Abstract

The nonlinear stage of development of the dust particle chain instabilities is studied. It is assumed that dust particles interact with the plasma consisting of Maxwellian electrons and a directed flow of cold ions. The truncated equations are derived describing the nonlinear dynamics of the standing wave in the range of parameters close to the threshold for the development of the instability of coupled waves. It is shown that, in a narrow range of the ion flow Mach numbers, the instability of coupled waves becomes saturated in the weakly nonlinear stage of its development. In the remaining cases, the instability development becomes explosive. The nonlinear dynamics is also considered of the aperiodic period-doubling instability, which always becomes saturated in the weakly nonlinear stage of its development.

中文翻译：

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线性尘埃粒子链的非线性动力学

摘要

研究了尘埃颗粒链不稳定性的非线性发展阶段。假定尘埃粒子与由麦克斯韦电子和定向冷离子流组成的等离子体相互作用。推导了截断方程，描述了在接近耦合波不稳定性发展的阈值的参数范围内，驻波的非线性动力学。结果表明，在离子流马赫数的狭窄范围内，耦合波的不稳定性在其发展的弱非线性阶段变得饱和。在其他情况下，不稳定发展具有爆炸性。非线性动力学也被认为是非周期性的倍增不稳定性，它在其发展的弱非线性阶段总是饱和。