VIII.          I. Magda, A. V. Pashchenko,

S.  S. Romanov, I. N. ShapovalTfte NSC “Kharkov Institute of Physics and Technology"

1      Academicheskaya Str., Kharkov, 61108 Ukraine V. E. Novikov

The Center for Electrophysics and Technology ofNASU 4 Chaykovskaya Str., Kharkov, 61002 Ukraine

Abstract The self-consistent nonstationary model of beam feedback in devices with virtual cathode (VC), which uses the flow instability in the cathode anode gap and nonlinear particle interaction with VC oscillations is presented. Nonlinear process involving both areas is featured as an interaction between coupled Van der Pol-Duffing oscillators.

I.  Introduction

The feedback variants provided by means of beam particles (BFB) and electromagnetic field (EMFB) are effectively used for the performances increase and control in microwave devices with VC [1,2], however no reasonable analytical feedback theory for such kind of systems has not been created to the present time.

The approach proposes that feedback can be modeled by an effective potential introduced in the area of interest. Also it is taken into account, that the dynamics of high-current diode is provided by instability of electron flow in the cathode-anode gap. A self-consistent analytical model of BFB in the vircator that considers the instability processes in the diode with supercritical current and in the VC area is presented. This model is based on analysis of stationary states ofthe diode and their stability.

II.     Theory of stationary states of electron flow in the diode and analysis of stability

Equations of hydrodynamic, motion and continuities for electrons and Poisson equation for an electric field in the high-current diode [3-5] are used. The use of Lagrange variables and linearization procedure results in obtaining the stability conditions for electron flow in the diode and the spectrum of eigenfrequencies. Relevant phase relations for a stream determine unstable solutions. They provide frequencies and increments for oscillation excited in accelerating gap. Transit-time instability of high-current diode depends on the following: size and potential difference across acceleration gap, parameters of electron beam.

III.   Model of beam feedback

Initially, oscillations of VC by means of BFB create a “seed" signal for instability in accelerating gap. This signal, enforced by instability, is transmitted back by the beam and additionally modulates oscillations of VC. The optimum condition for BFB corresponds to the most unstable mode of VC with maximum gain for specific frequency. A self-consistent interaction between oscillations in cathode-anode gap and VC area arises, and it can be modeled as a dynamics of two coupled nonlinear Van der PolDuffing oscillators. This interaction essentially depends on a degree of BFB determined by the transparence of anode. Nonlinear oscillations go in synchronism while the transparence is increased. The difference in phase is stabilized, and the nonlinear system as a whole oscillates in narrow frequency band.

IV.  Conclusions

The models of feedback and means of its creation in the systems with virtual cathode are studied. Electron flow stability in the diode is studied. The stability boundaries as a function of parameters of vircator system, as well as the frequency characteristics of instability depended on features of space charge dynamics in the diode are found.

The mechanism of BFB based on instability in the accelerating gap is offered. Operation of feedback is modeled as interaction between two coupled nonlinear Van der Pol-Duffing oscillators. The synchronization between VC and diode beam flow oscillations at the expense of BFB is shown.

Джерело: Матеріали Міжнародної Кримської конференції «СВЧ-техніка і телекомунікаційні технології», 2003р.