c) and 0 < k < (3/4)k(c), where k(c) is the critical value of k below which the modulational instability (MI) occurs. In the former, where the MI growth rate is low, the periodic and/or quasi-periodic states are shown to occur, whereas the latter, where the MI growth is high, brings about the chaotic states. The existence of these states is established by the analyses of Lyapunov exponent spectra together with the bifurcation diagram and phase-space portraits of dynamical variables. Furthermore, the complexities of chaotic phase spaces in the nonlinear motion are measured by the estimations of the correlation dimension as well as the approximate entropy and compared with those for the known Henon map and the Lorenz system in which a good qualitative agreement is noted. The chaotic motion, thus, predicted in a low-dimensional model can be a prerequisite for the onset of Alfvenic wave turbulence to be observed in a higher dimensional model that is relevant in the Earth's ionosphere and magnetosphere.

Automated summary

This study investigates the nonlinear dynamics of circularly polarized dispersive Alfven wave envelopes coupled to driven ion-sound waves in a uniform magnetoplasma. A low-dimensional dynamical model is proposed to describe the nonlinear wave-wave interactions by restricting the wave dynamics to a few harmonic modes. The existence of periodic, quasi-periodic, and chaotic states is established by analyzing Lyapunov exponent spectra, bifurcation diagrams, and phase-space portraits. The chaotic motion predicted in this low-dimensional model can be a prerequisite for the onset of Alfvenic wave turbulence observed in higher dimensional models relevant to the Earth's ionosphere and magnetosphere.