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.     

Electron temperature in nitrogen afterglow: Dependence of theoretical results on the adopted set of cross sections and on the type of molecular distribution over vibrational levels

The electron energy distribution function in nitrogen afterglow is simulated using different available sets of cross sections for electron scattering by vibrationally excited molecules. The calculations are performed for two types of molecular distribution over vibrational levels, namely, for the Boltzmann and Treanor-Gordiets distributions. It is shown that the calculated values of the electron temperature in nitrogen afterglow depend strongly on the set of cross sections used and on the type of molecular distribution over vibrational levels. The validity of comparison between theoretical and experimental results is discussed.     

Double layer in a cylindrical hollow-cathode discharge

A dc cylindrical coaxial glow discharge with an inner grid anode has been studied. The region between the two electrodes is seen dark, while a brightly glowing region forms inside the grid anode up to the center. The current-voltage characteristic of a dc cylindrical glow discharge in nitrogen is similar to that of a normal glow discharge, while the normal glow discharge voltage decreases with increasing pressure. The minimum plasma potentials are observed in the hollow cathode region due to the accumulation of electrons at the back of the grid anode. At the center, some of the passed electrons are converged, so their potential is decreased. These electrons have a sufficient time to be redistributed to form one group with a Maxwellian electron energy distribution function. The electron temperature measured by electric probes varies from 1.6 to 3.6 eV, while the plasma density varies from 3.9 × 10¹⁶ to 7 × 10¹³ m⁻³, depending on the discharge current and probe position. The plasma density increases as the electrons move radially from the grid toward the central region, while their temperature decreases.     

Theoretical investigation of the bistability effect in non-self-sustained discharges in Kr and Ar

The electron energy distribution function and the related plasma parameters in non-self-sustained discharges in Kr and Ar are studied theoretically. The investigations are carried out by numerically solving the corresponding Boltzmann equation for the electron energy distribution function with allowance for electron-electron collisions. The electron energy distribution and electron density are calculated self-consistently as functions of the intensity q of the source of secondary electrons and the magnitude of the reduced electric field E/N. The main goal of the investigations was to determine the conditions under which the plasma exhibits bistable parameters. Calculations show that, for discharges in Kr, there is a certain range of q and E/N values in which the Boltzmann equation has two different stable solutions. For an Ar plasma, such a bistability effect was not found: over the parameter range under consideration, the Boltzmann equation has a unique solution. Various plasma parameters (such as the effective electron temperature, electron drift velocity, and electron current density) are calculated for different discharge conditions, including those corresponding to the bistability effect.     

Vibrational distribution of nitrogen molecules in the C3Πu state in a near-surface microwave plasma in nitrogen at pressures of 1–5 Torr

The radiation of the second positive nitrogen system has been used to study the spatial dependence of the vibrational distribution of nitrogen molecules in the C³Π_u state in the near-surface plasma layer of an electrode microwave discharge in nitrogen at pressures of 1–5 Torr. It has been shown that the vibrational distribution changes at a scale of 100 μm. It has been concluded that this state is populated owing to the electron impact from the ground state. The possibility of using the local approximation for the electron energy distribution function to explain the experimental results has been analyzed.     

One-dimensional semiempirical model of plasma in an accelerator with closed electron drifts

The plasma structure in an accelerator with closed electron drifts is investigated experimentally and numerically based on the measured data on the angular and energy ion distribution in a plasma jet. The mathematical model is constructed in a one-dimensional steady-state approximation and is aimed at calculating spatial distributions of the electric potential and plasma density in the region of the most intense ionization of neutral atoms. A comparison of the numerically calculated model potential distributions with the results from direct probe measurements shows that the proposed approach provides an online analysis of the plasma structure in the ionization-acceleration zone.     

Dissipation of Energy of an AC Electric Field in a Semi-Infinite Electron Plasma with Mirror Boundary Conditions

Absorption of the electromagnetic energy in a semi-infinite electron plasma is calculated for an arbitrary degree of the electron gas degeneracy. Absorption is determined by solving the boundary-value problem on the oscillations of electron plasma in a half-space with mirror boundary conditions for electrons. The Vlasov?Boltzmann kinetic equation with the Bhatnagar–Gross–Krook collision integral for the electron distribution function and Maxwell’s equation for the electric field are employed. The electron distribution function and the electric field inside plasma are searched for in the form of expansions in the eigenfunctions of the initial set of equations. The expansion coefficients are found for the case of mirror boundary conditions. The contribution of the plasma surface to absorption is analyzed. Cases with different degrees of electron gas degeneracy are considered. It is shown that absorption of the electromagnetic energy near the surface depends substantially on the ratio between the electric field frequency and the volumetric electron collision frequency.     

Free energy distributions in proteins.

Protein molecules in solution have a broad distribution of enthalpy states. A good approximation to the distribution function for enthalpy states can be calculated, using the maximum-entropy method, from the moments of the distribution that, in turn, are obtained from the experimental temperature dependence of the heat capacity. In the present paper, we show that the enthalpy probability distribution can then be formulated in terms of a free energy function that gives the free energy of the protein corresponding to a particular value of the enthalpy. By the location of the minima in this function, the free energy distribution graphically indicates the most probable values of the enthalpy for the protein. We find that the behavior of the free energy functions for proteins falls somewhere between two different cases: a two-state like function with two minima, the relative levels of the two states changing with temperature; and, a single-minimum function where the position of the minimum shifts to higher enthalpy values as the temperature is increased. We show that the temperature dependence of the free energy function can be expressed in terms of a central free energy distribution for a given, fixed temperature (which is most conveniently chosen as the temperature of the maximum in the heat capacity). The nature of this central free energy function for a given protein thus yields all of the thermodynamic behavior of that protein over the temperature range of the denaturation process.     

Diagnostics of a nonequilibrium nitrogen plasma from the emission spectra of the second positive system of N2

A method is proposed for determining the electron density N _e and the electric field E in the non-equilibrium nitrogen plasma of a low-pressure discharge from the spectra of the second positive system of N₂. The method is based on measuring the specific energy deposition in the plasma and the distribution of nitrogen molecules over the vibrational levels of the C ³Π _u state, as well as on modeling this distribution for a given energy deposition. The fitting parameters of the model are the values of N _e and E. A kinetic model of the processes governing the steady-state density of the C ³Π _u nitrogen molecules is developed. The testing of this method showed it to be quite reliable. The method is of particular interest for diagnosing electrodeless discharges and provides detailed information on the processes occurring in the discharge plasma. Preliminary data are obtained on the plasma parameters in a cavity microwave discharge and an electrode microwave discharge. In particular, it is found that the electric field in an electrode microwave discharge in nitrogen is lower than that in a hydrogen discharge. This effect is shown to be produced by stepwise and associative processes with the participation of excited particles in nitrogen.     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.     

Possibility of revealing the role of nonresonant energy exchange between electrons and CO molecules at high vibrational levels

An experimental method providing information about the interaction of electrons with excited CO molecules at high vibrational levels is proposed and justified theoretically. The suggested experimental scheme is based on the use of two successive discharge pulses under the conditions prevailing in an electroionization CO laser. The first pulse should ensure a sufficiently high energy input in order for a nonequilibrium vibrational distribution function to form. The second pulse serves to study the effect of the electric current on the vibrational distribution function of excited molecules at high vibrational levels. The theoretical analysis is based on the simultaneous solution of the Boltzmann equation for the electron energy distribution function and the vibrational kinetic equations realistically describing the multiquantum vibrational-vibrational exchange processes. The calculated results show that the sensitivity of the proposed measurement technique promises to be high.     

Charging of dust grains in a nonequilibrium plasma of a stratified glow discharge

A theoretical model is presented that describes the charging of dust grains in the positive plasma column of a stratified glow dc discharge in argon. A one-dimensional self-consistent model is used to obtain axial profiles of the electric field, as well as the electron energy distribution function along the axis of the discharge tube. Radial profiles of the electric field are determined in the ambipolar diffusion approximation. It is assumed that, in the radial direction, the electron distribution function depends only on the total electron energy. Two-dimensional distributions of the discharge plasma parameters are calculated and used to determine the potential and charge of a test dust grain at a certain point within the discharge and the electrostatic forces acting on it. It is shown that the grain charge distribution depends strongly on the nonequilibrium electron distribution function and on the nonuniform distribution of the electric field in a stratified glow discharge. A discussion is presented on the suspension of dust grains, the separation of grains by size in the discharge striations, and a possible mechanism for the onset of vortex dust motion at the edge of a dust cloud.     

Measurements and calculations of the electron distribution function in the electronegative plasma of a hollow-cathode discharge in N<Subscript>2</Subscript>: SF<Subscript>6</Subscript> mixtures

Results are presented from measurements and numerical calculations of the electron energy distribution function in the plasma of a hollow-cathode glow discharge in N₂: SF₆ mixtures. It is shown that, when a small amount of SF₆ is added to nitrogen, the number of electrons in the inverse region of the distribution function (2–6 eV) increases by about one order of magnitude. As the electric field in plasma increases to ≈0.5 V/cm, the dip in the distribution function disappears and the inversion region vanishes.     

Kinetic theory of the positive column of a low-pressure discharge in a transverse magnetic field

The influence of a transverse magnetic field on the characteristics of the positive column of a planar low-pressure discharge is studied theoretically. The motion of magnetized electrons is described in the framework of a continuous-medium model, while the ion motion in the ambipolar electric field is described by means of a kinetic equation. Using mathematical transformations, the problem is reduced to a secondorder ordinary differential equation, from which the spatial distribution of the potential is found in an analytic form. The spatial distributions of the plasma density, mean plasma velocity, and electric potential are calculated, the ion velocity distribution function at the plasma boundary is found, and the electron energy as a function of the magnetic field is determined. It is shown that, as the magnetic field rises, the electron energy increases, the distributions of the plasma density and mean plasma velocity become asymmetric, the maximum of the plasma density is displaced in the direction of the Ampère force, and the ion flux in this direction becomes substantially larger than the counter-directed ion flux.     

Optical characteristics and parameters of gas-discharge plasma in a mixture of mercury dibromide vapor with neon

Results are presented from studies of the optical characteristics and parameters of plasma of a dielectric barrier discharge in a mixture of mercury dibromide vapor with neon—the working medium of a non-coaxial exciplex gas-discharge emitter. The electron energy distribution function, the transport characteristics, the specific power losses for electron processes, the electron density and temperature, and the rate constants for the processes of elastic and inelastic electron scattering by the working mixture components are determined as functions of the reduced electric field. The rate constant of the process leading to the formation of exciplex mercury monobromide molecules is found to be 1.6 × 10^?14 m³/s for a reduced electric field of E/N = 15 Td, at which the maximum emission intensity in the blue-green spectral region (λ_max = 502 nm) was observed in this experiment.     

Dynamics of beam instability in a finite plasma volume: Numerical experiment

Results are presented from numerical simulations of the dynamics of beam instability in a finite plasma volume (plasma-filled cavity) in a weak magnetic field. It is shown that, in such a system, the low group velocity of the plasma waves excited by an electron beam can result in the generation and amplification of an electric field; strong electron heating in the axial region; and, as a consequence, the generation of a high potential at the axis. The quasistatic radial electric field so produced accelerates ions toward the periphery of the plasma column, forming a directed ion beam with an energy much higher than the thermal energy of the bulk plasma electrons.     

Simulation of the ignition of a methane-air mixture by a high-voltage nanosecond discharge

The ignition dynamics of a CH₄: O₂: N₂: Ar = 1: 4: 15: 80 mixture by a high-voltage nanosecond discharge is simulated numerically with allowance for experimental data on the dynamics of the discharge current and discharge electric field. The calculated induction time agrees well with experimental data. It is shown that active particles produced in the discharge at a relatively low deposited energy can reduce the induction time by two orders of magnitude. Comparison of simulation results for mixtures with and without nitrogen shows that addition of nitrogen to the mixture leads to a decrease in the average electron energy in the discharge and gives rise to new mechanisms for accumulation of oxygen atoms due to the excitation of nitrogen electronic states and their subsequent quenching in collisions with oxygen molecules. Acceleration of the discharge-initiated ignition is caused by a faster initiation of chain reactions due to the production of active particles, first of all oxygen atoms, in the discharge.     

Transverse glow discharges in supersonic air and methane flows

Transverse glow discharges in supersonic air and methane flows are studied both experimentally and theoretically. The experiments show that a diffuse volume discharge filling the whole cross section of the flow can easily be initiated in air, whereas a diffuse discharge in a methane flow shows a tendency to transition into a constricted mode. The electron transport coefficients (mobility and drift velocity) and the kinetic coefficients (such as collisional excitation rates of the vibrational levels of a methane molecule, as well as dissociation and ionization rates) are calculated by numerically solving the Boltzmann equation for the electron energy distribution function. The calculated coefficients are used to estimate the parameters of the plasma and the electric field in the positive column of a discharge in methane.     

Plasma decay in the afterglow of a high-voltage nanosecond discharge in air

The decay of air plasma produced by a high-voltage nanosecond discharge at room temperature and gas pressures in the range of 1–10 Torr was studied experimentally and theoretically. The time dependence of the electron density was measured with a microwave interferometer. The initial electron density was about 10¹² cm⁻³. The discharge homogeneity was monitored using optical methods. The dynamics of the charged particle densities in the discharge afterglow was simulated by numerically solving the balance equations for electron and ions and the equation for the electron temperature. It was shown that, under these experimental conditions, plasma electrons are mainly lost due to dissociative and three-body recombination with ions. Agreement between the measured and calculated electron densities was achieved only when the rate constant of the three-body electron-ion recombination was increased by one order of magnitude and the temperature dependence of this rate constant was modified. This indicates that the mechanism for three-body recombination of molecular ions differs from that of the well-studied mechanism of atomic ion recombination.     

Thermal nonlinearity of potential surface waves at a plasma-metal interface

A study is made of the effect of the heating of plasma electrons in the field of a potential surface wave on the wave dispersion properties. The wave is assumed to propagate along the boundary between a metal and a finite-pressure plasma. Different mechanisms for electron energy losses are considered in the weak heating approximation. The spatial distribution of the plasma electron temperature under nonlocal heating conditions is derived on the basis of the electron energy balance equation. Expressions for the spatial damping rate and the nonlinear shift of the wavenumber are analyzed for different values of the plasma parameters. The results obtained are valid for both semiconductor and gaseous plasmas.