Nonlinear dynamics and microwave electronics
D.I. Trubetskov
Saratov State University, Russia
Microwave electronics is always using the language of oscillations and waves. Moreover, it became one of the first nonlinear sciences, applying methods of the computational physics, such as the large particles method. But because of the need of proper description of electrons overtaking microwave electronics specialists denied the principle, based on nonlinear wave theory and turned to Lagrange description. On the other hand recent impressive advance of nonlinear dynamics gave rise to an active exploration of solitary waves, deterministic chaos and pattern formation in electron beams and systems 'electron beam - electromagnetic field'.
The aim of this report is to demonstrate, how the ideas and methods of nonlinear dynamics are applied in microwave electronics. The major part of presented results is carried out in Saratov University.
1. Nonlinear waves in electron flows.
Numerical simulation have proved the existance of fast and slow solitary space-charge waves. It is important, that the results of simulation distinguish from the solutions of model equations (such as the Korteweg - de Vries equation) derived from the basic equations by standard methods.
2. Pierce diode is the simplest model of the destributed microwave system with complex dynamics.
Results of complex dynamics investigation in the diode are detailed both for hydrodynamical regimes and for regimes with virtual cathode formation.
3. Self-oscillations and complex dynamics in distributed system 'electron beam - backward (or counterward) electromagnetic wave'.
Results of numerical simulation for different models of devices with distributed electrons and waves interaction are presented. The main feature of the transition to chaos in such a system, in comparison with well-known scenarii in simple system, is the abcense of severely determined scenario.
4. Phenomenological model of electronic turbulence.
The complex dynamics of the interacting pattern stream is investigated numerically. All results were obtained with supposition that the patterns consist of classical nonlinear oscillators and effect of superradiation presents for each pattern.
5. The further idea from nonlinear dynamics has been embodied in radiotechnical analog-circuit experiment as applied to analysis of new autooscillator based on vacuum microtriode with field-emission cathode.
The results of radiotechnical analog-circuit and numerical experiments are discussed for autonomous and non-autonomous autooscillators.