Method of the calculation of spectrum of Lyapunov exponents for the analysis of dynamics of beam-plasma systems

Summary form only given. Nonlinear dynamics and chaos in plasma devices and microwave systems with interacting electron and electromagnetic waves are often observed in bounded plasmas and electron and ions beams, where the nonlinearity and plasma instabilities are combined with dissipation caused by current flow to the boundary electrodes. Therefore, the development of the methods of analysis of nonlinear dynamics in the spatially extended beam-plasma systems is a very important and actual problem due to possible applications of chaos theory in plasma physics, such as the identification of chaotic spatial-temporal oscillations in microwave electronic and plasma devices (e.g., free electron lasers, pasotrons, vircators, etc), chaos control and suppression of turbulence, and chaotic synchronization in the plasma and microwave electronic systems.The Lyapunov exponents are powerful and useful tool for the complex system dynamics to be analyzed. They are used widely to characterize the systems with small number of degrees of freedom (that is systems with finite phase space) in the different fields of science [1], such as physics, physiology and medicine, molecular dynamics, and astronomy. At the same time, the majority of the plasma systems are characterized by the infinite phase space, since they are the spatially extended active media. Unfortunately, the direct application of the Lyapunov exponent calculation technique (developed for the systems with the small number of degrees of freedom) to the objects of the beam-plasma and electron-wave spatially extended systems is problematic [2]. Recently, the successful attempt to compute the highest Lyapunov exponent taking into account the core features of the spatially extended systems has been made for plasma system models by our scientific group [3]. In the present work, we present the technique of the spectrum of the spatial Lyapunov exponents calculation for the hydrodynamic and particle-in-cell models of distributed be- m-plasma systems and electron-wave devices. The developed calculation technique is applied to the analysis of dynamics of the beamplasma Pierce-like diode and vircator models.