Spatiotemporal chaos and the dynamics of coupled Langmuir and ion-acoustic waves in plasmas

Abstract

A simulation study is performed to investigate the dynamics of coupled Langmuir waves (LWs) and ion-acoustic waves (IAWs) in an unmagnetized plasma. The effects of dispersion due to charge separation and the density nonlinearity associated with the IAWs, are considered to modify the properties of Langmuir solitons, as well as to model the dynamics of relatively large amplitude wave envelopes. It is found that the Langmuir wave electric field, indeed, increases by the effect of ion-wave nonlinearity (IWN). Use of a low-dimensional model, based on three Fourier modes shows that a transition to temporal chaos is possible, when the length scale of the linearly excited modes is larger than that of the most unstable ones. The chaotic behaviors of the unstable modes are identified by the analysis of Lyapunov exponent spectra. The space-time evolution of the coupled LWs and IAWs shows that the IWN can cause the excitation of many unstable harmonic modes, and can lead to strong IAW emission. This occurs when the initial wave field is relatively large or the length scale of IAWs is larger than the soliton characteristic size. Numerical simulation also reveals that many solitary patterns can be excited and generated through the modulational instability (MI) of unstable harmonic modes. As time goes on, these solitons are seen to appear in the spatially partial coherence (SPC) state due to the free ion-acoustic radiation as well as in the state of spatiotemporal chaos (STC) due to collision and fusion in the stochastic motion. The latter results the redistribution of initial wave energy into a few modes with small length scales, which may lead to the onset of Langmuir turbulence in laboratory as well as space plasmas.

Simple environment for developing methods of controlling chaos in spatially distributed systems

“…The origin of this phenomenon in nonlinear dynamic systems is connected with their sensitivity to initial conditions. In fact, chaotic behavior is a common phenomenon discovered in physics (liquids (Procaccia and Meron, 1986;Langenberg et al, 2004), lasers (Yamada and Graham, 1980;Used and Martin, 2010), plasma (Held et al, 1984;Banerjee et al, 2010)), mechanics (Chui and Ma, 1982;Ott, 2002), electronics (Gunaratne et al, 1989;Yim et al, 2004), chemistry (Argoul et al, 1987;Córdo-ba et al, 2006), biology (action of human heart (Govindan et al, 1998) and brain (Andrzejak et al, 2001;Gautama et al, 2003)), and in many other branches of science and industry.…”

Synchronization and control in time-delayed complex networks and spatio-temporal patterns

“…Spatio-temporal chaos can be observed in Ecological and Biological models, Semiconductor device, Laser and Plasma models [14][15][16][17]. Synchronization and control phenomenon can also be investigated well in specially extended systems [22].…”

Nonlinear Wave-Wave Interactions in Quantum Plasmas

“…The latter have been widely studied in the context of solitons, chaos and Langmuir turbulence in many areas of plasma physics (see, e.g., Refs. [11][12][13]). It is thus of natural interest to investigate the QZEs in the quantum realm, which may be useful for understanding the onset of plasma wave turbulence at nanoscales in both laboratory and astrophysical plasmas.…”