# virtual cathode

## Dynamics of cylindrical electron beams injecting in a half-space with perfectly-conducting boundary

The purpose of this work is to study the dynamics of electron beams and bunches in a system with an ideally conducting plane and a uniform magnetic field in the presence of delayed electromagnetic waves when a virtual cathode is formed in the system and with parameters close to this state. Methods. The dynamics of a cylindrical electron beam flying through an ideally conducting plane into a strong longitudinal magnetic field is studied by numerical simulation. Particles are large.

## Dynamics of electron flow with virtual cathode in low-voltage vircator under external force

Theoretical research of dynamics of electron flow with virtual cathode in lowvoltage vircator under external harmonic force has been held in this work. The behavior of electron flow was considered within the framework of both stationary analytic model and numerical simulation of electron flow nonstationary processes. The increasing of lowvoltage vircator output power while increasing external force has been shown in both cases. The results of theoretical research let us to explain physical phenomenon leading to output power increasing.

## Nonlinear dynamics and chaos in the counterstreaming electron beams with virtual cathodes in vircator without external magnetic field

Virtual cathode nonstationary dynamics has been numerically studied for the two counterstreaming electron beams. The variety of the virtual cathode oscillatory regimes has been discovered from regular to wide band chaotic oscillations. Connection between value of the largest Lyapunov exponent and output signal power has been revealed.

## Three-dimensional simulation of virtode with toroidal cavities

The results of preliminary 3D fully electromagnetic simulation of microwave generator with virtual cathode and external feedback loop (virtode) are discussed in this paper. The feedback is realized by the velocity modulation of electron beam in the accelerating gap of electron gun with the electromagnetic signal taken with output cavity placed in the virtual cathode area.

## Nonlinear dynamics of helical electron flow in the regime of the virtual cathode forming

We produce the results of computer analysis of complex dynamics of non-relativistic electron beam being placed in crossed electric and magnetic fields, in the regime of a virtual cathod forming in additional braking field. The modeling has been made in the framework of 2D numerical model in the geometry of magnetron-injector gun.

## Wideband chaotic generation and optimization of characteristics in microwave generator with electronic feedback and magnetic periodic focusing system

With the help of 2D numerical model it has been investigated the nonlinear dynamics and generation of wideband chaotic signals in the generator based on electron beam with the virtual cathode. It has been discovered the strong influence of the external non-uniform magnetic field on the nonlinear dynamics of the virtual cathode in the system. It has been analyzed the physical processes responsible for the discovered dependency of dynamics of the electron beam with the virtual cathode on the parameters of the external nonuniform magnetic field.

## Mathematical model and its numerical realization for the investigation and optimization of generators with electron feedback

It was stated in the paper the mathematical model and its numerical realization for the investigation of wideband chaotic oscillations and of physical processes in the electron beams with virtual cathode at the generators with electron feedback. Also it was briefly described the developed program package for the modeling of nonstationary nonlinear physical processes at the electron generators with virtual cathode and for calculating of output characteristics of devices.

## On the mechanism of «compressed»state formation at relativistic electron beam in twosection drift tube

This paper is devoted to the threedimensional numerical simulation of the «compressed» state of the relativistic electron beam in twosection vircator system with drift tubes with different diameters. We have discovered the mechanism of formation of the «compressed» state of the relativistic beam through the formation of two virtual cathode near the anode grid and between connected sections, which will eventually merged into one distributed in the drift space virtual cathode (compressed state of the beam).

## Higher harmonics generation in a relativistic electron beam with virtual cathode

The study of the microwave generation regimes with intense higher harmonics taking place in a high-power vircator consisting of a relativistic electron beam with a virtual cathode has been made. The characteristics of these regimes, in particular, the typical spectra and their variations with the change of the system parameters (beam current, the induction of external magnetic field) as well as physical processes occurring in the system have been analyzed by means of 3D electromagnetic simulation.

## Numerical simulation of electron-beam «squeezed» state in purpose to study the possibility of effective plasma frequency increase

Three-dimensional electromagnetic numerical simulation is carried out of «squeezed» state of the electron beam in two-section vircator system with drift tubes of different diameters. We have studied the influence of two-section system geometric parameters on the nonlinear dynamics of electron beam. We have obtained an effective plasma frequency depending on the system parameters.