Beam-plasma interaction in a hybrid plasma waveguide in the pulsed mode of microwave generation

Results are presented from experimental studies of the energy spectra of an electron beam in a model beam-plasma oscillator based on a hybrid plasma waveguide in the pulsed mode of microwave generation with a pulse duration of 1 µs or shorter. The beam energy spent on sustaining the beam-plasma discharge in a slow-wave structure is measured. A correlation between the type of excited waves and the generation of a group of accelerated beam electrons with energies exceeding the injection energy is revealed. It is shown that the pulsed mode of microwave generation is related to the time variations in the plasma density profile in the waveguide and the trapping of beam electrons by the excited microwave field.     

Mechanism for ion acceleration along the normal to the axis of a beam-plasma discharge in a weak magnetic field

The mechanism responsible for the previously discovered phenomenon of acceleration of an ion flow along the normal to the axis of a beam-plasma discharge in a weak magnetic field is investigated. It is suggested that the ions are accelerated in the field of a helicon wave excited in the discharge plasma column. It is shown theoretically that, under actual experimental conditions, a helicon wave can be excited at the expense of the energy of an electron beam. The spectral parameters and spatial structure of the waves excited in a beam-plasma discharge in the frequency ranges of Langmuir and helicon waves are studied experimentally and are shown to be related to the parameters of the ion flow. Theoretical estimates are found to agree well with the experimental results.     

Electron beam relaxation in nonuniform plasma of a steady-state beam-plasma discharge at moderately low gas pressures

Electron beam relaxation in plasma under conditions typical of laboratory plasma devices based on a steady-state beam-plasma discharge was investigated. It is shown that the measured dependences of the beam loss factor in a discharge operating at a moderately low gas pressure disagree with theoretical dependences calculated for a longitudinally uniform plasma. Analytic dependences obtained in the framework of quasilinear theory with allowance for longitudinal plasma inhomogeneity agree with experimental data. Some effects caused by the influence of the main discharge parameters on electron beam relaxation are analyzed.     

Effect of plasma nonlinearity on the beam-plasma interaction in a hybrid plasma waveguide

A study is made of the characteristic features of the effect of plasma nonlinearity in a slow-wave structure on microwave generation by an electron beam and on electron beam energy losses. Theoretical results on the plasma density variation, the amplitude of the excited microwaves, and the velocity distribution function of the beam electrons are compared with the experimental data. It is shown that the self-consistency between the decreasing plasma density gradient and the spatial variation of the amplitude of an amplified wave in a slowwave structure leads to a significant (severalfold) increase in the efficiency with which the electron beam energy is converted into microwave energy in short pulses. The predictions of the theoretical model developed to describe the non-steady-state beam-plasma interaction agree well with the experimental data.     

Effect of an external RF field on the beam-plasma discharge in a magnetic field

The effect of an RF field on a steady-state beam-plasma discharge with a plane electrode placed parallel to a sheetlike electron beam is studied experimentally. The plasma parameters were measured by a single probe, and the electron distribution function was determined with the use of an electrostatic analyzer. The energy and current of the electron beam were E _B=2.5 keV and J _B=0.05–1.5 A, respectively. The working pressure was p=2×10^?5–10^?3 torr. The frequency of the external RF field was 13.56 MHz. Both the steady-state regimes in which the RF field had no effect on the plasma parameters and regimes with a pronounced effect of the RF field were observed. The experiments show that the regime of the discharge depends strongly on the plasma density and the magnetic field. The parametric instability is studied theoretically in the weak-turbulence approximation. It is shown that, due to the decay nature of the spectrum of plasma oscillations, the onset of instability is accompanied by the transfer of the energy of fluctuations over the spectrum, from the pump frequency toward its harmonics.     

Electric potential of a macroparticle in beam-plasma systems

Dusty plasma research is one of the most extensively developed areas of modern plasma physics. In spite of the large number of papers devoted to determining the electric potential of dust grains in gas discharge plasmas, this problem is still far from being resolved completely. In this paper, the behavior of the floating electric potential of a macroparticle in an electron beam-plasma system is studied in the framework of the orbit motion limited model taking into account secondary electron emission.     

Effect of the ponderomotive force on the development of beam-plasma instability

The amplitude of the wave generated in a plasma during the development of beam-plasma instability is nonuniform in the longitudinal direction. The ponderomotive force associated with this nonuniformity leads to a redistribution of the plasma density; as a result, the wave amplitude and its spatial distribution change. As the beam current grows, the ponderomotive force plays an increasingly important role and radically changes the mechanism by which the beam-plasma instability saturates. Ion acoustic waves generated by the ponderomotive force propagate in the direction opposite to the propagation direction of the beam, thereby ensuring distributed feedback and giving rise to a strong low-frequency self-modulation of the wave amplitude and phase. Results are presented from experimental investigations of the self-modulation regime of the beam-plasma instability in a magnetized plasma waveguide. Theoretical estimates of the parameters of the low-frequency self-modulation agree well with the experimental data.     

Nonlinear theory of the collective Cherenkov interaction of a dense relativistic electron beam with a dense plasma in a waveguide

A nonlinear theory of the instability of a straight relativistic dense electron beam in a plasma waveguide is derived for conditions of the stimulated collective Cherenkov effect. A study is made of a waveguide with a dense plasma such that the plasma wave excited by the beam during the instability can be escribed, with a good degree of accuracy, as a potential wave. General relativistic nonlinear equations are btained that describe the temporal dynamics of beam-plasma instabilities with allowance for plasma nonlinearity and the generation of harmonics of the initial perturbation. Under the assumption that the resonant interaction between the beam waves and the plasma waves is weak, the general equations are reduced to relativistic equations with cubic nonlinearities by using the method of expansion in small perturbations of the trajectories and momenta of the beam and plasma electrons. The reduced equations are solved analytically, the time scales on which the instability saturates are determined, and the nonlinear saturation amplitudes are obtained. A comparison between analytical solutions to the reduced equations and numerical solutions to the general nonlinear equations shows them to be in good agreement. Nonlinear processes caused by the relativistic nature of the beam are found to prevent stochastization of the system in the nonlinear stage of the well-developed instability. In contrast, a nonrelativistic electron beam is found to be subject to significant anomalous nonlinear stochastization.     

Electromagnetic beam-plasma interactions in a magnetic field

The excitation of plasma oscillations in a thin-walled annular plasma by an annular electron beam in a cylindrical waveguide is considered in the linear approximation. The instability growth rates and spatial amplification coefficients in the beam-plasma system under the conditions of the Cherenkov and anomalous Doppler resonances are obtained and compared with those in a transversely homogeneous system. The contributions from different instability mechanisms are analyzed.     

Tunable plasma relativistic microwave amplifier

A stable regime of the amplification of a slow plasma wave in a plasma waveguide during the injection of a high-current relativistic electron beam is obtained. For an input-signal frequency of 9.1 GHz, there exists a range of plasma densities in which the spectrum of the output microwave radiation lies in a 0.5-GHz-wide band. For a 40-kW input power at a frequency of 9.1 GHz, the maximum output power is 8 MW. It is shown experimentally for the first time that the beam-plasma amplifier can operate at frequencies of 9.1 GHz and 12.9 GHz. The range of plasma densities in which the regime of amplification is observed agrees with the results of calculations based on linear theory.     

Design of an experiment on wakefield acceleration on the VEPP-5 injection complex

Relativistic beams produced by the VEPP-5 injection complex (Budker Institute of Nuclear Physics, Siberian Division, Russian Academy of Sciences) can be used to generate plasma waves with a longitudinal electric field of 1 GV/m. A part of the electron (or positron) driver bunch is accelerated by this field over a distance of up to 1 m. The main advantage of the proposed design over the previous wakefield acceleration experiments is the beam preparation system capable of compressing bunches to a length of σ_z = 0.1 mm in the longitudinal direction and producing an optimal longitudinal profile of the beam density. The main parameters of the planned device are as follows: the electron energy at the entrance to the plasma is 510 MeV, the number of particles in the bunch is 2 × 10¹⁰, the plasma density is up to 10¹⁶ cm^?3, the number of accelerated particles is up to 3 × 10⁹, and their energy spread is less than 10%. The physical project of the experiment is presented, and the results of computer simulations of the beam-plasma interaction are described.     

Ion flows from a beam-plasma discharge

The results of measurements of the energy distribution function of ions escaping from a beam-plasma discharge are compared with the data from probe measurements in the discharge region. It is shown that, on the discharge axis, there is a region with a higher degree of ionization, whose position depends on the external parameters, in particular, on the gas pressure. The mean energy of the ions that leave the plasma from the outside of this region is determined by the potential of the plasma column. Inside the region with a higher degree of ionization, there is an additional mechanism for ion acceleration; as a result, the energy of the ions that leave the plasma from this region is higher than the energy of the electrostatically accelerated ions by a factor of 1.5 to 5. The results obtained show promise for creating a plasma-processing reactor with controlled ion parameters for the purposes of treating materials for microelectronics.     

Nonlineart theory of relativistic beam-plasma instabilities in the regime of the collective Cherenkov effect

A general mathematical model is proposed that is based on the Vlasov kinetic equation with a self-consistent field and describes the nonlinear dynamics of the electromagnetic instabilities of a relativistic electron beam in a spatially bounded plasma. Two limiting cases are analyzed, namely, high-frequency (HF) and low-frequency (LF) instabilities of a relativistic electron beam, of which the LF instability is a qualitatively new phenomenon in comparison with the known Cherenkov resonance effects. For instabilities in the regime of the collective Cherenkov effect, the equations containing cubic nonlinearities and describing the nonlinear saturation of the instabilities of a relativistic beam in a plasma are derived by using the methods of expansion in small perturbations of the trajectories and momenta of the beam electrons. Analytic expressions for the amplitudes of the interacting beam and plasma waves are obtained. The analytical results are shown to agree well with the exact solutions obtained numerically from the basic general mathematical model of the instabilities in question. The general mathematical model is also used to discuss the effects associated with variation in the constant component of the electron current in a beam-plasma system.     

Interaction of a modulated electron beam with an inhomogeneous plasma: Two-dimensional electrostatic simulations

Nonlinear beam-plasma interaction in a two-dimensional geometry was studied via numerical simulations. The generation of Langmuir waves and transverse oscillations of the beam electrons, as well as the formation of cavities of the plasma density, was observed. Correlation between the electric field structure in the stage of electron nonlinearity and the shape of cavities in the late stage of interaction is revealed.     

Control of power characteristics of ion flow in plasma-etching reactor based on beam-plasma discharge

It is shown that on the basis of the earlier revealed effect of generating the ion flow in the beam-plasma discharge from the discharge axis, a plasma processing reactor can be created for low-energy etching of semiconductor structures. The possibility of easily controlling the density and energy of ion flow by means of varying the potential of the discharge collector is demonstrated. The charge compensation of the ion flow incident on the nonconducting surface is implemented using the modulation of the potential of the substrate holder as well as the plasma-potential modulation.     

On the theory of a Cherenkov relativistic plasma emitter with a coaxial electrodynamic system

A plasma microwave amplifier based on a relativistic electron beam in an electrodynamic system in the form of a coaxial waveguide with a thin tubular plasma in a strong external magnetic field has been considered. Dispersion relations for determining the spectra of plasma and beam waves in the coaxial waveguide, as well as the general dispersion relation describing beam-plasma interaction, have been obtained in the linear approximation. The frequency dependences of the spatial growth rates for different plasma radii and different plasma frequencies, as well as the characteristic frequencies of the plasma amplifier, have been obtained by numerically and analytically solving the dispersion relations. The parameters of the plasma amplifier and generator with the coaxial electrodynamic system have been estimated for their experimental implementation.     

Beam discharge excited by distributed virtual cathode

A new type of beam discharge, i.e., beam discharge with a distributed virtual cathode (VC) is proposed and considered by numerical simulation. The discharge is established during counter motion of high-current electron beams in a gas-filled equipotential cavity and is characterized by a state of hot dense electron plasma of primary electrons. The discharge temporal dynamics is studied. It is shown that the VC lifetime depends linearly from this sum in a wide range of the sum of beam currents, from the boundary current of two-beam instability to the critical current of Pierce instability. Generation of nonlinear electrostatic structures shaped as phase bubbles in the discharge is detected, and their dynamics is studied. The parameters are determined, at which the multiple coexistence of phase bubbles and their coalescence during collisions is observed.     

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.     

Investigation of the electron energy distribution function in hollow-cathode glow discharges in nitrogen and oxygen

The mechanism for the formation of the inverse electron distribution function is proposed and realized experimentally in a nitrogen plasma of a hollow-cathode glow discharge. It is shown theoretically and experimentally that, for a broad range of the parameters of an N₂ discharge, it is possible to form a significant dip in the profile of the electron distribution function in the energy range ε=2–4 eV and, accordingly, to produce the inverse distribution with df(ε)/d?>0. The formation of a dip is associated with both the vibrational excitation of N₂ molecules and the characteristic features of a hollow-cathode glow discharge. In such a discharge, the applied voltage drops preferentially across a narrow cathode sheath. In the main discharge region, the electric field E is weak (E<0.1 V/cm at a pressure of about p～0.1 torr) and does not heat the discharge plasma. The gas is ionized and the ionization-produced electrons are heated by a beam of fast electrons (with an energy of about 400 eV) emitted from the cathode. A high-energy electron beam plays an important role in the formation of a dip in the profile of the electron distribution function in the energy range in which the cross section for the vibrational excitation of nitrogen molecules is maximum. A plasma with an inverted electron distribution function can be used to create a population inversion in which more impurity molecules and atoms will exist in electronically excited states.     

Low-pressure discharge induced by microwave radiation with a stochastically jumping phase

Results are presented from experimental studies on the unique beam-plasma generator of microwave radiation with a stochastically jumping phase (MWRSJP). To interpret the experimental results, a computer code was developed that allows one to simulate the process of gas ionization by electrons heated in the MWRSJP field and the behavior of plasma particles in such a field. The conditions for ignition and maintenance of a microwave discharge in air by MWRSJP are found both experimentally and theoretically, and the pressure range in which the power required for discharge ignition and maintenance is minimum are determined.