Computation of the spectrum of spatial Lyapunov exponents for the spatially extended beam-plasma systems and electron-wave devices

TL;DR

This paper introduces a method to compute the spectrum of spatial Lyapunov exponents for spatially extended beam-plasma systems, enabling analysis of complex spatio-temporal chaos in plasma devices.

Contribution

The paper proposes a novel technique for calculating spatial Lyapunov exponents in extended plasma systems, addressing limitations of existing temporal methods.

Findings

The method accurately characterizes chaotic spatio-temporal oscillations.

Excellent agreement between system dynamics and SLE spectrum behavior.

Reduction of system state quantities simplifies SLE calculation for plasma systems.

Abstract

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.