The thermodynamic characterization of thermal plasma is a fundamental aspect in many fields, such as high-pressure plasma torches, LIBS (Laser induced Breakdown Spectroscopy), lightning physics and so on. Different aspects must be considered to determine equilibrium quantities. In this paper, we will describe the approach implemented in the code EquilTheTA [1], a web tool to calculate equilibrium composition and the corresponding thermodynamic and transport properties of a plasma. The tool is based on the statistical physics of gases, accessing to an accurate core database of single species internal levels [2]. The tool includes ortho-para separation, important at low temperature for light molecules such as H2 (and isotopologues) and O2. For atomic species, multiply ionized atoms are included and to cope with the divergence of the internal partition function, the number of levels, limited according to the Fermi and Griem cutoff criteria [2], is calculated self-consistently with the composition. The tool has been used also to investigate plasma in high density conditions [3], when also the internal structure of the atoms is influenced by the electron density. In these conditions, quantum effects become important and the Fermi-Dirac distribution must be used for the electron gas [4]. To reduce the size of the core database a general expression, based on the lumped level approach [4], allows to accurately determine the internal thermodynamic properties of species in a wide temperature range. To determine the composition of complex plasmas a novel algorithm has been included, finding one reaction equilibrium, consisting in finding the root of a polynomial, in each step, up to convergence. The possibility of using analytical solution for polynomials up to fourth degree speedup the convergence.

The new impulse to the solar system exploration, testified by the planned NASA missions to the Ice Giants [1], i.e. Neptune and Uranus, is triggering the theoretical activity on the modeling of the hypersonic entry in the planets' atmospheres. In this context it is relevant to characterize the thermodynamics and transport properties of the plasma formed in the shock layer, also accounting on the role of chemical species ablated from the carbon phenolic thermal protection systems. For the accurate estimation of thermodynamic properties and transport coefficients, here the webaccess tool EquilTheTA (EQUILibrium for plasma THErmodynamics and Transport Applications) [2] is exploited. The tool, stable and reliable in wide temperature and pressure ranges, derives the quantities from core databases of atomic and molecular energy levels and collision integrals, in the frame of the classical theory of statistical thermodynamics and the Chapman-Enskog theory, respectively. The creation of a complete database of transport cross sections for binary heavy-particle interactions in complex mixtures including large number of species has been successfully tackled adopting a hybrid approach [3] that combines the traditional multi-potential with the phenomenological approach [4]. In the multi-potential approach, the effective collision integrals for a given interaction results from the averaging procedure of terms corresponding to each allowed interaction between the two colliding partners, while the phenomenological approach is very attractive, allowing the derivation of complete and consistent datasets of collision integrals for any interaction, estimating the interaction potential on a physically sound basis. In fact, the average interaction is modeled by an Improved Lennard Jones (ILJ) potential, whose features (depth and position of the well) are derived by correlation formulas given in terms of fundamental physical properties of interacting partners (dipole polarizability, charge, number of electrons effective in polarization). These approaches, combined with the asymptotic approach for the estimation of the resonant chargeexchange contribution to odd-order collision integrals, represent a powerful strategy to extend the collision integral database. The transport cross sections for the matrix of binary interactions involving chemical species relevant to the H2/He/C/H system are derived, including molecules, molecular ions, neutral and ionized atoms, so as to fully describe the low temperature, dissociative and ionization regimes of the plasma.

Chapter 21 is dedicated to the calculation of thermodynamic and transport properties of a complex mixture, presenting simplified approaches to calculate the internal partition function of atoms and molecules and the phenomenological potential approach to determine the transport cross sections from species parameters, depending on the molecular properties such as polarization.

The entry of meteoroids into the Earth's atmosphere at high speeds produces a bow shock wave and the high temperatures in the shock layer induce an intense heat flux that melts and vaporizes the body. The shock is then structured in two regions: the 'ablation layer' close to the meteoroid surface and constituted by a vapor in equilibrium with the liquid film at the meteoroid surface, and the air shock layer, separated by an interface, whose thickness depends on the meteoroid's dimensions and its entry conditions (velocity and altitude). Across the layer the temperature changes from around 3000 K at the surface of the body to about 20 000 K at the interface [1], reaching very high temperatures at the shock front. Any chemical model of meteoric ablation [1-3] should accurately characterize the ablation layer and the interface, deriving the equilibrium composition, the thermodynamic properties and also the transport coefficients for the estimation of the flow characteristics during hypersonic entry, such as friction and surface heat load. The model should describe the transition between the vapor layer, the composition reproducing the elemental fractions characteristic of the meteoroid, and the interface region, where the complexity of the chemistry increases due to the mixing with air components and the properties of the resulting plasma depend on the fraction of the ablated species in the mixture. The chemical and mineralogical nature of the meteorites (chapter 5) is the basis of their classification and indicates that for chondrites (stony meteorites) the most abundant phases are silicates, producing a differential ablation profile (see figure 4.2 of chapter 4) that shows the dominant ablation of Si, Fe and Mg at an altitude of around 90 km. In this chapter recent efforts to derive accurate thermodynamic and transport properties of silicon compounds, SiO2 or SiC, regarded as models for chondriticmeteorites, are reported and the role of ablated silicon species in affecting the properties of air is also investigated, allowing a description of the interface region. The properties are calculated in a wide range of temperatures [3 × 103-5 × 104 K], i.e. using as lower limit the temperature at the melting surface of the meteoroid body. Advanced chemical models are considered, including molecular species such as C3, O3, Si2, Si3, Si2N, SiN, NO2, ..., potentially minority species but in some cases important at low temperatures, and also molecular positive and negative ions. The multiply charged atomic ions are included up to the fourth ionization level to ensure the soundness of results for high temperatures, where the plasma is fully ionized. The calculations are performed with the web-access EquilTheTA tool [4] and core databases, accessed by thermodynamic and transport computational modules, collecting physical-chemical data and transport cross sections for atomic and molecular species. These databases have been extended to include accurate internal partition functions of atomic and molecular silicon-based species and binary collision dynamical information for interactions involving silicon-carbon, silicon- oxygen and silicon-nitrogen compounds. The thermodynamic and transport properties of plasmas containing silicon-based chemical components represent fundamental information, not only for the simulation of meteoroid thermal ablation during atmosphere entry, but also for the experimental investigation of meteorites. In fact, the composition of the plasma formed in laser-ablation techniques allows, under the assumption of local thermodynamic equilibrium, the reconstruction of synthetic emission spectra that are useful for the elemental analysis of meteorites as well as terrestrial rocks [5-7] through a calibration-free approach [8]. Furthermore, this knowledge offers theoretical support for the design of ablative thermal protection systems for space vehicles [9, 10], as well as arc welding [11] for the production of silica powder.

The characterization of the thermodynamic and transport properties of plasmas including silicon species could be of great interest for the investigation of many different systems containing the product of the ablation of silicon-based materials. Different plasma systems (pure silicon, silicon-argon, silicon dioxide and silicon carbide) have been investigated in a wide temperature range (10(3) -4 10(4) K) and for different pressures (1, 10, 30 and 100 atm), relying on the construction of accurate and extended databases of internal energy levels and binary-interaction transport cross sections for the silicon compounds. The results have been compared with the available results in the literature also studying the dependence on the ratio of components.

This paper focuses on the calculation of the electrical conductivity of a methane-air flame in the presence of weak electric fields, solving the Boltzmann equation for free electrons self-consistently coupled with chemical kinetics. The chemical model GRI-Mech 3.0 has been completed with chemi-ionization reactions to model ionization in the absence of fields, and a database of cross sections for electron-impact-induced processes to account for reactions and transitions activated in the flame during discharge. The dependence of plasma properties on the frequency of an oscillating field has been studied under different pressure and gas temperature conditions. Fitting expressions of the electrical conductivity as a function of gas temperature and methane consumption are provided for different operational conditions in the Ansaldo Energia burner.

This chapter presents the solution of the Boltzmann equation for free electrons in two-term approximations. The two-term approximation is a good compromise between computational time and accuracy, so it is often used to model the electron energy distribution in stationary and time-dependent approaches.

Book Preface

Multiauthor Book om different approaches on plasma modeling

A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron-atom and atom-atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

New calculated thermodynamic properties and transport coefficients of high temperature air are presented. The calculations, which assume local thermodynamic equilibrium, are performed for different pressures (from 0.1 to 1000 atm) in the temperature range from 50 to 30000 K. The results have been obtained by means of the perturbative Chapman-Enskog method, after an appropriate selection of the collision integrals [1]. The calculations include viscosity, total thermal conductivity and electric conductivity. The collision integrals used in calculating the transport coefficients are significantly more accurate than values used in previous theoretical studies. In particular, accurate collision integrals, carried out by Mason [2, 3], for interactions between charged species were calculated using the attractive and repulsive screened Coulomb potentials.

A new Photovoltaic-Thermal (PV-T) module, based on crystalline silicon (c-Si) technology with plastic-laminated sandwich without glass, is studied from a theoretical point of view and tested in outdoor operating conditions in the presence of water cooling. A thermal model has been developed starting from solar irradiance, separated into its different components, from the frontsheet to the backsheet. The electrical conversion efficiency of solar cells is required to correctly assess the electricity production and the thermal balance. Thus, an iterative calculation procedure solves the thermal-electric problem and finds the cell temperature. Finally, experimental tests in outdoor conditions have been performed to validate theoretical current-voltage (I-V) characteristics of the PV-T module and its rated data.

Kinetic theory applies to systems with a large number of particles, while nanoplasma generated by the interaction of ultra-short laser pulses with atomic clusters are systems composed by a relatively small number (10 2 divided by 10 4) of electrons and ions. In the paper, the applicability of the kinetic theory for studying nanoplasmas is discussed. In particular, two typical phenomena are investigated: the collisionless expansion of electrons in a spherical nanoplasma with immobile ions and the formation of shock shells during Coulomb explosions. The analysis, which is carried out comparing ensemble averages obtained by solving the exact equations of motion with reference solutions of the Vlasov-Poisson model, shows that for the dynamics of the electrons the error of the usually employed models is of the order of few percents (but the standard deviation in a single experiment can be of the order of 10%). Instead, special care must be taken in the study of shock formation, as the discrete structure of the electric charge can destroy or strongly modify the phenomenon. (C) 2014 AIP Publishing LLC.

In this paper, a supersonic flow of an argon plasma around a cylinder has been investigated comparing shock fitting and shock capturing techniques. Shock-capturing codes are algorithmically simple, but are plagued by a number of numerical troubles, particularly evident when the shocks are strong and the grids unstructured. On the other hand, shock-fitting algorithms allow to accurately compute solutions on coarse meshes, but tend to be algorithmically complex. The kinetic scheme adopted includes the argon metastable state as an independent species and takes into account for electron-atom and atom-atom processes. Electron density distributions have been reported.

Fundamental Aspects of Plasma Chemical Physics - Thermodynamics develops basic and advanced concepts of plasma thermodynamics from both classical and statistical points of view. After a refreshment of classical thermodynamics applied to the dissociation and ionization regimes, the book invites the reader to discover the role of electronic excitation in affecting the properties of plasmas, a topic often overlooked by the thermal plasma community. Particular attention is devoted to the problem of the divergence of the partition function of atomic species and the state-to-state approach for calculating the partition function of diatomic and polyatomic molecules. The limit of ideal gas approximation is also discussed, by introducing Debye-Huckel and virial corrections. Throughout the book, worked examples are given in order to clarify concepts and mathematical approaches. This book is a first of a series of three books to be published by the authors on fundamental aspects of plasma chemical physics. The next books will discuss transport and kinetics.