Magnetic probe measurements of the current sheath on the PF-3 facility

Results are presented from experimental studies of the dynamics of the current sheath (CS) on the PF-3 plasma focus facility. The parameters of the sheath, including the current distribution in it, were measured using absolutely calibrated magnetic probes installed at different positions with respect to the facility axis and the anode surface. The CS dynamics in discharges operating in argon and neon was investigated, and the skin depth in different stages of the discharge was determined. One of the probes was installed at a distance of ≈2 cm from the facility axis, which made it possible to estimate the efficiency of current transfer to the region of pinch formation. Operating modes were obtained in which the current dynamics detected by magnetic probes at different distances from the axis agreed well with the dynamics of the total discharge current until the instant of singularity in the current time derivative. It is shown that shunting breakdowns can lead to the formation of closed current loops. The shunting of the discharge current by the residual plasma is directly related to the efficiency of snowplowing of the working gas by the CS as it propagates from the insulator toward the facility axis.     

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.     

Dynamics of the structure of the plasma current sheath in a plasma focus discharge

The study is aimed at investigating the fine structure of the plasma current sheath (PCS) in the PF-3 plasma focus facility. The PCS dynamics in a deuterium discharge was studied. The PCS parameters were measured using absolutely calibrated magnetic probes installed at different positions with respect to the facility axis and the anode surface. A magneto-optical probe recording both the magnetic signal and the PCS optical luminosity was first applied to analyze the PCS structure. This made it possible to spatially resolve the current and shock-wave regions. It is demonstrated that the current distribution is different in different discharge stages. It is shown that the neutron yield is determined by the value of the current compressed toward the axis, rather then the amplitude of the total discharge current.     

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.     

Kinetic theory of a gas-discharge positive column and wall sheath

The positive column and wall sheath in a gas discharge are studied with allowance for ion collisions in a plasma and ion reflection from a solid surface under conditions of incomplete ion neutralization. The kinetic equation for ions in a positive column is reduced to a Fredholm equation of the second kind. This makes it possible to solve the kinetic equation using a resolvent and thereby derive a single integrodifferential equation for the potential, which is referred to as a generalized plasma-sheath equation. Specific versions of the plasma-sheath equation are obtained that take into account charge exchange of the ions in a plasma and the thermal spread in velocities of the ionization-produced ions.     

Contactless method for studying the parameters of the electrode region of an RF discharge

A nonintrusive contactless method for studying the parameters of the electrode region of a capacitive low-pressure RF discharge is proposed. The method involves the measurements of dc and ac electric voltages at the elements of the discharge circuit with subsequent calculations of both the electrostatic potential drop across the electrode sheath and the sheath thickness by using relations derived in the paper. For a collisionless electrode sheath, the density of the positive-ion current onto the electrode and the charge density at the plasma boundary are determined. It is shown experimentally that the method can be successfully applied to studying capacitive RF discharges with inner or outer electrodes.     

Saturation of the neutron yield from megajoule plasma focus facilities

A relation is investigated between the saturation of the neutron yield from megajoule plasma focus facilities and that of the total discharge current. An analytic formula for the neutron yield as a function of the facility energy is derived by simple calculations of the discharge circuit and is verified by computer simulations of the dynamics of the current sheath. The dependence obtained differs from the generally accepted one but agrees well with experimental data.     

Magnetic and neutron measurements on the PF-400 plasma focus facility

Parasitic currents shunting up to one-half of the total discharge current were detected using magnetic probes on a Filippov-type plasma focus facility with a maximum total current of 1 MA and stored energy of 80 kJ. The measured time dependence of neutron emission from the discharge indicates that the parameters of the neutron pulse are closely related to those of the imploding current sheath.     

Drift model of the cathode region of a glow discharge

A one-dimensional drift model of the cathode region of a glow discharge with allowance for both electron-impact ionization and charged particle loss is proposed. An exact solution to the model equations is obtained for the case of similar power-law dependences of the ion and electron drift velocities on the electric field strength. It is shown that, even in the drift approximation, a relatively wide transition layer in which the ion-to-electron current ratio approaches a constant value typical of the positive column of a glow discharge should occur between the thin space-charge sheath and the quasineutral plasma, the voltage drop across the space-charge sheath being comparable to that across the transition layer. The calculated parameters of the normal and anomalous glow discharges are in good agreement with available experimental data.     

Evolution of the channel of a long leader in air after a sharp decrease in the discharge current

The dynamics of the plasma parameters in a given cross section of a long-lived leader channel in air after a jumplike decrease in the discharge current is simulated numerically with the help of a one-dimensional non-steady-state model constructed with allowance for the dynamics of the energy input into the channel, the expansion of the channel, and the nonequilibrium ionization kinetics in the leader plasma. It is shown that, after a decrease in the current, the electric field in the channel, first, rapidly decreases and, then, increases gradually as the gas cools. The higher the energy input into the discharge before the decrease in the current, the longer the time scale on which the electric field increases. The results of simulations of the electric field in the channel agree with the data from the experimental modeling of the actual leader channel by a short spark.     

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.     

Experimental study of magnetized plasma rotation in crossed fields

Rotation of magnetized plasma between two coaxial electrodes in crossed electric and magnetic fields was studied experimentally. Three regimes of plasma rotation were observed. In the first regime, the radial electric field is created by a beam?plasma discharge due to the charging of the inner axial electrode by electrons, the outer electrode being grounded. Plasma rotation in this case is accompanied by strong high-frequency current oscillations detected by a Mach probe. When a negative voltage was applied to the coaxial electrodes, the second regime was observed, in which weakly perturbed quasi-stationary plasma rotation occurred at a relatively low radial current. The third regime of plasma rotation was observed upon a spontaneous disruption of the second regime. It is characterized by high currents of ~1 kA, sheared plasma rotation, and excitation of high-frequency perturbations.     

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.     

Formation of electrode sheaths during the acceleration of a magnetized plasma

A study is made of the motion of a plasma with a frozen-in magnetic field along the electrode surfaces in the direction transverse to the magnetic field. A one-dimensional problem of an electrode sheath is formulated in which all of the quantities depend only on the coordinate orthogonal to the electrode surface. Viscous plasma heating, plasma cooling via heat conduction, and other kinetic effects are taken into consideration. Account is also taken of the effect of plasma acceleration and of the related current that is transverse to the electrode surfaces and, due to the Hall effect, carries the magnetic flux away from the cathode and toward the anode. Solving the one-dimensional problem with a constant electric current and constant magnetic field shows that, in a sheath that forms near the cathode, the solution becomes self-similar, the plasma mass grows linearly, and the electron magnetization parameter remains unchanged. It is found that the anode sheath cannot be described in the magnetohydrodynamic approximation, according to which the plasma density in the sheath rapidly vanishes, while the current through the sheath remains constant. This difficulty can be overcome by incorporating some of the nonhydrodynamic effects (primarily, electron dispersion), thereby making the problem physically correct. Solving the problem numerically shows that a decrease in the plasma density in the anode sheath due to the Hall effect gives rise to additional significant plasma acceleration.     

Influence of the radiation of the plasma-focus current sheath on the implosion dynamics of condensed targets

Results are presented from experimental and theoretical studies of the influence of the radiation of the plasma-focus current sheath on the implosion dynamics of condensed targets. Radiative losses from the current sheath of a plasma focus in neon, argon, and hydrogen with a 2% admixture of Xe are calculated with allowance for the line, bremsstrahlung, and recombination radiation. It is shown that the temperature of the neon plasma (10–15 eV) is quite sufficient to evaporate Al₂O₃ grains of radii 10–20 μm. The use of neon as a working gas makes it possible to alter the cold-start condition in experiments on the implosion of foam liners.     

On the Structure and Intensity of Vortex in RF Inductively Coupled Argon Plasma

Numerical simulation of a specific technical RF inductively coupled argon plasma with three coils, discharge current in the range of J_coil = 100–250 A, and generator frequency 3 MHz is presented. The temperature, pressure, and velocity fields are obtained under different discharge currents and different flow rates of central gas. A reversed flow (vortex) is found between the injected cool gas and high-temperature plasma-forming gas. The formation mechanisms of such a vortex and the influence of the discharge current and flow rate of central gas on the vortex structure and intensity are studied. Special attention is paid to investigating two different kinds of vortex flow patterns—Benard and toroidal. A critical flow rate of central gas above which the flow pattern would transform from Benard to toroidal is determined and approximated as a function of the discharge current by theoretical calculations and numerical simulations. The maximum negative velocities along the axis in the vortex zone are also determined under different discharge currents and different flow rates of central gas.     

Low-current moderate-pressure RF discharge with secondary electron photoemission

A model is proposed for a low-current RF discharge with secondary electron photoemission from the electrode surface caused by photons originating in the electrode sheath. The low-current state of RF discharges at moderate pressures is peculiar in that the electrons and ions produced during the preceding periods of the RF field promote the development of the discharge during subsequent periods. Since the ion space charge is induced during many periods of the RF field, even comparatively moderate fields in the electrode sheath are sufficient to ensure the conditions under which the current is self-sustaining, in which case the electron photoemission dominates over the remaining secondary processes at the electrode surface. In a low-current RF discharge, the ion-electron emission has essentially no impact on the formation of the electrode sheath because the half-period of the RF field is much shorter than the ion transit time through the sheath. The sheath results from the overlap of the secondary electron avalanches triggered by electron photoemission from the electrode surface. The sheath parameters are determined by the conditions under which the current in the sheath is selfsustaining due to the secondary electron photoemission from the electrode surface. The capacitive susceptance of the electrode sheath is substantially higher than its electrical conductance. Low-current RF discharges can only exist when the time required for the ions to drift through the sheath and reach the electrode is much longer than the half-period of the RF field.     

Determination of the electron density and electric field in the plasma of a low-pressure microwave electrode discharge in hydrogen from the measured spectral line intensities

The parameters of the plasma of a microwave electrode discharge in hydrogen at pressures of 1–8 torr and incident powers of 20–80 W are measured by the so-called “relative intensity” method. The method allows one to determine the electron density and electric field in plasma by measuring the relative intensities of the H_α, H_β, and 763.5-nm Ar line emission and calculating the electron-impact rate constants from the homogeneous Boltzmann equation. The measurements show that there are regions in the discharge where the electron density is higher (a bright electrode sheath) and lower (a spherical region) than the critical density for the frequency 2.45 GHz (n_cr～7×10¹⁰ cm^?3). Inside the spherical region, the electric field varies slightly over the radius and the electron density increases as the discharge boundary is approached. The observed discharge structure can be attributed to the presence of a self-sustained discharge zone (electrode sheath); a non-self-sustained discharge zone (spherical region); and a decaying plasma region, which is separated from the active discharge zone by an electric double layer.     

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.     

Study of the implosion of wire arrays at the PF-3 facility

Results of experiments on the compression of tungsten wire arrays by the plasma current sheath (PCS) of the PF-3 facility at currents of up to 2 MA are presented. The efficiency of current transportation to the wire array and switching-over of the discharge current to the array were studied. Information on the penetration of the magnetic field into the wire array obtained using microprobes made it possible to compare the obtained experimental data with the results of magnetic field measurements carried out at other high-power electrophysical devices. The intensity of plasma production from tungsten wires under the action of the plasma focus PCS is estimated. The experimental results are tested against the existing models of wire array implosion with prolonged plasma production.