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.     

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.     

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.     

Process of compensation of the space charge of a negative ion beam in a gas

The process of compensation of the space charge of a negative ion beam propagating through a neutral gas is investigated numerically. A comparison of the results obtained with experimental data unambiguously proves that, at high gas pressures, when the beam space charge is overcompensated, the electric field within the beam is determined by Coulomb collisions of the beam ions with plasma electrons. At low pressures, when the space charge is undercompensated, the field within the beam is determined by the dynamic processes related to oscillations of the beam current.     

Low-current medium-pressure RF discharge with electron photoemission in the electrode sheath and penetration of the sheath electrons into the discharge column

A model is developed for simulating a low-current moderate-pressure RF discharge with allowance for such characteristic discharge properties as the existence of two sheaths near both electrodes throughout the RF field period; the formation of an electron cloud at the sheath boundary that periodically fills the sheath and leaves it, depending on the phase of the applied RF voltage; the production by the sheath electrons of metastable gas particles that interact with the cloud electrons during subsequent field periods, followed by the excitation of metastable states to the emitting levels; the formation of a sheath in a low-current RF discharge due to the overlap of the secondary electron avalanches triggered by electron photoemission from the electrode surface; and the conditions under which the sheath electrons penetrate into the positive column and accumulate there, which makes, thereby making a low-current RF discharge similar to a non-self-sustained discharge. The parameters of the sheath in a low-current RF discharge are determined by the conditions under which the electron photoemission current from the electrode surface in the sheath is self-sustaining and, like the parameters of the positive discharge column, depend on the sort of gas, the gas pressure, the frequency of the applied RF field, and the interelectrode distance. The results of calculating the parameters of the sheath and column of a low-current RF discharge for nitrogen and helium at different pressures, as well as for different field frequencies and interelectrode distances, are presented and are compared with the experimental data.     

Estimation of the electron density and radiative energy losses in a calcium plasma source based on an electron cyclotron resonance discharge

The parameters of a calcium plasma source based on an electron cyclotron resonance (ECR) discharge were calculated. The analysis was performed as applied to an ion cyclotron resonance system designed for separation of calcium isotopes. The plasma electrons in the source were heated by gyrotron microwave radiation in the zone of the inhomogeneous magnetic field. It was assumed that, in such a combined trap, the energy of the extraordinary microwave propagating from the high-field side was initially transferred to a small group of resonance electrons. As a result, two electron components with different transverse temperatures—the hot resonance component and the cold nonresonance component—were created in the plasma. The longitudinal temperatures of both components were assumed to be equal. The entire discharge space was divided into a narrow ECR zone, where resonance electrons acquired transverse energy, and the region of the discharge itself, where the gas was ionized. The transverse energy of resonance electrons was calculated by solving the equations for electron motion in an inhomogeneous magnetic field. Using the law of energy conservation and the balance condition for the number of hot electrons entering the discharge zone and cooled due to ionization and elastic collisions, the density of hot electrons was estimated and the dependence of the longitudinal temperature T _e∥ of the main (cold) electron component on the energy fraction β lost for radiation was obtained.     

Subnanosecond processes in the stage of breakdown formation in gas at a high pressure

Results are presented from experimental studies of the prebreakdown stage of a discharge in nitrogen at pressures of a few tens of atmospheres, gap voltages higher than 140 kV, and a voltage rise time of about 1 ns. Breakdown occurs at the front of the voltage pulse; i.e., the time of breakdown formation is shorter than the front duration. It is shown that, in gaps with a nonuniform electric field, the breakdown formation time is mainly determined by the time of avalanche development to the critical number of charge carriers. The subsequent stages of breakdown (the development of the ionization wave and the buildup of the conductivity in the weakly conducting channel bridging the gap) turn out to be shorter than this time or comparable to it.     

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.     

Picosecond runaway electron beams in air

Experimental data on the generation of picosecond runaway electron beams in an air gap with an inhomogeneous electric field at a cathode voltage of up to 500 kV are presented. The methods and equipment developed for these experiments made it possible to measure the beam characteristics with a time resolution of better than 10⁻¹¹ s, determine the voltage range and the beam formation time in the breakdown delay stage, and demonstrate the influence of the state of the cathode surface on the stability of runaway electron generation. It is demonstrated that the critical electron runaway field in air agrees with the classical concepts and that the accelerated beam can be compressed to ∼20 ps. It is unlikely that, under these conditions, the beam duration is limited due to the transition of field emission from the cathode to a microexplosion of inhomogeneities. The maximum energy acquired by runaway electrons in the course of acceleration does not exceed the value corresponding to the electrode voltage.     

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.”     

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.     

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.     

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.     

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.     

Investigation of plasma characteristics in an unbalanced magnetron sputtering system

Results are presented from experimental studies of a magnetron sputtering system for different configurations of the magnetic field above the cathode surface. The current-voltage characteristics of a magnetron discharge at different working gas pressures (0.08–0.3 Pa) and currents in the unbalancing coil were studied. The production and transport of charge carriers in a magnetron discharge with an unbalanced magnetic field was investigated by means of probe measurements of plasma characteristics and ion energies in the region between the substrate and the magnetic trap at the cathode surface. The radial distributions of the ion current density, plasma potential, and floating potential in the unbalanced operating mode are found to have pronounced extrema at the magnetron axis. It is shown that the plasma density near the substrate can be increased considerably when the axial magnetic field is high enough to efficiently confine plasma electrons and prevent their escape to the chamber wall.     

Model for calculating low-current moderate-pressure RF discharges with photon-driven secondary electron photoemission from the electrode surface

A model is developed for calculating a low-current moderate-pressure RF discharge with allowance for an electron cloud that is formed by electrons produced during the preceding periods of the RF field and fills the electrode sheath at regular intervals in accordance with the phase of the RF voltage applied to the electrodes. The cloud arises due to a phase shift of π/2 between the voltage across the sheath and that across the column of a low-current RF discharge plasma. The photon generation mechanism is as follows: as the cloud electrons fill the sheath, they acquire energy in superelastic collisions with metastables produced by the sheath electrons during the preceding periods of the RF field and then excite the metastable states to emitting levels. The discharge sheath forms due to the overlap of the secondary electron avalanches triggered by electron photoemission from the electrode surface. The parameters of the sheath in a low-current RF discharge are determined by the conditions under which the electron photoemission current in the sheath is self-sustaining, but the capacitive susceptance of the sheath is substantially higher than its active electrical conductance. The results of calculations are compared with the experimental data.     

Diffuse and constricted modes of a dc discharge in neon: Simulation of the hysteresis transition

Results are presented from theoretical studies of high-pressure (～100 Torr) dc discharges in neon. The diffuse and constricted discharge modes are studied using a model including the equation of balance for charged and excited particles, heat conduction equations for the neutral gas and plasma electrons, and Poisson’s equation for the radial electric field at a fixed total discharge current. A specific feature of the constricted mode in the investigated range of low fields and high degrees of ionization is that the excitation and ionization rates in the center of the discharge tube and at the periphery differ by several orders of magnitude. This implies that, in the constricted mode, the region where the electron energy distribution function is Maxwellian due to electron-electron collisions may adjoin the region (beyond the constriction zone) where the high-energy part of the distribution function is depleted. The hysteresis transition between the diffuse and constricted modes is analyzed. A transition from the constricted to the diffuse mode can be regarded as a manifestation of the nonlocal character of the formation of the electron distribution function, specifically, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region toward the periphery. The nonlocal formation of the distribution function is described by a nonlocal kinetic equation accounting for electron-electron collisions and electron transport along the radius of the discharge tube. Since only high-energy electrons produce gas ionization, the effect of the nonlocal formation of the electron distribution function is taken into account by introducing the effective temperature of the high-energy part of the distribution function and solving the equation for the radial profile of the high-energy part of the distribution function. This approach allows one to approximately take into account the nonlocal character of the electron distribution function without substantial expenditure of computer resources. The nonlocal model makes it possible to numerically simulate the hysteresis transition between the diffuse and constricted modes, which is impossible in the local approximation.     

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.     

Peculiarities of detecting pulses of runaway electrons and X-rays generated by high-voltage nanosecond discharges in open atmosphere

Peculiarities of detecting pulses of high-energy runaway electrons and the accompanying X-rays generated by high-voltage nanosecond discharges at high overvoltages in dense gases are discussed. Methods for overcoming difficulties encountered in such measurements are demonstrated. Different techniques for detecting runaway electrons and X-rays generated by discharges in open atmosphere are described, and typical errors that may be done when interpreting measurement results are considered. Experiments with the use of a small-size generator of nanosecond pulses with the idle-running voltage of 250–270 kV and stored energy of ～0.5 J have been carried out. It is shown that, in measuring runaway electron pulses by using an experimental configuration with a grid anode, a major portion of the recorded signal is attributed to electromagnetic disturbances. It is found that X-rays are mainly generated due to the deceleration of runaway electrons in the anode, rather than in gas. The number of runaway electrons with energies ～300 keV does not exceed 10⁹ per shot, and the X-ray dose is 60–200 μR/shot, depending on the anode material.     

Ribbon electron beam formation by a forevacuum plasma electron source

Results of the numerical analysis and experimental research on ribbon electron beam generation based on hollow cathode discharge at forevacuum gas pressure are presented. Geometry of the accelerating gap has modified. It lets us focus the ribbon electron beam and to transport it on a distance of several tens of centimeters in the absence of an axial magnetic field. The results of numerical simulations are confirmed by the experiment.