A global (volume averaged) model is developed for an argon-acetylene plasma afterglow. The model is used to study the electron and ion densities, electron temperature and densities of argon metastable atoms in the afterglow plasma. The calculated time dependence for the electron density is found to be in agreement with the existing experimental data. These calculated plasma characteristics are used to investigate the dust charge distribution function (DCDF) for particles with radii of 10-200 nm. The DCDF is found by solving numerically the master equation describing dust discharging as a one-step stochastic process and is also calculated as a Gaussian distribution with mean dust charge and variance, which are functions of time. The time dependences for mean dust charge, variance and dust charging time are obtained and analysed. If the electronegativity of the plasma in the steady-state is low, negative ions do not affect much discharging of dust particles in the afterglow, while at large electronegativity their role is essential. In the case of low electronegativity, discharging of dust particles is mainly due to deposition of positive ions with small and moderate masses (less than the mass of C10H6 + ions). Increasing electronegativity, the effect of heavy positive ions on dust discharging in the late afterglow is important. Secondary electron emission from dust surface at collisions of metastable atoms appears to be negligible.

Properties of an Ar/C2H2 plasma afterglow with dust particles are investigated at different assumptions concerning negative ion formation. First, numerical calculations are carried out assuming that C2nH2- negative ions, where n is a natural number, are the dominant anions in the plasma afterglow (the case (i)). Second, the studies are conducted assuming that C2nH- anions are only the negative ions, which are present in the afterglow plasma (the case (ii)). It is shown that the total density of negative ions n_ in the case (ii) is smaller than n_ in the case (i). Due to smaller n_, the positive ion densities are smaller and the absolute values of the mean dust charge and its variances are larger in the case (ii) than the corresponding values calculated using the approach (i). We also calculated the dust charge distribution functions (DCDFs) for late afterglow times. It is found that the DCDFs obtained in the case (ii) are shifted to the region of larger negative charges comparing with the dust charge distributions obtained in the case (i). The differences are mainly due to the loss of C2nH- anions in collisions with H atoms in the case (ii). In the case when the loss of negative ions in collisions with H atoms is not taken into account in the models, the both approaches give nearly the same time dependences for positive and negative ion densities, electron density, mean dust charge and its variance.

A global (volume averaged) model is developed for the ionization region (IR) of a gas aggregation source (GAS) plasma. The case of using argon gas and a copper target is considered. The model describes the densities of thermal and hot electrons, argon and copper ions, copper atoms and argon atoms in different excited states, the temperature of thermal electrons, the kinetic energies of the ions with which they bombard the target, the sheath width near the target cathode and the energy fluxes by different plasma species to a planar probe in the IR. Also, the fraction of input power is estimated which is dissipated to energize the thermal electrons in the IR. The gas discharge properties are analyzed for different pressures and discharge currents under conditions corresponding to the experimental conditions (Gauter et al 2018 J. Appl. Phys. 124 073301). The calculated pressure- and current-dependences for the GAS properties are used to explain the measured dependences for the deposition rate and the energy flux. It is found that the deposition rate increases with increasing discharge current because of the growth of currents of copper atoms and ions. With increasing pressure, the rate decreases due to drop of the densities of copper atoms and ions because of decreasing the kinetic energies of the ions with which they bombard the target. The model indicates that in the gas-aggregation-source relevant pressure regime, the energy flux by ions dominates over the energy fluxes of other plasma species.

The transport and kinetic coefficients of copper plasma are studied. The temperature dependences of momentum transfer cross sections, collision frequencies (electron–atom, ion–atom), ionization and recombination rates, thermal diffusion, and thermal and electrical conductivity coefficients are calculated. Formulas are proposed that approximate the results of calculations with high accuracy. The temperature dependence of electrical and thermal conductivity is studied and compared with literature data. The obtained coefficients are necessary for the description of transfer processes in a copper non-equilibrium plasma.

Using a global model, the ionization region (IR) of a magnetron discharge in argon with copper target is studied for the conditions corresponding to carried out experiments (the neutral gas pressure is in the range 0.01... 0.1 Torr and the magnetron current is between 10 and 300 mA). It is found how the densities of thermal and hot electrons (emitted secondary electrons at ion bombardment of the target), copper and argon ions, copper atoms and metastable argon atoms in the IR depend on the magnetron current and gas pressure. The current dependences for the voltage drop across the sheath near the target, the sheath size and the energies of ions with which they bombard the target are also determined for different pressures. It is found that the temperature of thermal electrons decreases with increasing the magnetron current and pressure, in agreement with experimental data on the temperature of energy level population (so called excitation temperature) of argon atoms determined by Boltzmann plot technique on the basis of argon spectral lines.

The dust charge distribution function (DCDF) in an argon plasma afterglow is obtained by solving numerically the master equation describing dust discharging as a one-step stochastic process. The calculated DCDFs are compared with Gaussian distributions, and it is found that the dust charge distribution functions can be approximated quite well by the latter ones for different external conditions. It is found how the DCDF, mean dust charge, variance and charging time depend on dust size. For late afterglow times, it is also analyzed how the emission of electrons in the collisions of excited argon atoms with dust particles affects the DCDF. It is shown that the emission effect is more essential for larger nanoparticles than for smaller ones.

Discharging of dust particles in an argon plasma afterglow is investigated using different approaches. First, the dust charge distribution function (DCDF) is obtained by solving numerically the master equation describing dust discharging as a one-step stochastic process. Second, the DCDF is calculated as a Gaussian distribution with mean dust charge and variance, which are functions of time. Additionally, the time-dependencies for the mean dust charge are obtained assuming that the charge changes continuously in the afterglow plasma. Calculation results are compared with available experimental data and are found to be in good qualitative agreement if the dust discharging model accounts for the emission of electrons in the collisions of excited argon atoms with dust particles. This study is carried out taking into account the transition from ambipolar to free diffusion as well as multistep ionization, excitation, and deexcitation of argon atoms in the plasma afterglow.

The charge and dynamics of dust particles in an afterglow plasma are studied using a 1D model in the diffusion approximation, taking into account the transition from ambipolar to free diffusion. It is analyzed how external conditions (dust particle size, neutral gas pressure and initial electron density) affect the dust motion. The dust particle dynamics has been examined in microgravity conditions and in presence of gravity. Without gravity, the location of dust particles in plasma volume may change essentially during the afterglow if the dust size and pressure are small (⩽10 nm and ⩽30 mTorr, respectively). At small pressures, in the very beginning of afterglow, small nanoparticles move to the plasma boundary because the ion drag force dominates over the electric force. At afterglow times when the electron temperature becomes time-independent, the ion drag force decreases faster with time than the electric force due to the ion density decrease, and dust particles may move to the slab center. In presence of gravity, the effect of gravity force on dust particles is important only at large afterglow times ( t ⩾ 10 ms), when the electric and ion drag forces are small. The dust dynamics depends essentially on the initial plasma density. If the density is large (∼10 12 cm −3 ), small nanoparticles (⩽10 nm) may deposit on plasma walls in the beginning of plasma afterglow because of an enhancement of the ion drag force.

The properties (densities of electrons and metastable argon atoms, effective electron temperature and dust charge) of argon/dust and pure argon pulsed plasmas are studied using a spatially-averaged model. The calculated time-dependencies for the densities of electrons and metastable atoms are compared with the experimental measurements and are found to be in a good qualitative agreement. It is analyzed how the plasma properties depend on the shape of the electron energy probability function (EEPF), the pulsing frequency and the duty cycle for both dust-free and dusty plasma. The analysis reveals that the agreement between theory and experiment is better with Druyvesteyn EEPF than the Maxwellian EEPF. Further, the variation in the pulsing frequency nu(p) differently affects the metastable density n(m) in a dust-free and in a dusty plasma. For large nu(p), the metastable density in the dust-free pulsed plasma is larger than in the continuous-wave (CW) discharge, while the opposite is obtained in the presence of dust particles. This difference probably arises because of faster variation in the effective electron temperature in the dusty plasma due to collection of electrons by dust particles. Our calculations also show that dust particles may affect the behavior of electron density in the beginning of the on-period due to an enhancement in electron collection by dust particles.

The time-dependent properties of an Ar/C2H2 dusty plasma (neutral, ion and electron densities, effective electron temperature and dust charge) are studied using a volume-averaged model for conditions corresponding to experiments on nanoparticle growth. The calculated density evolution for C2H2, H2 and C4H2 molecules are compared with time-resolved measurement of the mass peaks of the neutral species and the effects of the dust density on the plasma properties are analyzed. Time evolutions of the main positive and negative ions are also obtained thanks to the calculations. As a consistency check the time-dependence of the dust radius is also obtained numerically, assuming that an increase of the dust radius is due to deposition of hydrocarbon ions and C2H radicals on the surface of dust particles. It is shown that for conditions corresponding to the experiment, the ions are the main contributor to the particle growth. The calculated dust growth rate is compared to the time-dependence of the dust particle size obtained in the experimental measurements. The results of the numerical calculations are found to be in a good qualitative agreement with the experimental data.

It is studied how dissociation and ionization of acetylene molecules in their collisions with argon atoms in excited states Ar* may affect properties of argon-acetylene plasma with growing inside of plasma volume dust particles. The study is carried out using a volume-averaged model. To analyze the effects of Ar* atoms on the electron and ion densities, the effective electron temperature and the densities of radical and nonradical neutral species, the values of ionization and dissociation rates for collisions of acetylene molecules with Ar* atoms are varied in numerical calculations. It is found that the collisions of Ar* atoms with acetylene molecules affect essentially the argon-acetylene dusty plasma.

A volume-averaged model and numerical simulations are used to clarify the effects of process conditions on the plasma chemistry and species initiating the formation of nanoparticles in an Ar/C2H2 plasma. It is shown that Ar/C2H2 plasmas with low electron density, moderate input flux of acetylene and an electron energy distribution function (EEDF) close to the Druyvesteyn EEDF are the most suitable for the production of carbonaceous nanoparticles. These results are verified by direct comparison with experimental data and enable to formulate recommendations for future experiments with a controlled growth of nanoparticles in chemically active plasmas.

The properties of an Ar/C2H2 dusty plasma (ion, electron and neutral particle densities, effective electron temperature and dust charge) in glow and afterglow regimes are studied using a volume-averaged model and the results for the glow plasma are compared with mass spectrometry measurements. It is shown that dust particles affect essentially the properties of glow and afterglow plasmas. Due to collection of electrons and ions by dust particles, the effective electron temperature, the densities of argon ions and metastable atoms are larger in the dusty glow plasma comparing with the dust-free case, while the densities of most hydrocarbon ions and acetylene molecules are smaller. Because of a larger density of metastable argon atoms and, as a result, of the enhancement of electron generation in their collisions with acetylene molecules, the electron density in the afterglow dusty plasma can have a peak in its time-dependence. The results of numerical calculations are in a good qualitative agreement with experimental results.

Analytical expressions for the electron energy probability function (EEPF) in an argon plasma afterglow with large dust density, which are obtained from the homogeneous Boltzmann equation for different steady-state EEPFs (including both Maxwellian and Druyvesteyn distributions at electron energies larger than the dust-surface potential), are presented. The casewhen the rate for electron-neutral momentum-transfer collisions is independent of the electron energy is considered. It is analyzed how the EEPF shape depends on the afterglow time and the decay time of dust charge. It is also found how the decay time of dust charge depends on the decay time of effective electron temperature and that of electron density. The conditions when the energy derivative of the EEPF may be positive are obtained.

The kinetic description of the electron energy probability function (EEPF) in a dusty afterglow plasma is considered for two typical cases: when the rate of electron-neutral momentum-transfer collisions is independent of the electron energy and when it is a power function of the electron energy. The electron Boltzmann equation is solved using the method of characteristics and analytical expressions for the EEPF are obtained for different initial EEPFs (including both Maxwellian and Druyvesteyn distributions) at electron energies larger than the dust-surface potential. The analytical EEPF functions are then used to analyze several experimental parameter regimes of the dust radius and density, the dust-charge decay time, the afterglow duration, etc. It is also found that absorption of electrons by the dust particles plays an important role in determining the EEPF in a dusty afterglow.

The densities of C 2 H 2 and C 4 H 2 molecules, C 2 H radicals, C 2 H - anions and electrons in an argon-acetylene plasma, which are responsible for the formation of carbonaceous nanoparticles in the plasma, as functions of the shape of electron energy distribution function, the electron density and the nanoparticle size and density are studied numerically using a volume-averaged model. Analyzing the dependencies, the conditions suitable for production of the nanoparticles are determined. In particular, it is found that low-density plasmas where electrons have the Druyvesteyn energy distribution are more favorable for the production of nanoparticles than high-density plasmas with the Maxwellian distribution for electrons. The production of nanoparticles in the case of plasma with large density and radius of nanoparticles is not intensive because of small density of C 2 H - anions. These conclusions are in a good agreement with experimental measurements.

We studied transmission of a p-polarized electromagnetic wave through two- and four-layer plasma structure immersed in an external magnetic field perpendicular to the incidence plane. The structure was composed of alternating layers of high and low density plasma. The layers had equal width. The transmission and reflection coefficients were derived using transfer matrix method. In this study we calculated spatial distribution of the tangential energy flux of the wave in the case of reflectionless transmission.

Analytical expressions describing electron energy probability functions (EEPFs) in glow and afterglow dusty plasmas are obtained from the homogeneous Boltzmann equation for electrons. At large energies in a glow dusty plasma, the quasiclassical approach for calculation of the EEPF is applied. Considering the afterglow case, the analytical expressions are obtained assuming that the electron energy loss is mainly due to momentum-transfer electron-neutral collisions and due to deposition of electrons on dust particles. Effect of dust particles on the EEPF is analyzed.

Analytical expressions describing the variation of electron energy distribution function (EEDF) in an afterglow of a plasma are obtained. Especially, the case when the electron energy loss is mainly due to momentum-transfer electron-neutral collisions is considered. The study is carried out for different EEDFs in the steady state, including Maxwellian and Druyvesteyn distributions. The analytical results are not only obtained for the case when the rate for momentum-transfer electron-neutral collisions is independent on electron energy but also for the case when the collisions are a power function of electron energy. Using analytical expressions for the EEDF, the effective electron temperature and charge of the dust particles, which are assumed to be present in plasma, are calculated for different afterglow durations. An analytical expression for the rate describing collection of electrons by dust particles for the case when the rate for momentum-transfer electron-neutral collisions is independent on electron energy is also derived. The EEDF profile and, as a result, the effective electron temperature and dust charge are sufficiently different in the cases when the rate for momentum-transfer electron-neutral collisions is independent on electron energy and when the rate is a power function of electron energy.

Analytical expressions describing the electron energy distribution function (EEDF) in a dusty plasma are obtained from the homogeneous Boltzmann equation for electrons. The expressions are derived neglecting electron-electron collisions, as well as transformation of high-energy electrons into low-energy electrons at inelastic electron-atom collisions. At large electron energies, the quasiclassical approach for calculation of the EEDF is applied. For the moderate energies, we account for inelastic electron-atom collisions in the dust-free case and both inelastic electron-atom and electron-dust collisions in the dusty plasma case. Using these analytical expressions and the balance equation for dust charging, the electron energy distribution function, the effective electron temperature, the dust charge, and the dust surface potential are obtained for different dust radii and densities, as well as for different electron densities and radio-frequency (rf) field amplitudes and frequencies. The dusty plasma parameters are compared with those calculated numerically by a finite-difference method taking into account electron-electron collisions and the transformation of high-energy electrons at inelastic electron-neutral collisions. It is shown that the analytical expressions can be used for calculation of the EEDF and dusty plasma parameters at typical experimental conditions, in particular, in the positive column of a direct-current glow discharge and in the case of an rf plasma maintained by an electric field with frequency f=13.56MHz.