-Results are presented from experimental investigations of oscillatory phenomena in an electron beam with a virtual cathode in a diode gap with a decelerating field. Experiments have revealed a stochastic broadband generation of the microwave oscillations of a virtual cathode in a decelerating field. Numerical simulations based on a simple one-dimensional model have shown that the onset of the stochastic generation and the broadening of the oscillation spectrum with increasing beam deceleration rate are governed by the processes of regrouping of the electrons in a beam with a virtual cathode.

-The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring in an electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beam and interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased, the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation and interaction of spatiotemporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator is achieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.

Electron-wave systems with the active medium in the form of an electron beam with a virtual cathode (VC) are among the promising sources of high-power microwave radiation [1][2][3][4] and are extensively studied in the context of various applications [5,6].Recently [7][8][9], we proposed and studied a new scheme of the oscillator with a VC (vircator) making use of an intense nonrelativistic electron beam (i.e., a beam with a microperveance p µ > 3 µ A/V 3/2 [10]). In order to form a VC in the electron beam, this system employs a scheme with an additional retardation of electrons. According to this scheme (called a low-voltage vircator), a nonstationary oscillating VC is formed at the expense of strong retardation of electrons in the drift region, which makes possible the generation of both single-frequency and broadband microwave signals using electron beams with small total currents and low densities [7]. In such regimes, it is possible to study in much detail the physical processes in electron beams with VCs. It should be noted that the system with a VC and a retarded electron beam is also of interest as a controlled source of medium-power broadband chaotic signals in the centimeter and millimeter wavelength range [8].This Letter presents the results of an experimental and theoretical investigation of the output energy characteristics of a low-voltage vircator.The experimental investigation of oscillations in the electron beam with a VC was performed using as diode scheme in which the beam formed by an electron-optical system (EOS) was injected into a system (see Fig. 1) comprising two grid electrodes ( 5 and 6 ) forming a retarding field. The retarding field was created by applying a negative potential V r to the exit (second) grid 6 relative to the entrance (first) grid 5 . The EOS formed an axisymmetric converging cylindrical electron beam 4 . The accelerating voltage in our experiments was 2.0 kV, the beam current at the EOS output was varied within 50-100 mA (depending on the cathode filament voltage), the EOS length was l = 70 mm, and the beam radius was r b = 4 mm.The electron beam generated in the EOS with a certain initial scatter of electron velocities enters into the space between grids (diode gap). The first grid poten-Abstract -The power of microwave generation in a nonrelativistic electron beam with virtual cathode formed in a static retarding electric field (low-voltage vircator system) has been studied experimentally and by means of numerical simulation within the framework of a one-dimensional theory. The limits of applicability of the one-dimensional theory have been experimentally determined. 1 2 3 4 5 6 7 8 9 10 VC V 0 V r Fig. 1. Schematic diagram of the experimental setup used for the investigation of oscillations in a nonrelativistic electron beam with virtual cathode formed in a system with additional retardation of electrons: ( 1 ) thermionic cathode;( 2 ) grid electrode of the electron gun;( 3 ) second anode of the electron gun; ( 4 ) converging electron beam formed by the EOS; ( 5 ) e...

1 Note a certain relation between oscillations in such an electron system with deceleration and oscillations in the BarkhausenKurz oscillator [19] and oscillations in an electron-wave oscillator with a decelerating field ([20, Chapter 5] Abstract -A nonrelativistic electron beam with a virtual cathode situated in the diode gap with a decelerating field is experimentally and theoretically studied. A 1D model of the electron beam in the presence of a decelerating field is constructed. Nonlinear nonstationary processes in this system are investigated by means of numerical analysis of the model. The processes are described and interpreted with regard to formation and interaction of structures in the electron flow. The theoretical results are qualitatively confirmed by the experimental data showing that the system under study can be considered as a promising controlled source of chaotic oscillations in the microwave range.

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