Parameters of a supershort avalanche electron beam generated in atmospheric-pressure air

Conditions under which the number of runaway electrons in atmospheric-pressure air reaches ∼5 × 10¹⁰ are determined. Recommendations for creating runaway electron accelerators are given. Methods for measuring the parameters of a supershort avalanche electron beam and X-ray pulses from gas-filled diodes, as well as the discharge current and gap voltage, are described. A technique for determining the instant of runaway electron generation with respect to the voltage pulse is proposed. It is shown that the reduction in the gap voltage and the decrease in the beam current coincide in time. The mechanism of intense electron beam generation in gas-filled diodes is analyzed. It is confirmed experimentally that, in optimal regimes, the number of electrons generated in atmospheric-pressure air with energies T > eU _m , where U _m is the maximum gap voltage, is relatively small.     

Runaway electron beams in the gas discharge for UV nitrogen laser excitation

The review of the methods for obtaining the runaway electron beams in the gas discharge is performed. The new method is offered, using which the beam is first formed in a narrow gap (∼1 mm) between the cathode and the grid and then it is accelerated by the field of the plasma column of the anomalous self-sustained discharge in the main gap (10–20 mm long). The electron beams with an energy of about 10 keV and current density of 10³ A/cm² at a molecular nitrogen pressure of up to 100 Torr have been obtained experimentally. The results of research of the UV nitrogen laser with an excitation via runaway electron beam and radiation of energy of ∼1 mJ are given. The UV nitrogen laser generation with the energy of ∼1 mJ has been obtained by the runaway electron beams.     

Two-component structure of the current pulse of a ranaway electron beam generated during electric breakdown of elevated-pressure nitrogen

Conditions are investigated at which two current pulses of ranaway electron beams are generated in elevated-pressure nitrogen during one voltage pulse. It is shown that the regime with two runaway electron beam current pulses takes place at decreased values of the electric field strength E in the gap (or decreased values of the parameter E/p, where p is the gas pressure). The regime with two runaway electron beam current pulses is observed both at high (1500?C3000 Torr) and low (below 100 Torr) pressures. It is shown that, for the second runaway electron beam current pulse to form, the voltage across the gap should be partially reduced during the first pulse. At low nitrogen pressures (~10 Torr), the regime in which two runaway electron beams are generated can be implemented by increasing the breakdown strength of the gap and/or increasing the value of E/p. In experiments carried out in atmospheric-pressure air with a picosecond time resolution, a rather complicated structure of the beam current pulse is observed at a voltage rise time of ~300 ps.     

Amplitude−temporal characteristics of a supershort avalanche electron beam generated during subnanosecond breakdown in air and nitrogen

The amplitude?temporal characteristics of a supershort avalanche electron beam (SAEB) with an amplitude of up to 100 A, as well as of the breakdown voltage and discharge current, are studied experimentally with a picosecond time resolution. The waveforms of discharge and SAEB currents are synchronized with those of the voltage pulses. It is shown that the amplitude?temporal characteristics of the SAEB depend on the gap length and the designs of the gas diode and cathode. The mechanism for the generation of runaway electron beams in atmospheric-pressure gases is analyzed on the basis of the obtained experimental data.     

Conditions for electron runaway under leader breakdown of long gaps

An original hydrodynamic model in which inelastic collisions in the equations of motion and energy balance play a decisive role is developed and applied to simulate electron avalanches in strong electric fields. The mean energy and drift velocity of electrons, as well as the ionization coefficient and electric field in a wide range of mean electron energies, are determined for helium and xenon. A criterion is derived for the runaway of the average electron in discharges with ionization multiplication. It is shown that runaway can take place at any value of E/p, provided that the momentum mean free path exceeds the gap length. The voltage corresponding to electron runaway is found for helium, xenon, and air as a function of the electric field, the electron mean energy, and the parameter pd. Conditions for the formation of a precursor in electronegative gases are analyzed. It is shown that the presence of a precursor with a high electric conductance is necessary for the formation of a new leader step. The voltage and time ranges corresponding to efficient electron runaway and X-ray generation during leader breakdown in air are determined.     

Ecton processes in the generation of pulsed runaway electron beams in a gas discharge

As was shown earlier for pulsed discharges that occur in electric fields rising with extremely high rates (10¹⁸ V/(cm s)) during the pulse rise time, the electron current in a vacuum discharge is lower than the current of runaway electrons in an atmospheric air discharge in a 1-cm-long gap. In this paper, this is explained by that the field emission current from cathode microprotrusions in a gas discharge is enhanced due to gas ionization. This hastens the initiation of explosive electron emission, which occurs within 10^–11 s at a current density of up to 10¹⁰ A/cm². Thereafter, a first-type cathode spot starts forming. The temperature of the cathode spot decreases due to heat conduction, and the explosive emission current ceases. Thus, the runaway electron current pulse is similar in nature to the ecton phenomenon in a vacuum discharge.     

Energy distribution of runaway electrons generated by a nanosecond discharge in atmospheric-pressure air

The spectra of an ultrashort avalanche electron beam generated by a nanosecond discharge in atmospheric-pressure air were investigated. The temporal characteristics of the beam current pulses, gap voltage, and discharge current in a gas diode were measured with a time resolution of ～0.1 ns. A simple technique was developed for recovering electron spectra from the curves of beam attenuation by aluminum foils. The effect of the cathode design, electrode gap length, and generator parameters on the electron spectra were studied using seven setups. It is shown that generation of electrons with anomalously high energies requires the use of cathodes with increased curvature radius.     

Study of the Formation Time of a Self-Sustained Subnanosecond Discharge at High and Ultrahigh Gas Pressures

The formation times of self-sustained subnanosecond discharges in nitrogen at pressures of 1?40 atm and in hydrogen at pressures of 1–60 atm are analyzed in terms of the avalanche model. In experiments, a subnanosecond voltage pulse with an amplitude of 102 ± 2 kV was applied to a 0.5-mm-long discharge gap with a uniformly distributed electric field (the curvature radii of both the cathode and anode ends were 1 cm). The rise time of the voltage pulse from 0.1 to 0.9 of its amplitude value was about 250 ps. Breakdown occurred at the leading edge of the pulse. The discharge formation time was measured at different gas pressures with a step of 5–10 atm. Analysis of the experimental results shows that, in nitrogen at pressures of 10–40 atm and in hydrogen at pressures of 20–50 atm, breakdown occurs earlier than the electron avalanche reaches its critical length and that the critical avalanche length lies in the range of (2–8) × 10^–2 mm, which is one order of magnitude shorter than the discharge gap length. This means that the avalanche–streamer model is inapplicable in this case. The fast formation of a conducting channel under these conditions can be explained by ionization of gas by runaway electrons. In this case, the conducting column develops as a result of simultaneous development of a large number of electron avalanches in the gas volume. An increase in the hydrogen pressure from 50 to 60 atm leads to an abrupt increase in the discharge formation time by about 50%. As a result, the growth time of the electron avalanche to its critical length becomes shorter than the discharge formation time. In this case, the electrons cease to pass into the runaway regime and the discharge is initiated from the cathode due to field emission from microinhomogeneities on its surface. Under these conditions, the discharge formation time is well described by the avalanche–streamer model.     

Mechanism of Runaway Electron Generation at Gas Pressures from a Few Atmospheres to Several Tens of Atmospheres

The mechanism of runaway electron generation at gas pressures from a few atmospheres to several tens of atmospheres is proposed. According to this mechanism, the electrons pass into the runaway mode in the enhanced field zone that arises between a cathode micropoint—a source of field-emission electrons—and the region of the positive ion space charge accumulated near the cathode in the tails of the developing electron avalanches. As a result, volume gas ionization by runaway electrons begins with a time delay required for the formation of the enhanced field zone. This process determines the delay time of breakdown. The influence of the gas pressure on the formation dynamics of the space charge region is analyzed. At gas pressures of a few atmospheres, the space charge arises due to the avalanche multiplication of the very first field-emission electron, whereas at pressures of several tens of atmospheres, the space charge forms as a result of superposition of many electron avalanches with a relatively small number of charge carriers in each.     

Electron cyclotron resonance acceleration of electrons to relativistic energies by a microwave field in a mirror trap

Results are presented from experiments on the acceleration of electrons by a 2.45-GHz microwave field in an adiabatic mirror trap under electron cyclotron resonance conditions, the electric and wave vectors of the wave being orthogonal to the trap axis. At a microwave electric field of ≥10 V/cm and air pressures of 10^?6–10^?4 Torr (the experiments were also performed with helium and argon), a self-sustained discharge was initiated in which a fraction of plasma electrons were accelerated to energies of 0.3–0.5 MeV. After the onset of instability, the acceleration terminated; the plasma decayed; and the accelerated electrons escaped toward the chamber wall, causing the generation of X-ray emission. Estimates show that electrons can be accelerated to the above energies only in the regime of self-phased interaction with the microwave field, provided that the electrons with a relativistically increased mass penetrate into the region with a higher magnetic field. It is shown that the negative-mass instability also can contribute to electron acceleration. The dynamic friction of the fast electrons by neutral particles in the drift space between the resonance zones does not suppress electron acceleration, so the electrons pass into a runaway regime. Since the air molecules excited by relativistic runaway electrons radiate primarily in the red spectral region, this experiment can be considered as a model of high-altitude atmospheric discharges, known as “red sprites.”     

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.     

Study of the formation of a fast electron beam in a coaxial gas diode in the unlimited emission model

The formation of a fast electron beam in a coaxial gas diode is simulated using the OOPIC Pro particle-in-cell code under the assumption of unlimited cathode emissivity. It is shown that fast electrons are generated near the cathode. The so-called “contracting-capacitor” mechanism of electron acceleration does not operate in the parameter range under study, because the boundary of the dense plasma is spread out due to preionization of the electrode gap by fast electrons.     

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.     

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.     

Breakdown in helium in high-voltage open discharge with subnanosecond current front rise

Investigations of high-voltage open discharge in helium have shown a possibility of generation of current pulses with subnanosecond front rise, due to ultra-fast breakdown development. The open discharge is ignited between two planar cathodes with mesh anode in the middle between them. For gas pressure 6 Torr and 20 kV applied voltage, the rate of current rise reaches 500 A/(cm² ns) for current density 200 A/cm² and more. The time of breakdown development was measured for different helium pressures and a kinetic model of breakdown in open discharge is presented, based on elementary reactions for electrons, ions and fast atoms. The model also includes various cathode emission processes due to cathode bombardment by ions, fast atoms, electrons and photons of resonant radiation with Doppler shift of frequency. It is shown, that the dominating emission processes depend on the evolution of the discharge voltage during the breakdown. In the simulations, two cases of voltage behavior were considered: (i) the voltage is kept constant during the breakdown; (ii) the voltage is reduced with the growth of current. For the first case, the exponentially growing current is maintained due to photoemission by the resonant photons with Doppler-shifted frequency. For the second case, the dominating factor of current growth is the secondary electron emission. In both cases, the subnanosecond rise of discharge current was obtained. Also the effect of gas pressure on breakdown development was considered. It was found that for 20 Torr gas pressure the time of current rise decreases to 0.1 ns, which is in agreement with experimental data.     

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.     

Pulse-periodic generation of supershort avalanche electron beams and X-ray emission

Pulse-periodic generation of supershort avalanche electron beams (SAEBs) and X-ray emission in nitrogen, as well as the transition from a single-pulse mode to a pulse-periodic mode with a high repetition frequency, was studied experimentally. It is shown that, in the pulse-periodic mode, the full width at halfmaximum of the SAEB is larger and the decrease rate of the gap voltage is lower than those in the single-pulse mode. It is found that, when the front duration of the voltage pulse at a nitrogen pressure of 90 Torr decreases from 2.5 to 0.3 ns, the X-ray exposure dose in the pulse-periodic mode increases by more than one order of magnitude and the number of SAEB electrons also increases. It is shown that, in the pulse-periodic mode of a diffuse discharge, gas heating in the discharge gap results in a severalfold increase in the SAEB amplitude (the number of electrons in the beam). At a generator voltage of 25 kV, nitrogen pressure of 90 Torr, and pulse repetition frequency of 3.5 kHz, a runaway electron beam was detected behind the anode foil.     

Investigation of the chaotic dynamics of an electron beam with a virtual cathode in an external magnetic field

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.     

Inertial electrostatic confinement and nuclear fusion in the interelectrode plasma of a nanosecond vacuum discharge. II: Particle-in-cell simulations

Results of particle-in-sell simulations of ion acceleration by using the KARAT code in a cylindrical geometry in the problem formulation corresponding to an actual experiment with a low-energy vacuum discharge with a hollow cathode are presented. The fundamental role of the formed virtual cathode is analyzed. The space-time dynamics of potential wells related to the formation of the virtual cathode is discussed. Quasi-steady potential wells (with a depth of ∼80% of the applied voltage) cause acceleration of deuterium ions to energies about the electron beam energy (∼50 keV). In the well, a quasi-isotropic velocity distribution function of fast ions forms. The results obtained are compared with available data on inertial electrostatic confinement fusion (IECF). In particular, similar correlations between the structure of potential wells and the neutron yield, as well as the scaling of the fusion power density, which increases with decreasing virtual cathode radius and increasing potential well depth, are considered. The chosen electrode configuration and potential well parameters provide power densities of nuclear DD fusion in a nanosecond vacuum discharge noticeably higher than those achieved in other similar IECF systems.     

Influence of a transverse magnetic field on the characteristics of a dc gas discharge

The influence of a transverse magnetic field and the working-gas pressure on the rotation frequency of the current channel, as well as on the electric field in the positive column and the cathode voltage drop in a dc gas discharge, was studied experimentally. The working gases were pure hydrogen and hydrogen-methane, hydrogen-argon, and hydrogen-argon-methane mixtures. It is shown that a transverse (with respect to the discharge current) magnetic field stabilizes a normal glow discharge against a transition to an arc discharge at specific absorbed powers above 300 W/cm³. The cathode voltage drop and the electric field in the positive column are measured. It is shown that the electric field does not depend on the magnetic field strength, whereas the cathode voltage drop increases with increasing magnetic field. It is found that the rotation frequency of the current channel is a complicated function of the discharge parameters and attains 400 Hz.