Nonlinear dynamics and chaotization of oscillations of a virtual cathode in an annular electron beam in a uniform external magnetic field

Results are presented from a numerical study of the effect of an external magnetic field on the conditions and mechanisms for the formation of a virtual cathode in a relativistic electron beam. Characteristic features of the nonlinear dynamics of an electron beam with a virtual cathode are considered when the external magnetic field is varied. Various mechanisms are investigated by which the virtual cathode oscillations become chaotic and their spectrum becomes a multifrequency spectrum, thereby complicating the dynamics of the vircator system. A general mechanism for chaotization of the oscillations of a virtual cathode in a vircator system is revealed: the electron structures that form in an electron beam interact by means of a common space charge field to give rise to additional internal feedback. That the oscillations of a virtual cathode change from the chaotic to the periodic regime is due to the suppression of the mechanism for forming secondary electron structures.     

Simulation of oscillatory processes in a beam-plasma system with a virtual cathode in gas-filled interaction space

Physical processes occurring in an intense electron beam with a virtual cathode in an interaction space filled with neutral gas are studied in a two-dimensional model. A mathematical model is proposed for investigating complicated self-consistent processes of neutral gas ionization by the beam electrons and the dynamics of an electron beam and heavy positive ions in the common space charge field with allowance for the two-dimensional motion of charged particles. Three characteristic dynamic regimes of the system are revealed: complete suppression of oscillations of the virtual cathode as a result of neutralizing its space charge by positive ions; the pulsed generation regime, in which the ions dynamics repeatedly suppresses and restores the virtual cathode oscillations; and the continuous generation regime with an anomalously high level of noisy oscillations.     

Effect of the external magnetic field on the critical current for the onset of a virtual cathode in an electron beam

The critical current at which an unsteady oscillating virtual cathode forms in an electron beam is studied as a function of the external magnetic field guiding the beam electrons. It is shown that the critical beam current decreases with external magnetic field and that there is an optimum magnetic induction at which the critical current for the onset of an oscillating virtual cathode in the beam is minimum. For a strong guiding magnetic field, the critical beam current is described by relationships derived under the assumption that the motion of the beam electrons is one-dimensional. Such behavior is explained by the characteristic features of the dynamics of the beam electrons in longitudinal and radial directions in the interaction space at different inductions of the external magnetic field.     

Specific features of virtual cathode formation and dynamics with allowance for the magnetic self-field of a relativistic electron beam

The conditions and mechanisms of virtual cathode formation in relativistic and ultrarelativistic electron beams are analyzed with allowance for the magnetic self-field for different magnitudes of the external magnetic field. The typical behavior of the critical current at which an oscillating virtual cathode forms in a relativistic electron beam is investigated as a function of the electron energy and the magnitude of the uniform external magnetic field. It is shown that the conditions for virtual cathode formation in a low external magnetic field are determined by the influence of the magnetic self-field of the relativistic electron beam. In particular, azimuthal instability of the electron beam caused by the action of the beam magnetic self-field, which leads to a reduction in the critical current of the relativistic electron beam, is revealed.     

Simulation of the development and interaction of instabilities in a relativistic electron beam under variation of the beam wall thickness

The development and interaction of Bursian and diocotron instabilities in an annular relativistic electron beam propagating in a cylindrical drift chamber are investigated analytically and numerically as functions of the beam wall thickness and the magnitude of the external uniform magnetic field. It is found that the interaction of instabilities results in the formation of a virtual cathode with a complicated rotating helical structure and several reflection regions (electron bunches) in the azimuthal direction. It is shown that the number of electron bunches in the azimuthal direction increases with decreasing beam wall thickness and depends in a complicated manner on the magnitude of the external magnetic field.     

Hybrid microwave oscillators with a virtual cathode

A review is given of the developments and theoretical investigations of a fundamentally new class of microwave devices, namely, hybrid microwave oscillators with a virtual cathode, which combine the useful properties of virtual cathodes with the advantages of those traditional microwave oscillators that operate with subcritical-current beams and have a high efficiency in generating ultrarelativistic electron beams. Among such devices are the following: a hybrid diffractional microwave oscillator with a virtual cathode, a hybrid gyrodevice with a virtual cathode, a hybrid beam-plasma vircator, a hybrid gyrocon with a virtual cathode, a hybrid Cherenkov oscillator with a virtual cathode, a hybrid microwave oscillator of the “vircator + traveling-wave tube” type, an original two-beam tube with a virtual cathode, and a klystron-like vircator.     

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

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.     

Erosion of the Leading Edge of a Low-Energy High-Current Electron Beam Injected into Gas in the Absence of an External Magnetic Field

Erosion of the leading edge a low-energy high-current electron beam injected into a low-pressure neutral gas under conditions of virtual cathode formation in the absence of an external magnetic field is studied theoretically. Beam losses are calculated as functions of the pressure and sort of gas, beam electron energy, and system geometry. The dependence of the duration of the leading edge erosion on the system parameters is analyzed.     

Wavelet bicoherence analysis as a method for investigating coherent structures in an electron beam with an overcritical current

Results are presented from numerical modeling of the effect of the inhomogeneity of the ion background on the complicated spatiotemporal dynamics of an electron beam with a virtual cathode in plane geometry. The possibility is demonstrated of increasing the generation frequency without changing the beam current. The spatiotemporal structures that form in the beam and govern the complicated stochastic dynamics of the nonuniform electron-plasma system under consideration are investigated by the methods of wavelet bicoherence and by analyzing the calculated electron trajectories on the space-time diagrams.     

Electron dynamics and kinetics during the formation of a virtual cathode in different media

Results are presented from the first systematic investigation of how various factors in material media influence electron kinetics during the formation of a virtual cathode in an overcritical-current electron beam. A study is made of such factors as the viscous frictional force acting on the electrons in the medium, the dielectric constant of the medium, and ionization processes induced by the electrons in the medium. The dynamics of formation of a virtual cathode and the kinetics of the so-called metastable electrons in the cathode are considered.     

Nonlinear theory of the low-frequency interaction of ion beams with the virtual cathode of a relativistic electron beam

A study was made of the nonlinear low-frequency interaction of a longitudinal ion beam with a virtual cathode of a relativistic high-current electron beam injected into a cylindrical drift chamber. Cases are considered in which the electron and ion beams have the same radii and in which the radius an ion beam is greaterthan that of an electron beam.     

A high-power vircator operating as an X-ray bremsstrahlung generator

Avircator capable of generating high-power X-ray pulses due to the multiple transitions of electrons through a thin anode foil transparent to X radiation has been created and put into operation for the first time. The vircator is created on the basis of a direct-action electron accelerator supplied from an inductive energy storage operating with a plasma opening switch. Self-consistent two-dimensional simulations of the electron beam dynamics in the vircator chamber are performed, and the spectra of the generated microwave radiation are determined. Self-consistent one-dimensional simulations of the beam dynamics with allowance for electron scattering in the foil were also carried out, and the X-ray bremsstrahlung spectra were measured. Results are presented from the first experiments on the generation of X-ray bremsstrahlung in vircators with thin (10 μm) and thick (100 μm) tantalum anode foils. For a thin foil, the X-ray (E _γ>30 keV) dose is eight times as high as that for a thick foil and the average photon energy is 30 keV (against 80 keV for a thick foil). __________ Translated from Fizika Plazmy, Vol. 30, No. 9, 2004, pp. 828–834. Original Russian Text Copyright ￠ 2004 by Selemir, Dubinov, Ryaslov, Kargin, Efimova, Loyko.     

Longitudinal ion source with the current self-compensation of the focused ion beam

Utilization of ballistic focusing in the longitudinal Hall-type ion source is described. It allows transformation of the ion beam shape from an “ellipsoidal” one to a linear one, as well as increasing the ion beam current density per the operating surface. Both the influence of transverse magnetic field and edge effects on the beam shape are investigated. The ion beam is charge compensated by a plasma neutralizer designed on the basis of a supplementary semi-self-maintained magnetron-type discharge and hollow cathode effect.     

Simulation of a Magnetically Isolated Vircator with an Under-Limit Electron Beam

Plasma Physics Reports - A method is proposed for producing microwave generation in a relativistic magnetically insulated vircator in the under-limit mode of an electron beam. The method is...     

Formation of space-charge bunches in a multivelocity-electron-beam-based microwave oscillator with a cathode unshielded from the magnetic field

The influence of the magnitude and configuration of the magnetic field on the parameters of electron bunches formed in a multivelocity electron beam is analyzed. It is shown that the use of a cathode unshielded from the magnetic field and a nonuniform magnetic field increasing along the drift space enables the formation of compact electron bunches. The ratio between the current density in such bunches and the beam current density at the entrance to the drift space reaches 10⁶, which results in a substantial broadening of the output microwave spectrum due to an increase in the amplitudes of the higher harmonics of the fundamental frequency.     

An annular high-current electron beam with an energy spread in a coaxial magnetically insulated diode

An elementary theory of an annular high-current electron beam in a uniform transport channel and a coaxial magnetically insulated diode is generalized to the case of counterpropagating electron beams with a spread over kinetic energies. Expressions for the sum of the absolute values of the forward and backward currents in a uniform transport channel and for the flux of the longitudinal component of the generalized momentum in a coaxial magnetically insulated diode as functions of the maximum electron kinetic energy are derived for different values of the relative width of the energy distribution function. It is shown that, in a diode with an expanding transport channel and a virtual cathode limiting the extracted current, counterpropagating particle flows are established between the cathode and the virtual cathode within a certain time interval after the beginning of electron emission. The accumulation of electrons in these flows is accompanied by an increase in their spread over kinetic energies and the simultaneous decrease in the maximum kinetic energy. The developed model agrees with the results of particle-in-cell simulations performed using the KARAT and OOPIC-Pro codes.     

Mechanism for efficient electron beam generation in a pixel of an open-discharge plasma display

A concept is proposed of a plasma pixel based on an open-discharge microstructure. The concept employs the capability of an open discharge to generate an electron beam at moderate (1–3 kV) discharge voltages with an efficiency close to 100%. To determine the possible application of this type of discharge, the parameters of the electron beams generated in open discharges operating in different working gases at various geometries of the discharge cell and various dimensions of the discharge channel were investigated. The electric potential distributions in the dielectric plate channel and in the cathode cavity were measured. The effect of additional illumination by radiation generated in the drift space on the current-voltage characteristic of the discharge is studied. Based on the results obtained, a noncontradictory model of a discharge capable of very efficiently generating an electron beam is proposed. According to this model, the main contribution to the electron beam comes from the photoelectron emission from the cathode under the action of radiation from the working-gas atoms excited by fast heavy particles in a highly nonuniform electric field in the cathode cavity. Such a field also scatters ions and fast atoms, thus reducing their fluxes toward the cathode. The results obtained indicate that highly efficient light sources and plasma panels can be created on the basis of open-discharge microstructures with a cathode cavity. Such microstructures allow very efficient conversion of electric energy into light.     

Numerical simulations of a high-current plasma lens

The dynamic processes by which an electrostatic plasma lens with a wide-aperture ion beam and electrons produced from the secondary ion-electron emission relaxes to a steady state is investigated for the first time by the particle-in-cell method. The parameters of a two-dimensional mathematical model were chosen to correspond to those of actual plasma lenses used in experimental studies on the focusing of high-current heavy-ion beams at the Institute of Physics of the National Academy of Sciences of Ukraine (Kiev, Ukraine) and the Lawrence Berkeley National Laboratory (Berkeley, USA). It is revealed that the ion background plays a fundamental role in the formation of a high potential relief in the cross section of a plasma lens. It is established that, in the volume of the plasma lens, a stratified electron structure appears that is governed by the nonuniform distribution of the external potential over the fixing electrodes and the insulating magnetic field. The stratification is very pronounced because of the finite sizes of the cylindrical fixing electrodes of the lens. It is shown that the presence of such a structure limits the maximum compression ratio for an ion beam to values that agree with those observed experimentally.     

Waves of states in an electron beam with a distributed virtual cathode

Results are presented from computer simulations of the dynamics of an electron beam injected into the drift space between two parallel conducting planes. The specific features of the competitive coexistence of states with and without a virtual cathode are investigated.     

Formation and nonlinear dynamics of the squeezed state of a helical electron beam with additional deceleration

Results of numerical simulations and analysis of the formation and nonlinear dynamics of the squeezed state of a helical electron beam in a vircator with a magnetron injection gun as an electron source and with additional electron deceleration are presented. The ranges of control parameters where the squeezed state can form in such a system are revealed, and specific features of the system dynamics are analyzed. It is shown that the formation of a squeezed state of a nonrelativistic helical electron beam in a system with electron deceleration is accompanied by low-frequency longitudinal dynamics of the space charge.