Investigation of the complex dynamics and regime control in Pierce diode with the delay feedback

Abstract

In this paper the dynamics of Pierce diode with overcritical current under the influence of delay feedback is investigated. The system without feedback demonstrates complex behaviour including chaotic regimes. The possibility of oscillation regime control depending on the delay feedback parameter values is shown. Also the paper describes construction of a finite-dimensional model of electron beam behaviour, which is based on the Galerkin approximation by linear modes expansion. The dynamics of the model is close to the one given by the distributed model.

Chaotic synchronization in coupled spatially extended beam–plasma systems

“…The present paper deals with research of chaotic synchronization in coupled beam-plasma microwave systems with overcritical current -Pierce diode fluid models [42][43][44], which seems to be interesting as an important model of beamplasma systems showing various types of chaotic behavior [43][44][45][46][47][48].…”

Experimental and theoretical investigations of stochastic oscillatory phenomena in a nonrelativistic electron beam with a virtual cathode

“…A system like this, in which the electron motion is thought of as being one-dimensional, can be regarded as a model of the drift space and can also serve to investigate the nonlinear dynamics of the processes in such high-power electronic devices as vircators [29]. In recent years, a model of this type has also attracted attention as one of the simplest models of a distributed self-oscillating electron-plasma system for studying stochastic oscillations [17,26,[29][30][31].…”

“…One of the simplest systems for studying the formation of a VC and its unsteady stochastic oscillations is a Pierce diode [17,[27][28][29]-a system of two infinitely wide parallel equipotential grids penetrated by an electron beam with an overcritical current. A system like this, in which the electron motion is thought of as being one-dimensional, can be regarded as a model of the drift space and can also serve to investigate the nonlinear dynamics of the processes in such high-power electronic devices as vircators [29].…”

“…Even the first experiments and numerical simulations revealed the complicated unsteady dynamics of radiation from vircators, i.e., microwave oscillators with a VC [9][10][11][12][13]. Quite a number of theoretical and experimental papers were devoted to studying the stochastic generation of radiation in vircators [5][6][7][13][14][15][16][17], the processes responsible for the onset of coherent spatiotemporal structures in an electron beam with a VC and for their interaction [16,[18][19][20][21], and the mutual synchronization of VC-based devices [6,[22][23][24][25]. In particular, by applying different methods for separating out coherent structures, it was shown theoretically [18][19][20]26] that the complication of the spectral composition of radiation from a vircator is closely related to the formation of electron structures in a beam with an overcritical current.…”

Experimental and theoretical investigation into the effect of the electron velocity distribution on chaotic oscillations in an electron beam under virtual cathode formation conditions

“…Even in pioneering experiments and calculations, the complicated time-varying radiation pattern of VC oscillators was noted [10][11][12][13][14]. VC chaotic oscillations were investigated both theoretically and experimentally [6,8,9,[14][15][16][17][18]. The occurrence of and interaction between coherent space-time structures in an electron beam with a VC were studied in [17,[19][20][21][22][23].…”