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Length scale, quasiperiodicity, resonances, separatrix crossings, and chaos in the weakly relativistic Zakharov equations

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Length scale, quasiperiodicity, resonances, separatrix crossings, and chaos in the weakly relativistic Zakharov equations

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Título Length scale, quasiperiodicity, resonances, separatrix crossings, and chaos in the weakly relativistic Zakharov equations
Autor Oliveira, Glaucius Iahnke de
Rizzato, Felipe Barbedo
Chian, Abraham Chian-Long
Abstract Nonlinear saturation of unstable solutions to the weakly relativistic, one-dimensional Zakharov equations is considered in this paper. In order to perform the analysis, two quantities are introduced. One of them, p* is proportional to the initial energy of the high-frequency 6eld, and the other is the basic wave vector of the low-frequency perturbing mode k = 2π/L, with L as the length scale. With these quantities it becomes possible to identify a number of regions on a p* versus k parametric plane. For very small values of p*, steady-state solutions become unstable when k is also very small. In this case ion-acoustic dynamics is found to be unimportant and the system is numerically shown to be approximately integrable, even if k is below a critical value where the solutions are not simply periodic. For larger values of p the unstable wave vectors also become larger and the ion-acoustic Huctuations turn into active dynamical modes of the system, driving a transition to chaos, which follows initial inverse pitchfork bifurcations. The transition includes resonant and quasiperiodic features; separatrix crossing phenomena are also found. The in6uence of relativistic terms on the chaotic dynamics is studied in the context of the Zakharov equations; it is shown that relativistic terms generally enhance the instabilities of the system, therefore anticipating the transition.
Contido em Physical Review. E, Statistical physics, plasmas, fluids and related interdisciplinary topics. New York. Vol. 52, no. 2 (Aug. 1995), p. 2025-2036
Assunto Fisica dos fluidos, fisica de plasmas e descargas eletricas
Plasmas
Sistemas caoticos
Origem Estrangeiro
Tipo Artigo de periódico
URI http://hdl.handle.net/10183/103654
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