Investigations of the pattern formation
in the electron flow with virtual cathode
V.G. Anfinogentov
Saratov State University, Saratov, Russia
The bounded electron flow with virtual cathode [1] is one of the simplest model of the electron turbulence. The peculiarity of this model is the global feedback that connected with the electrostatic interaction. In the present paper the dynamic of the electron flow in this system is investigated with the help of the PIC simulation. The complex dynamical regimes are considered, the dynamical characteristics (e.g. correlation dimensions and Lapunov exponents) are analysed and the dynamical nature of the turbulence is shown for this system.
With the help of proper orthogonal decomposition method [2] for spatio- temporal data and mutual correlation analysis of the space charge density oscillations two structures are extracted. These structures are the virtual cathode and the bunch that arises in the processes of the virtual cathode disappearing. The dynamics of the structures for regular and chaotic regimes are investigated and the differences of the self-formation processes in these regimes are shown. There is different exiting of the patterns: simultaneously for chaotic regimes and consequently for regular regimes.
The influence of two-dimensional effects on the chaotic dynamics is investigated. The self-formation processes in the electron beam with virtual cathode in the bounded drift tube are considered. It is shown that chaotic behaviour determined by interaction of the same structures as in the plane case. The peculiarities in the dynamics are connected with the decreasing of the local instability in the system.
The influences of the feedback on the self-formation processes are analysed. We consider as internal (flow) as external (field) feedback. It is shown that changing of the feedback characteristics give the possibilities of effective control of the chaotic dynamics with the help of act on one of the structures.
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