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The accurate calculation of DC breakdown voltage thresholds solely from elementary electron-neutral interactions in complex gas mixtures using a multi-term Boltzmann equation (BE) kinetic model is demonstrated. SF6:N2 mixtures in the 100 Td < E/N < 400 Td field regime are explored to benchmark the model’s effectiveness. A ten-term BE model is found to yield DC breakdown voltages which, on average, agree within 3% of experimental measurements. A two-term BE model is also applied in order to characterize the error introduced in all calculations by the two-term approximation. These discrepancies are largest in pure N2 where error is greater than 10% for diffusion coefficients, within 6% for particular vibrational rate coefficients, and within 5% for breakdown voltages. However, this error falls to within 1% for most parameters and breakdown voltages in mixtures with large SF6 content.

Laser Thomson scattering (LTS) was used for the first time to measure the non-Maxwellian electron velocity distribution function (EVDF) in an atmospheric-pressure-air pulsed positive streamer discharge. The air streamer was generated with specially designed electrode configuration which provided good spatial reproducibility. The LTS was conducted at a secondary streamer phase with a repetition rate of 2 Hz. To reduce the measurement error caused by intense rotational Raman scattering from N2 and O2, 20 000 LTS signals were accumulated. The LTS spectrum, which was a 1D-projected EVDF in the streamer, has shown a non-Maxwellian EVDF predicted by solving the Boltzmann equation. The measured EVDF exhibited good agreement with an EVDF calculated with E/N = 150 Td. Electron density at the initial phase of the secondary streamer was obtained from the LTS spectrum as 2.7 × 1014 cm−3.

This study details the development, validation, and utilization of a multi-term Boltzmann equation (BE) model to benchmark argon cross-section sets for their use in low temperature plasma models. First, a complete derivation of the multi-term BE model is given. The multi-term BE model is verified by comparing calculated transport coefficients to known solutions for both conservative and non-conservative model gases. A general comparison between the solutions of the multi-term BE model and the solutions of the two-term BE model, BOLSIG+ , and the Monte Carlo collision model, METHES, is also reported. The multi-term BE model is used to calculate electron swarm parameters from three independently developed argon cross-section sets, which are compared with experimental data. Swarm parameters calculated from the Biagi cross-section set feature the best agreement with experimental data, with the exception of the first Townsend coefficient, which is best reproduced using the cross-section set of Zatsarinny and Bartschat.

The fluxes of chemical active particles in the effluent of plasma jets are very important parameters for different applications. Herein, we present a method of measurement and an algorithm to obtain plasma parameters and particle fluxes from the atmospheric pressure direct current (dc) plasma jet operated in nitrogen/oxygen mixtures. We determine the atom and radical steady state densities and particles fluxes by means of emission spectroscopy and numerical modelling. The plasma parameters, electron density ne and electron velocity distribution function, are obtained by means of emission spectroscopy, microphotography and solutions of the Boltzmann equation. The steady state densities of particles in the effluent region are calculated by solving transport equations (thermal conductivity and diffusion) and chemical kinetics equations. The calculated densities of nitrogen atoms are compared with emission spectroscopy measurements at various positions outside the nozzle of the plasma source. The measurements confirm model results. The fluxes of chemically active particles are determined by means of steady state particle densities and known gas flow rate.

An overview is presented of experimental and theoretical research in the field of physics and engineering of singlet delta oxygen (SDO) production in low-temperature plasma of various electric discharges. Attention is paid mainly to the SDO production with SDO yield adequate for the development of an electric discharge oxygen–iodine laser (DOIL). The review comprises a historical sketch describing the main experimental results on SDO physics in low-temperature plasma obtained since the first detection of SDO in electric discharge in the 1950s and the first attempt to launch a DOIL in the 1970s up to the mid-1980s when several research groups started their activity aimed at DOIL development, stimulated by success in the development of a chemical oxygen–iodine laser (COIL). A detailed analysis of theoretical and experimental research on SDO production in electric discharge from the mid-1980s to the present, when the first DOIL has been launched, is given. Different kinetic models of oxygen low-temperature plasma are compared with the model developed by the authors. The latter comprises electron kinetics based on the accompanying solution of the electron Boltzmann equation, plasma chemistry including reactions of excited molecules and numerous ion–molecular reactions, thermal energy balance and electric circuit equation. The experimental part of the overview is focused on the experimental methods of SDO detection including experiments on the measurements of the Einstein coefficient for SDO transition and experimental procedures of SDO production in self-sustained and non-self-sustained discharges and analysis of different plasma-chemical processes occurring in oxygen low-temperature plasma which brings limitation to the maximum SDO yield and to the lifetime of the SDO in an electric discharge and its afterglow. Quite recently obtained results on gain and output characteristics of DOIL and some projects aimed at the development of high-power DOIL are discussed.

A three-dimensional mesoscopic method is developed for predicting the effective thermal conductivity of multiphase random porous media. The energy transport equations are solved by a lattice Boltzmann method for multiphase conjugate heat transfer through a porous structure whose morphology is characterized by a random generation-growth algorithm. Our numerical results show that the cell number in the third dimension influences the resulting effective thermal conductivity of three-dimensional porous media. The predicted effective thermal conductivity varies with the cell number in the third dimension following an exponential relationship, and it requires in the examples at least 10 cells along the third dimension before the predictions stabilize. Comparisons with the experimental data show that the effective thermal conductivities measured by the hot-probe and hot-wire techniques agree well with the predicted results by the two-dimensional model, whereas those measured by the transient comparative method agree more with the three-dimensional predictions.

The time development of the electron distribution function and electron macroscopic parameters was studied by solving the time-dependent Boltzmann equation for low temperature plasma. A new technique for solving the time-dependent Boltzmann equation was developed. This technique is based on a multi-term approximation of the electron distribution function expansion in Legendre polynomials. The results for electron relaxation in Reid's ramp model and argon plasma are presented. The effect of negative mobility was studied and is discussed for argon plasma. Finally, the time-dependent Boltzmann equation was solved for pulsed microwave discharge in nitrogen. The accuracy of all results was confirmed by the Monte Carlo simulation.

A unified transport model for the bulk of a non-equilibrium low-temperature plasma is presented which consists of a fluid description of the heavy particles (neutrals and ions) in local thermal equilibrium, a reduced kinetic equation for the electrons and the assumption of quasi-neutrality. The transport model of the heavy particles is derived by approximately solving a linearized multi-component Boltzmann equation with the help of an expansion into tensorial Hermitian polynomials, while the electron model is taken from the literature. The description accounts for drift, ordinary diffusion and thermal diffusion, as well as for the effects of heat conduction and viscosity. The relation of the model to previously formulated transport theories is discussed and estimates for its range of validity are given.

We have studied the time-dependent development of electric double-layers (ionic sheaths) in saline solutions by simultaneously solving the sodium and chlorine ion continuity equations coupled with Poisson's equation in one dimension. The study of the effects of time-varying electric fields in solution is relevant to the possible health effect of radio-frequency electric fields on cells in the human body and to assessing the potential of using external electric fields to orient proteins for attachment to surfaces for biosensing applications. Our calculations, for applied voltages of 10–175 mV between the electrode and the solution, predict time scales of ~0.1–110 µs for the formation of double-layers in solutions of concentration between 0.001 and 1.0 M. We develop an empirical equation that can predict the double-layer formation time to within 10% over this wide parameter range. The method has been validated by comparing the solutions obtained, once the program has run to a steady state, with the standard non-linear Poisson–Boltzmann equations. Excellent agreement is found with the Gouy–Chapman solution of the non-linear Poisson–Boltzmann equation. Thus the method is not restricted in accuracy and applicability as is the case for the linear Poisson–Boltzmann equation. The method can also provide solutions for cases where there are orders of magnitude changes in the ion densities; this has not been the case for previous studies where small perturbation analysis has been employed. The method developed here can readily be extended to two and three dimensions using time-splitting methods.

The Boltzmann transport equation is solved to determine the time-dependent electron velocity distribution function in various mixtures of methane and argon subjected to an external electric field, E. In the solution of the equation no expansion of the distribution function is made. The concentration of methane in the mixture is varied systematically. The distribution function is used to calculate several time-dependent electron swarm parameters in these gas mixtures. For each gas mixture a wide range of E/N values, from 0.1 to 1000 Td, is investigated. Steady-state values of various calculated swarm parameters (drift velocity, Townsend ionization coefficient and characteristic energy) agree quite well with the corresponding experimental values.

This paper proposes a coherent set of electron impact inelastic cross sections for argon, based on recent experimental measurements. The updated set is validated by comparing calculated swarm parameters and rate coefficients (obtained by solving the two-term approximation electron Boltzmann equation) with available experimental data. This validation procedure is usually adopted when the cross section set is to be later used in plasma discharge modelling. Simulation results for the electron drift velocity and characteristic energy are in very good agreement with experimental values of these quantities. Calculations, using cross section sets proposed by different authors, of the total (direct + cascade) excitation coefficients to the 4s and 4p states, and of the Townsend ionization coefficient, show that the present set ensures the best overall agreement with measured values. The agreement is particularly good for the excitation coefficient to metastable 4s'[1/2]0 and the Townsend ionization coefficient, which are probably the most relevant electron macroscopic coefficients in the modelling of discharge plasmas.

Electron transport coefficients required for the modelling of bulk electron transport in an O2 magnetron discharge are calculated from solution of the non-conservative Boltzmann equation. The influence on the transport coefficients (rate coefficients, drift velocity vector elements, diffusion tensor elements) of the electric and magnetic field strengths and their orientation with respect to each other have been systematically investigated over ranges consistent with practical operation. The results represent the first multi-term solution of the non-conservative Boltzmann's equation for electric and magnetic fields at arbitrary orientations.

The effect of plasma nonuniformity on the electron energy distribution function (EEDF) and plasma parameters such as the ion density, electron temperature and dust charge in a dusty plasma are studied using a Boltzmann equation for the electrons and the fluid equations for the ions. The EEDF and the plasma parameters are obtained taking into account electron diffusion. The effect of the dusts on the electron energy-relaxation length is shown to be significant. The latter decreases as the dust density and/or size increase. Only at relatively high dust densities/sizes do the results of the homogeneous Boltzmann equation approach that of the more accurate kinetic equation.

A prediction method is proposed for dielectric strengths of hot N2/O2 mixtures as well as hot air in the heavy particle temperature range of 300–3500 K. Electrical breakdown in hot gases by application of an electric field occurs more easily than that in cold gases. Such an electrical breakdown in hot gases can be seen in a circuit breaker after arc interruption. First, equilibrium compositions of hot N2/O2 mixtures were calculated by means of Gibbs free energy minimization. Second, electron energy distribution functions (EEDF) for the hot mixtures to which electric fields were applied were computed using the derived composition by adoption of the two-term expansion approximation of Boltzmann equation. Third, the ionization coefficient α and the electron attachment coefficient η were calculated from the EEDF obtained. The reduced critical electric field strength (E/N)cr, which gives zero effective ionization coefficient , was derived for hot N2/O2 mixtures as a function of heavy particle temperature. The result indicates that (E/N)cr decreases with increasing heavy particle temperature from 1500 to 3500 K, which results mainly from NO formations and O2 dissociations. The predicted result for air was compared with experimental results, and they showed good agreement.

Heat transfer through a semiconductor or dielectric thin film is investigated by using the single relaxation time approximation to the Boltzmann equation. The radiance is expanded in terms of the Laguerre polynomial with time as argument, and the ensuing time-independent equation is solved with the aid of the Galerkin technique. Films of different thicknesses, ranging from 0.01 to 10 mean free paths, have been considered. The results, calculated for different time, ranging from 0.01 to 10 relaxation times, are presented in the forms of the following quantities (in dimensionless units): the temperature (normalized dimensionless internal energy), the heat flux, and the irradiance. Differences between the results obtained by this approach and those found by solving partial differential equations of heat conduction (Fourier's Law and Cattaneo's equation) are noted.

We have calculated data for electron transport in SiH4 and Si2H6 which may serve as the basis for modelling physical and chemical processes in radio frequency (rf) plasmas. A direct numerical procedure was used to solve the Boltzmann equation and to obtain exact transport coefficients. It was shown that the cross section set that was adopted gives good agreement with the available experimental transport coefficients. Furthermore, we have calculated the features of the transport coefficients in rf fields. In both gases we observe good examples of anomalous longitudinal diffusion, time-dependent negative differential conductivity and complex temporal relaxation of momentum and energy. The behaviour of the transport coefficients may be correlated with the temporal development of the components of the velocity distribution function.

A powerful fluid model to study the role of gas dynamics in a glow discharge considered as an excitation medium for XeCl lasers is presented. This model was employed using a numerical code including four strongly coupled parts: electric circuit equations, electron Boltzmann equation, kinetic equations and conservation equations. The theoretical formalism presented here is based on the two-dimensional Euler equations describing the perfect compressible fluid. The numerical calculations have been carried out considering the single shot regime and neglecting the gas flow. The monotonic upstream centred scheme for conservation laws corrections has been used in order to estimate the exchange flow surrounding the control volume walls. We show that the crossing discharge induces a thermal energy density enhancement located principally in the cavity centre.

Grid-enhanced plasma source ion implantation (GEPSII) is a newly proposed technique for inner surface modification of materials with cylindrical geometry. In this paper, a collisional fluid model is used to investigate the ion sheath dynamics between the grid electrode and the inner surface of a cylindrical bore during the GEPSII process. Assuming the initial ion density along the radial direction is not uniform but determined by diffusion mechanisms, the effects of grid electrode radius, target radius and ion-neutral collisions on the ion dose and impact energy are investigated by solving fluid equations for ions coupled with Boltzmann assumption for electrons and Poisson's equation. The results show that small gap distance between grid electrode and target is favourable to increase the ion dose and impact energy on the target. In addition, ion-neutral collisions can reduce both the ion dose and impact energy.

The effective reduced electron ionization coefficients (α−η)/N, with α and η denoting the first Townsend ionization and attachment coefficients, respectively, and the drift velocities are calculated for different mixture compositions of SF6 with He, Xe, CO2 and N2, by solving the electron Boltzmann equation, under the two-term approximation, in a steady-state Townsend discharge. It is shown that a self-contained equation for the isotropic component of the electron velocity distribution can be derived, in which the effects of the non-null divergence of the electron particle flow along the discharge and of the non-conservative collisions for the electron number density, i.e. electron attachment and ionization, are properly taken into account. The critical values of E/N for which the ionization exactly balances the electron attachment are determined. The effects produced by changing the electron energy partition Δ between the primary and the secondary electrons after an ionizing collision are evaluated. The calculated results obtained here are then compared with measured data reported in the literature for pulsed Townsend experiments.

In reference (Robson R E, Li B and White R D 2000 J. Phys. B: At. Mol. Opt. Phys. 33 507), we revisited the Franck–Hertz experiment, and gave solutions of the Boltzmann equation describing the spatially-resolved relaxation profiles of a non-hydrodynamic swarm of electrons streaming at a steady rate from a plane source into mercury vapour. In this paper, we extend this study to other cases and develop a formalism for both ions and electrons and consider situations where both conservative and non-conservative collisions may take place. As in Robson et al (2000), we employ a `two-temperature' Burnett function representation of operators in velocity space in the Boltzmann equation. Configuration space is represented by a finite mesh of points and a finite difference technique is developed accordingly. Boundary conditions are specified for the general problem and techniques for solving the resulting large system of algebraic equations are discussed. The importance of a `multi-term' analysis and the existence of negative differential conductivity (NDC) under non-hydrodynamic conditions is displayed by considering electrons in methane. The explicit effect of ionization on the spatial relaxation profiles is considered along with a study on the importance of treating ionization as a true non-conservative process as opposed to another inelastic process. The spatial relaxation profiles are compared with predictions from eigenvalue theory.

A recently developed method for the solution of the space-dependent electron Boltzmann equation in higher-order accuracy has been adopted to study the behaviour of the electrons in the anode region of a dc glow discharge. This method is based upon a multiterm approximation of the Legendre polynomial expansion of the electron velocity distribution function. Generalizing the boundary conditions, in particular for the partially absorbing anode, the impact of the anode fall and the influence of the electron absorption at the anode on the spatial behaviour of the electron kinetic properties have been investigated in various approximation orders. The analysis has shown that the simplified treatment of the kinetic equation using only the first two terms of the velocity distribution expansion can lead to considerable falsifications of the convergent behaviour. In general, the convergent solution of the significant components of the electron velocity distribution and all important macroscopic quantities is obtained by a multiterm approximation including six to eight terms of that expansion. The discrepancies between the two-term and convergent results are found to depend sensitively on the parameters of the anode fall. In addition, the multiterm results are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between the convergent eight-term Boltzmann and Monte Carlo simulations is found.

The relaxation of a nonequilibrium distribution of electrons in a mixture of SF6 and Ar is studied. In this paper, electron-SF6 and electron-inert gas elastic collisions, vibrationally inelastic collisions between electrons and SF6, as well as the electron attachment reaction with SF6 are included in the analysis. The time-dependent electron energy distribution function is determined from the Boltzmann equation and the energy relaxation times are determined. The coupling of the thermalization process and the attachment process are discussed in detail. The results from the calculations (for 300 K and a total pressure of 1 Torr) are analysed analogous to experimental studies, and the methodology of the experimental reduction of the data is studied.

The population density of a partially ionized Ar plasma has been calculated in a two-temperature reaction kinetic approach under steady-state condition, and at elevated electron temperatures (5000-20 000 K) and pressures (200-1000 Torr) with the ratio of electron temperature (Te) to heavy particle temperature (Th) ranging from 1 to 3. The methodology adapted here for population density calculation considered 11 chemical reactions, taking into account several excited states including the metastable state. Using the calculated population density data, the transport properties, which include viscosity, mass density, electrical and thermal conductivity, specific heat at constant pressure and enthalpy, have been computed hereafter for electron temperatures in the range 5000-20 000 K based on the modified Chapman-Enskog's first-order approximation of Boltzmann's equation. The effects of heavy particle temperature, pressure and the ratio of Te/Th upon the population density as well as transport properties have been elucidated.

Helium thermal plasmas are in widespread use in arc welding and many other industrial applications. Simulation of these processes relies on accurate plasma property data, such as plasma composition, thermodynamic properties and transport coefficients. Departures from LTE (local thermodynamic equilibrium) generally occur in some regions of helium plasmas. In this paper, properties are calculated allowing for different values of the electron temperature, T e, and heavy-species temperature, T h, at atmospheric pressure from 300 K to 30 000 K. The plasma composition is first calculated using the mass action law, and the two-temperature thermodynamic properties are then derived. The viscosity, diffusion coefficients, electrical conductivity and thermal conductivity of the two-temperature helium thermal plasma are obtained using a recently-developed method that retains coupling between electrons and heavy species by including the electron–heavy-species collision term in the heavy-species Boltzmann equation. It is shown that the viscosity and the diffusion coefficients strongly depend on non-equilibrium ratio θ (), through the plasma composition and the collision integrals. The electrical conductivity, which depends on the electron number density and ordinary diffusion coefficients, and the thermal conductivity have similar dependencies. The choice of definition of the Debye length is shown to affect the electrical conductivity significantly for θ > 1. By comparing with literature data, it is shown that the coupling between electrons and heavy species has a significant influence on the electrical conductivity, but not on the viscosity. Plasma properties are tabulated in the supplementary data.

The Boltzmann equation for ions and electrons in gases subject to arbitrarily oriented electric and magnetic fields is solved by a recently developed unified `multiterm' theory (White et al 1999a), and attention is focused on portrayal of the velocity distribution function. In particular, we take `slices' in velocity space to elucidate the effects of changing orientation angle, magnetic field strength and the ion to gas molecule mass ratio. The first results for electrons in CO2 and ion swarms in electric and magnetic fields are presented in this way. The implications of symmetries are discussed.

The space-dependent electron kinetics in the anode region of a cylindrical glow discharge is studied. In particular, the relevant Boltzmann equation of electrons is solved in two space dimensions to reveal the formation of the electron kinetic properties in the radial and axial directions. The solution method is based on a two-term expansion of the velocity distribution and the introduction of a total energy coordinate. The space-dependent description allows the investigation of the influence of electron absorption at the anode as well as the impact of anode fall on the spatial structure of the electron kinetic properties. The impact of radial space-charge confinement and its modification is studied in the transition region from the radially inhomogeneous positive column to the equipotential anode surface. A rigorous kinetic description allows among others the determination of axial and radial particle and energy fluxes of electrons in the anode region. Results are presented for a neon discharge at a pressure of about half a Torr.

The role played by the N2(A3Σu+) metastable on the overall kinetics of N2 and N2-O2 stationary discharges is illustrated by using a kinetic model based on the self-consistent solutions to the Boltzmann equation coupled to the rate balance equations for the vibrationally and electronically excited molecules, atoms and charged particles, in which the sustaining electric field is self-consistently determined. It is shown that together with the vibrational distribution of N2(X1Σg+,v) molecules, the metastable state N2(A3Σu+) plays a central role in the whole problem, since some important aspects of these discharges, such as ionization, gas phase chemistry and gas heating are associated with different processes involving the N2(A3Σu+) state.

The role of atomic and molecular electronically excited states on the whole kinetics of an high-enthalpy nozzle flow has been examined by using a self-consistent model which couples Euler equations with appropriate master equations and with the Boltzmann equation for the electron energy distribution function (eedf). The results show that in high-enthalpy flows metastable atomic nitrogen can form structures in the eedf through superelastic collisions, partially smoothed by electron-electron Coulomb collisions.

Numerical solution of the Boltzmann equation with a relaxation collision term is used to study gas-dynamic flows formed under nanosecond pulsed laser ablation. Atoms ejected from the surface of a target are assumed to have a Maxwell velocity distribution corresponding to the surface temperature and the saturated vapour pressure. The surface temperature is obtained from a transient heat transfer equation in the condensed phase. Atomic collisions in the ablation plume orient atoms towards the surface normal and speed up the plume expansion from the target. Atoms backscattered in the gas phase, stick to the target surface and cause back condensation of the vapour at later stages. When the mean free path is much less than the plume dimension, a Knudsen layer, a hydrodynamic flow region, and a low-density tail may be distinguished in the gas phase. The present numerical simulation is in good agreement with the analytical quasi-steady Mott-Smith approach to the Knudsen layer in the case of evaporation and at the early stages of condensation. Comparison with experiment reveals that the model underestimates both the width of the ablated material angular distribution and the amount of high-energy atoms. The difference increases with the laser fluence and may be caused by lateral expansion of the plume, by vapour acceleration due to laser radiation absorption or probably by non-thermal evaporation effects.

We consider the evaporation of material from a heated substrate into a vacuum, and the problem of determining the density, flow velocity and temperature of the vapour that streams off the surface. Treatments using the Boltzmann equation suggest that the vapour flows at the speed of sound, and with a temperature and density that depend on the substrate temperature. A simpler approach is to parametrize the velocity distribution function of vapour at the surface and then to use the conservation of mass, momentum and energy fluxes to characterize the flow. However, the mean velocity of the vapour is undetermined in this approach. We find, however, that by calculating the flux of Boltzmann's H function, we can exclude high mean velocities, since they correspond to the unphysical destruction of entropy in the evaporation process. Furthermore, it appears that the generation of vapour travelling at approximately the speed of sound corresponds to the maximum rate of entropy production. This lends support to this principle as a useful method for characterizing systems far from equilibrium.

In modelling the plasma kinetics in dielectric barrier discharges (DBDs), the electron energy conservation equation is often included in the rate equation analysis (rather than utilizing the local-field approximation) with the assumption that the electron energy distribution function (EEDF) has a Maxwellian profile. We show that adopting a Maxwellian EEDF leads to a serious overestimate of the calculated ionization/excitation rate coefficients and the electron mobility for typical plasma conditions in a xenon DBD. Alternative EEDF profiles are trialed (Druyvesteyn, bi-Maxwellian and bi-Druyvesteyn) and benchmarked against EEDFs obtained from solving the steady-state Boltzmann equation. A bi-Druyvesteyn EEDF is shown to be more inherently accurate for modelling simulations of xenon DBDs.

Electron transport coefficients and the excitation, attachment and ionization rates in pure CF4 and in CF4-Ar mixtures have been calculated for a set of cross-sections which was based on the work of Nakamura (1991 Gaseous Electronics and Their Applications ed R W Crompton et al (Tokyo: KTK Scientific) pp 178-200) but which was modified to include more complex dissociation and ionization kinetics required to develop an adequate plasma chemical model. The procedure for the calculation was the direct numerical procedure (DNP) solution to the Boltzmann equation which makes no approximations in the number of terms used to represent the anisotropy of the distribution function in the velocity space. However, its accuracy may be limited by the density of the grid used. In this paper, we apply the DNP technique to establish its adequacy for plasma modelling in pure CF4 and in 5% CF4-Ar mixture, as well as establishing the adequacy of the cross-section set that was used.

The electron energy distribution function (EEDF) in an afterglow of a pulsed direct current discharge has been measured in an Ar:N2 mixture by means of a time-resolved Langmuir probe technique. The vibrational temperature, Tv ,o f N 2 molecules has also been experimentally estimated. The results show that a correlation between an effective electron temperature, Te, and Tv strongly varies with experimental conditions. In particular the conditions exist under which the rapid decrease from high to low Te values is observed at some moment after the discharge pulse, while the vibrational temperature remains almost constant. The theoretical study of the EEDF in Ar:N2 afterglow plasma has also been made by the numerical solution of an appropriate Boltzmann equation by taking into account electron-electron collisions as well as superelastic vibrational and superelastic electronic collisions. Calculations show that for a given Tv the value of Te depends on the electron concentration, ne. Moreover, the ranges of ne and Tv exist, where two different solutions of Boltzmann equations can be obtained. Finally, the comparison of the theoretical and experimental results is performed and an explanation of the experimentally observed phenomenon is given.

A computational model of a low-pressure discharge having a negative-ion component is developed. Many existing models for this type of discharge consider collisionless positive ions and two negative species each obeying Boltzmann relations. Our aim is to relax the Boltzmann-negative-ion assumption and we use a more realistic model with kinetic positive ions, kinetic negative ions and Boltzmann electrons. Positive and negative ions are created uniformly in the discharge at a constant rate, and lost either to the walls or via volume recombination. This model is solved using a hybrid simulation with particle-in-cell (PIC) ions. The negative-ion distribution function is found to have cold and hot components of nearly equal densities for which Te/T-cold≈100 (the creation temperature) and Te/T-hot≈5-20. The computed positive ion flux exiting the discharge agrees approximately with those calculated from Boltzmann-negative-ion models when the negative-ion temperature is accounted for correctly. It has been predicted that three electronegative discharge structures can exist: uniform, stratified and double-layer stratified. All three structures are observed in our model. In particular, a double-layer stratified discharge is observed when the effective negative-ion temperature is sufficiently low, in qualitative agreement with Boltzmann-negative-ion models.

The simulation studies of free jets are required in order to understand the physical processes occurring during expansion of an atomic beam from a high-intensity source. The atomic beam undergoes transition from the continuum regime to the non-equilibrium transition regime of flow. Various models based on continuum equations of change and the simplified Boltzmann equation are inadequate to handle the flow in the transition regime, particularly for the effect of various geometrical boundary conditions. The numerical simulation of the free jet is more suitable for these studies. In this paper we have described the development of a direct simulation Monte Carlo (DSMC) code, which was implemented on parallel processors. The model calculations have been verified with published results for simpler conditions of free jet and have also been validated with experimental results. Studies of some of the parametric studies with various source as well as substrate geometries are discussed in this paper.

The electron energy distribution function and the electron drift velocity are studied numerically in a decaying plasma in the external electric field in the mixture Ar:F2 = 1:0.005 at atmospheric pressure. For a reduced electric field strength over the range 0.055-0.55 Td the negative electron mobility was predicted earlier by the solution of the Boltzmann equation using the two-term approximation for the velocity distribution function. The applicability of this approximation for calculations of negative mobility is discussed. The Monte Carlo simulation method is used to verify results obtained from Boltzmann equation analysis. It is shown that there is a reasonable agreement between the Boltzmann equation and Monte Carlo results.

The electron swarm parameters of Xe/He and Xe/Ne mixtures are analysed with a Boltzmann equation method in which secondary generations of electrons through excited atoms are properly considered. The swarm parameters are examined for a wide range of the electron concentrations from the Townsend discharge region to the working condition of plasma display panels (PDPs). Using ionization coefficients obtained in this work and referred values of secondary electron emission coefficients from MgO film, the discharge onset voltage V b is discussed. The Paschen curves around (p 0 d )min at which V b has a minimum are compared for Xe/He and Xe/Ne mixtures. Under the working conditions for PDP discharges, the radiation rates of ultraviolet light ( = 130, 147 and 173 nm) from the Xe resonance levels and Xe excimer are calculated. A suitable discharge condition for designing PDP is discussed with respect to various values of the gas mixture ratio, gas pressure and reduced electric field.

The effect of small amounts of electronegative NF3 molecules on the electron swarm characteristics in Ar:NF3 mixtures is studied numerically under steady-state Townsend conditions. Two different methods of calculation are used: the solution of the two-term Boltzmann equation (BE) and the Monte Carlo (MC) simulation. The BE analysis is performed for an established electron energy distribution function. The MC calculations give the distance at which the shape of the distribution function approaches that resulting from the BE analysis. It is shown that the losses of electrons in the attachment processes play a significant role in the formation of the electron energy distribution function. In a wide range of the reduced electric field strength E/N and NF3 concentrations the distribution function with a maximum at finite energy is established. It is also shown that the diffusion-modified drift velocity Vd is a non-monotonous function of E/N and that the so-called field-determined part of the Vd is negative in a wide range of E/N values. These effects are explained in terms of the specific energy dependence of the cross section for electron attachment to the NF3 molecules and the momentum transfer cross section of Ar.

The cylindrical magnetron consists of a coaxial inner cathode and an outer anode. The magnetic field is applied in the axial direction and is almost homogeneous in the whole magnetron volume. The electric field has radial direction and therefore the charged particles in the cylindrical magnetron discharge move under the influence of the × field. Due to its comparatively simple geometry, the cylindrical magnetron represents a suitable experimental tool that can be used to confirm theoretical results of modelling and theoretical studies of magnetrons in general. We studied experimentally the radial behaviour of the electron velocity distribution function (EVDF) in a cylindrical magnetron discharge in argon. We checked experimentally the anisotropy of the EVDF due to the influence of the magnetic field. For the assessment of the anisotropy of the EVDF we used a planar probe, whose collecting surface was adjustable at different angles to the direction of the magnetic field in the plane perpendicular to the electric field, as well as being movable in the radial direction. We found that in the measurable range of electron energies (energies greater than approximately 2 eV) and at magnetic fields up to 40 mT the anisotropy of the EVDF is not detectable within the experimental error limits. Therefore, for the study of the radial behaviour of the EVDF we used the thin (42 µm in diameter) tungsten cylindrical probe that was movable in the radial direction by a precise screw. For the theoretical determination of the EVDF in the cylindrical magnetron discharge we solved numerically the Boltzmann equation in a crossed × field, assuming the usual simplifications. The results of the calculation and the experiment in argon are compared and discussed.

Transport coefficients and velocity distribution functions for electron swarms in methane in the presence of uniform static electric and magnetic fields crossed at arbitrary angles to each other are calculated using a multi-term solution of the Boltzmann equation. Particular attention is paid to the effects of the relative orientation of the fields and how this affects the convergence in the spherical harmonic expansion that represents the velocity distribution function. The inadequacies and incorrect assumptions of previous treatments of this problem are also highlighted.

A zero-dimensional steady-state model of low-pressure (2-60 Torr) microwave-generated hydrogen plasmas was developed. The electron energy distribution function (EEDF) was determined using the Boltzmann equation, coupled to species, energy and power balances. The EEDF from the Boltzmann equation permitted computation of the rate constants and average electron temperature required for simultaneous solution to the six species balances, two for neutrals (H, ) and four for charged (, , and electron) species, and the energy balance. The average electron temperature and species concentrations were then employed in a power balance to check for self-consistency with the input power used to solve the Boltzmann equation. values were appropriately adjusted after each iteration until self-consistency was achieved. The model provides information on the details of the transfer of power from electrons via various processes (ionization, dissociation, vibration, rotation) to the neutral species. The mechanism of energy loss from the neutrals (radiation, convection) is also computed, and thus gas temperature can be estimated. Indeed, for low-pressure plasmas the model yields accurate absolute gas temperatures as a function of pressure, including the fact that gas temperature rises steeply at pressures in excess of 15 Torr. This results from the fact that at low pressures a very large fraction of the input power is transmitted by the electrons to the molecular vibration modes, such that .

A simulation technique for the analysis of the transverse evolution of electron swarms in gases was developed based on moment equations derived from the Boltzmann equation. A numerical calculation of the moment equations for an electron swarm was performed using a propagator method and it was demonstrated that the propagator method can be used to calculate the higher-order transverse diffusion coefficients stably. Applying a Hermite expansion technique, the electron distribution in real space and other electron swarm parameters were derived as functions of the transverse position. The calculation result was verified by comparisons with those by a Monte Carlo simulation and other methods. Features of the transverse electron swarm evolution were presented.

Studies of laser-induced breakdown in molecular nitrogen were carried out to investigate the dependence of the threshold irradiance on the wavelength at various pressures. The analysis was based on the numerical solution of the time-dependent Boltzmann equation for the electron energy distribution function (EEDF) and a set of rate equations describing the rate of change of the excited states population. The rate coefficients and cross-sections as functions of the electron energy were introduced into this analysis in order to probe the exact contribution of each physical process to the breakdown phenomenon. The calculations were performed under the experimental conditions of Davis et al. In this experiment the breakdown of nitrogen was measured at wavelengths of 1064, 532, 355 and 266 nm, over gas pressures in the range 25-760 Torr, with laser irradiances in the range to . The computed thresholds were found to be in good agreement with the measured ones at all wavelengths. The calculated EEDF and its parameters showed that, at nm, vibrational losses are dominant. Collisional ionization of ground and excited state molecules was found to make a minor contribution to the breakdown phenomenon at 532, 355 and 266 nm. However, the contribution to this process at 1064 nm was more effective. Therefore, the breakdown phenomenon proceeds via an electron-cascade process that converts the molecules only into the excited states, whence multiphoton ionization plays its role.

Two hydrodynamic models for a non-parabolic band structure are proposed in order to obtain closed sets of the first four moment equations derived from the Boltzmann transport equation. Instead of using the Fourier-law heat flux to determine the energy flux and to close the first three moment equations as applied to the conventional hydrodynamic model, the energy flux is solved directly from the third-order moment equation. The physical quantities introduced in the third-order moment equation are expressed in terms of the lower-order moments and the average parameters associated with the random velocity. To close the third-order moment equation, the average parameters related to the random velocity are assumed to be energy dependent. Transport results for a submicrometre silicon -n- diode obtained from the proposed four-moment hydrodynamic models, compared with those from Monte Carlo simulations and from three-moment hydrodynamic models, are studied in detail.

The arrival-time spectra (ATS) of electrons in mixtures of nitrogen and carbon dioxide have been measured for reduced electric fields from 100 to 1000 Td at room temperature by using a double-shutter drift tube. The drift velocity of the electrons in and mixtures was evaluated from a previously reported ATS method. In mixtures of and , we found that is larger than the value predicted by a linear combination of the drift velocities of the pure gases based on the mole fraction (partial pressure) of in the mixture, k, in the range of low . We refer to this as the `mixing effect'. In contrast, a linear combination of the drift velocities of the pure gases based on k was found to accurately predict the drift velocities in mixtures in the higher region . In addition to the experimental evaluation, calculations of in these gas mixtures were carried out by a Boltzmann equation analysis, and the results were compared with those from the ATS measurements. The ratio of the longitudinal diffusion coefficient to the electron mobility was also estimated. The value of , called the characteristic energy, also shows a small mixing effect with increasing k in the range of low and increases monotonically in the range of , while the value decreases linearly as k increases in the higher range.