空间扩展束-等离子体系统和电子波器件空间李雅普诺夫指数谱的计算
Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices
摘要：
李雅普诺夫指数谱是分析复杂系统动力学的有力工具。在非线性动力系统的一般框架下，已经发展了许多数值技术来获得具有少自由度的系统的复杂时间行为的李雅普诺夫指数的谱。然而，由于等离子体器件是空间扩展的有源介质，这些方法不能直接应用于具有无限相空间的等离子体器件中复杂的时空动力学分析。本文提出了空间扩展束-等离子体系统空间李雅普诺夫指数谱的计算方法。应用这种计算技术分析了三种不同的束-等离子体模型中的混沌时空振荡：（1）简单的等离子体皮尔斯二极管，（2）耦合的皮尔斯二极管，（3）后向电磁波的电子波系统。我们发现一个很好的协议之间的系统动力学和空间李雅普诺夫指数的频谱的行为。同时，还讨论了该方法在计算SLEs时可能存在的问题。结果表明，对于广泛的类的空间扩展系统的一组数量包括在系统状态的SLE计算可以减少使用适当的功能的等离子体系统。
英文摘要：
The spectrum of Lyapunov exponents is powerful tool for the analysis of the complex system dynamics. In the general framework of nonlinear dynamical systems a number of the numerical technics have been developed to obtain the spectrum of Lyapunov exponents for the complex temporal behavior of the systems with a few degree of freedom. Unfortunately, these methods can not apply directly to analysis of complex spatio-temporal dynamics in plasma devices which are characterized by the infinite phase space, since they are the spatially extended active media. In the present paper we propose the method for the calculation of the spectrum of the spatial Lyapunov exponents (SLEs) for the spatially extended beam-plasma systems. The calculation technique is applied to the analysis of chaotic spatio-temporal oscillations in three different beam-plasma model: (1) simple plasma Pierce diode, (2) coupled Pierce diodes, and (3) electron-wave system with backward electromagnetic wave. We find an excellent agreement between the system dynamics and the behavior of the spectrum of the spatial Lyapunov exponents. Along with the proposed method, the possible problems of SLEs calculation are also discussed. It is shown that for the wide class of the spatially extended systems the set of quantities included in the system state for SLEs calculation can be reduced using the appropriate feature of the plasma systems.
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