NONLINEAR DYNAMICS OF RELATIVISTIC BACKWARD-WAVE TUBE IN AUTOMODULATION AND CHAOTIC REGIME WITH ACCOUNTING THE EFFECTS WAVES REFLECTION, SPACE CHARGE FIELD AND DISSIPATION

Abstract

It has been performed quantitative modelling, analysis of dynamics relativistic backward-wave tube (RBWT) with accounting relativistic effects, dissipation, a presence of space charge etc. There are computed the temporal dependences of the normalized field amplitudes in a wide range of variation of the controlling parameters which are characteristic for distributed relativistic electron-waved selfvibrational systems: electric length of an interaction space N, bifurcation parameter L and relativistic factor γ0. The computed temporal dependence of the field amplitude is in a good agreement with theoretical data by Ryskin-Titov regarding the RBWT dynamics with accounting the reflection effect, but without accounting dissipation effect and space charge field influence etc. The analysis techniques including multi-fractal approach, methods of correlation integral, false nearest neighbour, Lyapunov exponent’s, surrogate data, is applied analysis of numerical parameters of chaotic dynamics of RBWT. There are computed the dynamic and topological invariants of the RBWT dynamics in automodulation, chaotic regimes, correlation dimensions values), embedding, Kaplan-York dimensions, LE(+,+) Kolmogorov entropy.