Nonisothermal theory of the positive column of an electric discharge in the axial magnetic field

A nonisothermal model of the positive column allowing for electron energy balance is analyzed. The influence of the axial magnetic field on the characteristics of the cylindrical positive column of a low-pressure discharge is investigated in the hydrodynamic approximation. It is shown that the magnetic field affects the plasma density distribution, plasma velocity, and electron energies. The radial dependences of the plasma density, electron energy, and plasma velocity, as well as the azimuthal velocities of electrons and ions, are calculated for helium at different values of the magnetic field strength. It is established that inertia should be taken into account in the equations for the azimuthal motion of electrons and ions. The results obtained in the hydrodynamic approximation differ significantly from those obtained in the framework of the common diffusion model of the positive column in the axial magnetic field. It is shown that the distributions of the plasma density and radial plasma velocity in the greater part of the positive column tend to those obtained in the diffusion approximation at higher values of the axial magnetic field and gas density, although substantial differences remain in the near-wall region.     

Instability of a low-pressure hollow-cathode discharge in a magnetic field

Mechanisms responsible for current oscillations at the ion branch of the probe characteristic are investigated experimentally and theoretically. A comparison between experiment and theory shows that the oscillations in a hollow-cathode discharge in a longitudinal magnetic field are most likely related to the onset of helical instability.     

Concerning arc discharge in a transverse magnetic field

The retrograde motion of an arc in a transverse magnetic field is attributed to the onset of a tangential flow of gas or vapor. The physics of a polarized plasma jet conducting the current between the cathode and anode is discussed.     

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.     

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.     

Effect of the transverse magnetic field on turbulence and parameters of a plasma column in the L-2M stellarator

The influence of magnetic configurations with magnetic hills or wells on the parameters of a plasma column and turbulence characteristics were studied in experiments in which the plasma was created and heated by a microwave beam at the second harmonic of the electron cyclotron frequency. Calculations show that, for 〈β〉=(1.5?2)×10^?, a configuration with a magnetic well takes place and the Mercier criterion for stability of the ideal MHD modes is satisfied. It is shown that the compensation of the Shafranov shift of the plasma column by a transverse (vertical) field (B _v /B ₀ =5×10^?3) leads to a configuration with a magnetic hill in which the Mercier stability criterion is violated in the central region of the plasma column. It is experimentally shown that the stored plasma energy in the magnetic-hill configuration is reduced by one-half in comparison with the magnetic-well configuration. In the case of a magnetic hill, the energy of fluctuations increases both in the plasma core and near the separatrix, and the quasi-regular components of the wavelet spectra grow. When the Shafranov shift is compensated only partially (B _v/B ₀～3×10^?3) and the system is near the instability threshold, the stored plasma energy and the central electron temperature are somewhat higher, and the radiation power of fast electrons from non-Maxwellian tails at the second harmonic of the electron gyrofrequency decreases. It is found that the wavelet spectra of fluctuations change, the coherence coefficient for spectral components increases, and the radial electric field near the separatrix decreases.     

Dark phase effect in the evolution of the positive column of a glow discharge in nitrogen

The characteristics of the initial stage of the formation of the positive column of a glow discharge in nitrogen at reduced pressures are studied experimentally and numerically. A dip in the plasma emission intensity in the initial stage of the discharge (the so-called “dark phase”) is observed experimentally at the positive polarity of the high-voltage electrode (the cathode is grounded). The dark phase is preceded by an ionization wave (IW). When the anode is grounded, neither an IW nor a dip in the discharge emission intensity are observed. A theoretical model capable of describing the discharge development under the actual experimental conditions is constructed. It is shown that the dark phase effect may be caused by the high electron density (above the steady-state one) produced in the gas during the passage of the IW across the discharge gap. This mechanism of the dark phase formation differs from the mechanism proposed earlier to explain a similar effect in noble gases. Additional experiments carried out with pure argon, helium, and helium with a nitrogen admixture have shown that, in the case of a grounded cathode, gas breakdown is also accompanied by the passage of an IW, whereas in the case of a grounded anode, no IW is observed; however, the dark phase is present in both cases. It is shown using computer simulations that, in nitrogen (in contrast to noble gases), the mechanism resulting in the dark phase effect does not operate in the absence of an IW.     

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.     

Antibiotics production in a fluidized bed reactor utilizing a transverse magnetic field

A mathematical model is developed to describe the performance of a three-phase fluidized bed reactor utilizing a transverse magnetic field. The model is based on the axially dispersed plug flow model for the bulk of liquid phase and on the Michaelis-Menten kinetics. The model equations are solved by the explicit finite difference method from transient to steady state conditions. The results of the numerical simulation indicate that the magnetic field increases the degree of bioconversion. The mathematical model is experimentally verified in a three-phase fluidized bed reactor with Penicillium chrysogenum immobilized on magnetic beads. The experimental results are well described by the developed model when the reactor operates in the stabilized regime. At low and relatively high magnetic field intensities certain discrepancy in the model solution is observed when the model over estimates the product concentration.     

Generation of plasma oscillations in a low-pressure microwave discharge

The resonant excitation of plasma (Langmuir) oscillations during the microwave breakdown of a low-pressure gas is studied both analytically and numerically using the simplest uniform model. It is shown that, because of a significant delay in electron heating and cooling, this effect ensures that the plasma density increases at a high (resonant) rate, even after exceeding a critical value, and can reach a very high (overcritical) level.     

Memory effect in the ignition of a low-pressure glow discharge in nitrogen in a long discharge tube

Results are presented from experimental studies of breakdown and the initial stage of a discharge in a long tube (with an interelectrode distance of 40 cm and a diameter of 2.8 cm) at a pressure of ～1 Torr and pulse discharge current of ～10 mA. Breakdown was produced by positive voltage pulses with a linearly growing leading edge with a steepness of dU/dt ～ 10⁶–10⁸ V/s. The time interval between pulses was varied from τ = 0.5 ms to 1 s, the pulse duration being 10 ms. The work was aimed at studying the memory effect of the discharge gap, namely, the influence of the previous pulse on the breakdown characteristics of the next one. In the experiments, the breakdown voltage was measured at different values of dU/dt and τ. It was found that the memory effect was absent at τ ～ 1 s. At the same time, an increase in the breakdown voltage with increasing dU/dt was observed. In the range of τ ≈ 50–200 ms, the breakdown voltage also did not depend on τ, but the memory effect took place. The memory effect in this case consisted in that the breakdown voltage decreased with increasing dU/dt, so that, at dU/dt ～ 10⁷ V/s, the breakdown voltage was two times lower than in the case of τ ～ 1 s. For τ ～ 1–10 ms, the memory effect manifested itself in that the breakdown voltage depended on τ: it could either decrease (the “normal” effect) or increase (the “anomalous” effect) with increasing τ. Breakdown of the discharge gap was preceded by the propagation of an ionization wave, except for the case of small τ values in the domain of existence of the anomalous effect. Estimates allowing one to qualitatively explain the experimental results are made.     

Formation of shock waves in a discharge plasma in the presence of a magnetic field

The effect of an external magnetic field on the dynamics of shock waves generated in an argon plasma due to both explosive processes on the cathode and expansion of the spark channel has been studied experimentally. It is shown that the expanding plasma of the cathode spot forms a shock wave and that the application of a longitudinal magnetic field decelerates the radial expansion of the cathode plasma. It is found that the intensities of some argon spectral lines increase in the presence of a magnetic field.     

Kinetic models of current sheets with a sheared magnetic field

Thin current sheets, whose existence in the Earth’s magnetotail is confirmed by numerous spacecraft measurements, are studied analytically and numerically. The thickness of such sheets is on the order of the ion Larmor radius, and the normal component of the magnetic field (B _z ) in the sheet is almost constant, while the tangential (B _x ) and shear (B _y ) components depend on the transverse coordinate z. The current density in the sheet also has two self-consistent components (j _x and j _y , respectively), and the magnetic field lines are deformed and do not lie in a single plane. To study such quasi-one-dimensional current configurations, two kinetic models are used, in particular, a numerical model based on the particle-in-cell method and an analytical model. The calculated results show that two different modes of the self-consistent shear magnetic field B _y and, accordingly, two thin current sheet configurations can exist for the same input parameters. For the mode with an antisymmetric z profile of the B _y component, the magnetic field lines within the sheet are twisted, whereas the profiles of the plasma density, current density component j _y , and magnetic field component B _x differ slightly from those in the case of a shearless magnetic field (B _y = 0). For the symmetric B _y mode, the magnetic field lines lie in a curved surface. In this case, the plasma density in the sheet varies slightly and the current sheet is two times thicker. Analysis of the dependence of the current sheet structure on the flow anisotropy shows that the sheet thickness decreases significantly with decreasing ratio between the thermal and drift plasma velocities, which is caused by the dynamics of quasi-adiabatic ions. It is shown that the results of the analytical and numerical models are in good agreement. The problems of application of these models to describe current sheets at the magnetopause and near magnetic reconnection regions are discussed.     

Study of the dark phase in the initial stage of the positive column formation in a neon glow discharge

The initial stage of the positive column formation in a neon glow discharge is investigated both experimentally and theoretically. A decrease in the plasma radiation intensity (the so-called “dark phase”) was observed experimentally over a time period of about 1 ms. A similar dip was also observed in the time dependence of the electric field strength. The measured population of the lower metastable states of Ne was found to have a maximum at the beginning of the dark phase. A relevant theoretical model has been developed and used to perform calculations for the actual experimental conditions. A comparison between the numerical and experimental results shows that the model adequately describes the processes that occur during the formation of the positive column in a neon glow discharge. Experimental and theoretical studies show that the dark-phase effect is related to the excessive amount of metastable Ne atoms at the beginning of a discharge and, accordingly, to the high rates of stepwise ionization and chemionization.     

Rates of glucose oxidation with a column reactor utilizing a magnetic field

Rates of glucose oxidation were measured with the use of a fluidized-bed column placed in a magnetic field and magnetite-containing beads of immobilized glucose oxidase and catalase. Its performance was predicted from the volumetric coefficient for liquid-phase mass transfer and the kinetic constants for glucose oxidation. Effusion of beads was negligible under the operating conditions employed.     

Quenching of an electric arc in a vacuum gap with a uniform transverse magnetic field

The breaking ability of a vacuum arc interrupter with a uniform transverse magnetic field formed by a system of permanent magnets was investigated experimentally. The vacuum interrupter with a 0.5-μF shunting capacitor switched off a dc current of up to 150 A at magnetic fields of 100–180 mT. At magnetic fields of 120–160 mT, the breaking ability of the vacuum interrupter was increased to 300 A by introducing a nonuniformity in the magnetic field distribution near the contact surface.     

Gas temperature in the plasma of a low-pressure electrode microwave discharge in hydrogen

The gas temperature in an electrode microwave discharge in hydrogen at pressures of 1–8 torr and input powers of 20–90 W is determined from the relative intensities of the rotational lines of the electronically excited molecules of the Fulcher α system of molecular hydrogen. It is found that the gas temperature in the discharge is no higher than 800 K over the entire range of the experimental conditions under study. For this reason, plasma resonance cannot be regarded as a factor determining the physical processes in the discharge over the entire pressure range. Since the discharge unit is a nonuniform gas-dynamic system (the gas is fed through a small hole into a chamber of limited size), there is a possibility of generating vortex flows that intensively mix the gas. This results in a uniform distribution of the gas temperature throughout the entire volume of the spherical plasma structure produced in the experiment.     

Effect of the electron drift in a transverse electric field on the width of spark channels in a multichannel sliding discharge

The effect of electron drift on the transverse size of the spark channels in a multichannel sliding discharge on a dielectric surface is considered in a semianalytic approximation. The strength of an electric field transverse to the channel axis is estimated by the mirror image method. The estimate obtained is used to analyze the differential equation for the density of electrons with allowance for their drift from the channel into the surrounding layers. It is shown that the channel expands to a certain steady-state radius at which an increase in the local electron density due to the ionization of atoms is balanced by its decrease due to the electron drift from the surface channel layer into the surrounding layers. Numerical estimates are carried out for the conditions of earlier experiments with discharges in He, Ne, Ar, and Xe. The analysis applies to the initial nanosecond stage of the spark development, when the hydrodynamic expansion of the channels is still insignificant.     

Properties of a low-pressure inductive RF discharge I: Experiment

Results are presented from experimental studies of low-pressure inductive RF discharges (including those with a capacitive component) employed in plasma technology. It is shown that both the RF power absorbed in the plasma and the electron density depend nonmonotonically on the external magnetic field. Discharge disruptions occurring at critical values of the magnetic field and the spatial redistribution and hysteresis of the plasma parameters were observed when varying the magnetic field and RF generator power. The parameters of the plasma of low-pressure (0.5–5 mTorr) inductive RF discharges were investigated, and the discharge properties related to the redistribution of the RF generator power between the plasma and the discharge external circuit were revealed. The experiments were performed with both conventional unmagnetized inductive plasma sources and plasma sources with a magnetic field.