[ Laboratory | <= S.B.Vrhovac ]
My research interests include:
Abstract: In this paper we develop general equations for the momentum transfer theory (MTT) for swarms of particles in mixtures of gases including the effect of nonconservative (reactive) collisions. MTT equations for mean energy, drift velocity, diffusion tensor components, and rate coefficients are derived for different degrees approximation including the hydrodynamic limit and small swarm to gas particle mass ratio. Specific formulas were developed for the criteria for negative differential conductivity (NDC) in mixtures of gases with elastic collisions only and for a single gas with reactions. The criteria and the numerical calculations are in excellent agreement, showing that NDC can be induced by light atomic constituents in purely elastic collision and also by ionization and attachment.
Abstract: In this paper we give a summary of the theory in purely electric field and some phenomena that were studied. Usefulness of MTT in developing analytical formulae is illustrated by the analysis of some of the processes supporting the development of NDC and in calculation of the higher order transport coefficients. We proceed to describe the steady state E X B theory and finally we summarize the MTT procedure and possible applications in gas discharge modeling including the development of the time dependent and spatially dependent theory and development of a non-local beam-equation theory.
Abstract: Momentum-transfer theory has been used to obtain a relationship between the n-th order tensorial transport coefficients in a swarm experiment, the (n-1)-th derivative of the mobility, and the n-th derivative of the reaction rate coefficient. Elastic, inelastic and reactive collisions for gas mixtures have been taken into consideration. Numerical comparisons show that the results obtained from this relationship are in good agreement with those obtained by solution of the Boltzmann equation. Finally, we have analyzed the structure of the third order tensorial transport coefficient by applying both momentum-transfer theory and group theory; both approaches show that in general there are three independent components of this rank-three tensor.
Abstract: This paper examines formal structure of the Boltzmann Equation (BE) theory of charged particle transport in neutral gases. The initial value problem of BE is studied by using perturbation theory generalized to non-Hermitian operators. The method developed by Resibois was generalized in order to be applied for the derivation of the transport coefficients of swarms of charged particles in gases. We reveal which intrinsic properties of the operators occurring in kinetic equation are sufficient for the Generalized Diffusion Equation (GDE) and density gradient expansion to be valid. Explicit expressions for transport coefficients from the (asymmetric) eigenvalue problem are also deduced. We demonstrate the equivalence between these microscopic expressions and the hierarchy of kinetic equations. The establishment of the hydrodynamic regime is further analyzed by using the time-dependent perturbation theory. We prove that for times t >> tau_0 (tau_0 is relaxation time), the one-particle distribution function of swarm particles can be transformed into hydrodynamics form. Introducing time-dependent transport coefficients omega^p (q,t), which can be related to various Fourier components of initial distribution function, we also show that for the long-time limit all omega^p (q,t) become time and q independent in the same characteristic time and achieve their hydrodynamics values.
Abstract: Transport properties of ion swarms in presence of Resonant Charge Transfer (RCT) collisions are studied using Momentum Transfer Theory (MTT). It was shown that, not surprisingly, RCT collisions may be represented as a special case of elastic scattering. Using the developed MTT we tested a previously available anisotropic set of cross sections for Ar+Ar^+ collisions by making the comparisons with the available data for the transverse diffusion coefficient. We also developed an anisotropic set of Ne+Ne^+ integral cross sections based on the available data for mobility, longitudinal and transverse diffusion. Anisotropic sets of cross sections are needed for Monte Carlo simulations of ion transport and plasma models.
Abstract: Application of Blanc's Law for drift velocities of electrons and ions in gas mixtures at arbitrary reduced electric field strengths E/n_0 was studied theoretically and by numerical examples. Corrections for Blanc's Law that include effects of inelastic collisions were derived. In addition we have derived the common mean energy procedure that was proposed by Chiflikyan in a general case both for ions and electrons. Both corrected common E/n_0 and common mean energy procedures provide excellent results even for electrons at moderate E/n_0 where application of Blanc's Law was regarded as impossible. In mixtures of two gases that have negative differential conductivity (NDC) even when neither of the two pure gases show NDC the Blanc's Law procedure was able to give excellent predictions.
Abstract: Transport properties of a swarm of charged test particles in rarefied neutral gas subjected to time-dependent and nonuniform external field is studied within the framework of the linear Boltzmann Equation (BE). We develop a new theoretical approach for the description of the pre-hydrodynamic stage of evolution of charged particle swarms. Initial value problem of BE is studied by using time-dependent perturbation theory generalized to non-Hermitian operators. The main result of this paper is a Generalized Diffusion Equation (GDE) valid for all times, with infinite set of transport coefficients which are expressed in terms of the solutions of a hierarchy of coupled linear integrodifferential equations. It is established that the time derivatives of spatial moments of the number density are expressed as spatial moments of generalized transport coefficients.
Abstract: We construct asymptotic (long-time) solution of the linear Boltzmann equation using the time-dependent perturbation theory generalized to non-Hermitian operators. We prove that for times much larger than the relaxation time $\tau_0$, $t \gg \tau_0$, one-particle distribution function separates into spatio-temporal and velocity dependent parts. Our analysis does not assume that relative density gradients $n^{-1}(\partial / \partial \vec{r}) n$ are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation.
Abstract: The spectral and spatial profile of H_beta from the low pressure RF and DC glow discharges in hydrogen is studied in order to reveal the excitation mechanism of the fast excited H fragments. Measurements were performed both for the normal and abnormal dc glow discharges. Spatial distributions of the Balmer_beta radiation reflect the local plasma conditions in the discharge, especially the excitation efficiency which is used to determine the excitation kinetics in hydrogen discharges. Spectral H_beta profiles were measured and used to determine the kinetic energy of excited H atoms and to check which of the mechanisms describes best the results observed in our experiment. We have also calculated the number densities of vibrationally excited levels by solving a set of vibrational master equations for the conditions similar to those of our experiments, as excitation from the vibrationally excited ground-state hydrogen molecules may be used to explain the changes in the intermediate wing component of the line profile with the changing current.
Abstract: The analysis of the Doppler profile of the Balmer_beta (H_beta) line emitted from the low current, low pressure H_2 DC, and low and high frequency RF discharges was used to get additional data on the fast excited hydrogen atom production in the cathode sheath region. The results show very broad line profile in both DC and low frequency discharges, due to the excited particles of several hundred electrovolt moving towards and away from the cathode. The effect of different heavy particle collisions on dissociative excitation and ionization in the cathode region for different discharge conditions is discussed.
Abstract: In this paper we present measurements of the electron energy distribution function (EEDF) for electrons in argon discharges at moderate and high E/N values (E being the electric field and N the gas density), for homogeneous electric fields and a low-current diffuse glow regime. Results were obtained for electric field to gas density ratios (E/N) from 500 Td to 50 kTd (1 Td = 10E-21 Vm^2). A multigidded energy analyser with a retarding grid potential was used to measure distribution functions of electrons sampled through an aperture in the anode. Experimental data are used to make a comparison with the two-term Boltzmann calculations for E/N < 1 kTd, and the single-beam model predictions, normally used to model electron kinetics at high values of E/N.
Abstract: In this paper, we extend the calculations for rare gas discharges, which aim to establish the influence of excited states on the kinetics of electron-induced excitation, to rare gas-methane mixtures and pure methane which are often used in diamond-like film deposition. In particular, we address the effects of non-thermal vibrational populations on the rate coefficients in methane-containing gas discharges using the procedure applied previously for pure silane. Furthermore, we investigate the kinetics of electronically excited levels of rare gases and methane in the presence of a significant population of excited states. These staes may contribute to the overall ionization, excitation and dissociation rates through stepwise processes, superelastic collisions and energy transfer processes.The influence of superelastic processes on the development of the nagative differential conductivity (NDC) is discussed on the basis of the momentum transfer theory, and it is shown that the NDC is reduced when significant populations of excited states are present. This is of importance for calculations of the transport coefficients for a.c. electric fields where NDC leads to a complex temporal dependence of the drift velocity and thus directly affects the power deposition in the discharge.
Finally, we present the rate and transport coefficients calculated for methane in r.f. fields based on the Monte Carlo simulation for time-dependent fields. A good agreement with the effective field approximation and earlier Boltzmann calculations is found.
Abstract: In this paper we study different effects of excited molecules on swarm parameters, electron energy distribution functions and gas discharge modeling. First we discuss a possible experiment in parahydrogen to resolve the discrepancy in hydrogen vibrational excitation cross section data. Negative differential conductivity (NDC) is a kinetic phenomenon which manifests itself in a particular dependence of the drift velocity on E/N and it is affected by superelastic collisions with excited states. A complete kinetic scheme for argon required to model excited state densities in gas discharges is also described. These results are used to explain experiments in capacitively and inductively coupled RF plasmas used for processing. The paper illustrates the application of atomic and molecular collision data, swarm data and the theoretical techniques in modelin of gas discharges with large abundances of excited molecules. It is pointed out that swarm experiments with excited molecules are lacking and that there is a shortage of reliable data, while the numerical procedures are sufficiently developed to include all the important effects.
Abstract: A brief review is given of the recent experimental and theoretical studies of low current diffuse discharges. Two models are developed, one that is based on phenomenological description by effective discharge circuit parameters and the other which is based on the calculation of the field profile from the ion distribution for uniform field. In the first case the physical process responsible for the development of the negative differential resistance is the dependence of the secondary electron yield on current through modification of the field close to the cathode. Experimental systems were developed to provide observables that include: breakdown voltage, volt-ampere characteristics (which in the low current limit is represented very well by negative differential resistance), limits and the profile of the low current oscillations, frequency and damping of the induced oscillations, current growth coefficients and the onsets for constrictions. All of the observables are very well predicted by the theory based on the data taken from independent sources, once the steady state secondary electron yield has been fitted to predict the breakdown voltage.
Abstract: We have measured the basic characteristics of low current diffuse discharges in argon for low pressures. The data for the voltage current characteristics and negative differential resistance were obtained together with the data for the frequency and for damping coefficient of the induced oscillations. These data were compared with the predictions of a simple analytic model of Phelps, Petrovic and Jelenkovic [A. V. Phelps, Z. Lj. Petrovic and B. M. Jelenkovic, Phys. Rev. E 47, 2825 (1993)] and it was found that, while most observables may be represented correctly, there is systematic discrepancy between the predictions for frequency of induced oscillations based on the data for transport coefficients from the literature and measurements. The basic idea of the present work is thus to check the fundamental assumptions of the theory and to extend the application of the experiment to study the transition to constrictions in order to initiate modifications of the theory to cover the transition to the constricted regime. Very good agreement was found between the spatial profiles of the electric field calculated from the model and the data obtained from the spatial profiles of emission and these data may be extended to follow the transition to the constricted regime and the development of the cathode sheath.
Abstract: Electron energy distribution functions (EEDF) in N_2 Townsend discharges for E/N between 1 and 30 kTd (1 Td = 10E-21 Vm^2) were measured using multi-gridded energy analyzer behind a small (0.1 mm) aperture in the graphite anode. Experimental results are further analyzed by applying Monte Carlo simulations in order to describe non-equilibrium transport in steady state Townsend discharges and to determine the origin of the observed EEDF features. Boundary effects at electrodes are described by allowing exact representation of absorption, reflection and secondary electron production at the anode. It was found that it is necessary to include electron reflection and secondary electron production in order to model the low energy part of the observed EEDF.
Abstract: We perform calculations of volt-ampere (V-A) characteristics of low-current low-pressure diffuse (Townsend) discharges in hydrogen and compare them to the experiment. The basis for the calculation is the numerical procedure for electric field calculation by solving integral equations for the surface charges. We have used analytic solutions for the homogeneous field as the initial approximation and made a cycle of calculations until the charge profile and the field were self-consistent. This procedure allows us to remove the field expansion from the physical perturbation theory of such discharges and to study the causes for negative differential resistances, oscillations, and nonlinear effects. Furthermore, we have developed a nonlinear version of the physical model of Phelps and coworkers wich helps us identify the features of the ionization coefficient and secondary electron yield that give rise to nonlinear development of the V-A characteristic of Townsend regime discharges.
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