Local thermodynamic equilibrium plasma

Local Thermodynamic Equilibrium (LTE). This LTE model is of historical importance only. The idea was that under ion bombardment a near-surface plasma is generated, in which the sputtered atoms are ionized [3.48]. The plasma should be under local equilibrium, so that the Saha-Eggert equation for determination of the ionization probability can be used. The important condition was the plasma temperature, and this could be determined from a knowledge of the concentration of one of the elements present. The theoretical background of the model is not applicable. The reason why it gives semi-quantitative results is that the exponential term of the Saha-Eggert equation also fits quantum-mechanical expressions. 

For spectra corresponding to transitions from excited levels, line intensities depend on the mode of production of the spectra, therefore, in such cases the general expressions for moments cannot be found. These moments become purely atomic quantities if the excited states of the electronic configuration considered are equally populated (level populations are proportional to their statistical weights). This is close to physical conditions in high temperature plasmas, in arcs and sparks, also when levels are populated by the cascade of elementary processes or even by one process obeying non-strict selection rules. The distribution of oscillator strengths is also excitation-independent. In all these cases spectral moments become purely atomic quantities. If, for local thermodynamic equilibrium, the Boltzmann factor can be expanded in a series of powers (AE/kT)n (this means the condition AE < kT), then the spectral moments are also expanded in a series of purely atomic moments. 

Obviously, plasmas can be used very efficiently within the synthetic approach (i), and all examples given in this paper are assigned to the synthetic approach. It is much less obvious whether plasmas can be used also in the counter-direction. In order to measure a stable and reproducible electromotive force (EMF) the corresponding electrochemical (galvanic) cell must be in (local) thermodynamic equilibrium. Low-temperature plasmas represent non-equilibrium states and are highly inhomogeneous systems from a thermodynamic point of view, often not... 

A glow discharge plasma is not in local thermodynamic equilibrium (LTE), as the number of collisions is too low to thermally stabilize the plasma. Thus the electron temperatures are high (5000 K for the electrons involved in recombination and >10000 K for the high-energy electrons responsible for excitation through electron impact) but the gas temperatures (below 1000 K) are low. 

A cross-sectional diagram of the reactor is presented in Figure 2. The isotherms indicated are those determined spectroscopically by Reed (32), and are representative of conditions in this study. Eckert and coworkers (7) have extended this work to spectroscopic observations of induction-coupled plasmas in both air and argon. Conditions of local thermodynamic equilibrium were approached and temperatures above 6000°K. were measured. No direct temperature measurements were attempted in the present study. 

Plasmas are strongly non-equilibrium systems with hot light particles (electrons) and cold heavy particles (neutrals and ions in the bulk plasma). Charged particles can achieve kinetic energies of 100s of eV in the sheath (Fig. 11). In this respect, electrochemical systems are closer to thermal plasmas [268] for which local thermodynamic equilibrium (LTE) may be assumed (i.e., all particles are at the same temperature ), and the pressure ( 1 atm) is well above the limit of applicability of the continuum approximation. 

The temperatiue difference between electrons and heavy neutral particles due to Joule heating in the collisional weakly ionized plasma is conventionally proportional to the sqirare of the ratio of the electric field ( ) to the pressure p). Only in the case of small values of E/p do the temperatiues of electrons and heavy particles approach each other. Thus, this is a basic requirement for local thermodynamic equilibrium (LTE) in plasma. Additionally, LTE conditions require chemical equilibrium as well as restrictions on the gradients. The LTE plasma follows the maj or laws of equilibrium thermodynamics and canbe characterized by a single temperature at each point of space. Ionization and chemical processes in such plasmas are determined by temperature (and only indirectly by the electric fields through Joule heating). The quasi-equilibrium plasma of this kind is usually called thermal plasma. Thermal plasmas in nature canbe represented by solar plasma (Fig. 1-4). 

Complete Thermodynamic Equilibrium (CTE) and Local Thermodynamic Equilibrium (LTE) in Plasma... 

The application of quasi-equilibrium statistics and thermodynamics to plasma-chemical systems requires a clear understanding and distinction between the concepts of complete thermodynamic equilibrium (CTE) and local thermodynamic equilibrium (LTE). CTE is related to uniform plasma, in which chemical equilibrium and all plasma properties are unambiguous functions of temperature. This temperature is supposed to be homogeneous and the same for all degrees of freedom, all components, and all possible reactions. In particular, the following five equilibrium statistical distributions should take place for the same temperature T ... 

For plasma in local thermodynamic equilibrium (L.T.E.), calculation of the transport pro( rties begins with the kinetic theory of gases. This theory is based on statisti< concepts, in particular, on the distribution Junction of the gas particles For a particle of the i-th type, the distribution function f,(f, j, t) represents the number of particles of type i present, at the instant t, in a elementary colume df, d of phase... 

CTE is not realized in laboratory plasmas wich are optically thin (Planck s law is not valid). But the mass action law, the Boltzmann distribution and Maxwell distribution may be obeyed by a unique local temperature such that T, = T e = T = T, then one introduces the (complete) local thermodynamic equilibrium (LTE). Boltzmann and Saha s law are often obeyed only for highly excited levels, the plasma is then said to be in Local Partial Thermodynamic Equilibrium (LPTE). 

Ta by a large factor. Typically, is of the order of3000 K, whereas 0.5 (Te + 7c). A plasma cannot greatly exceed the density at which as maiy ions recombine locally as are produced locally. In this condition, known as local thermodynamic equilibrium, the plasma properties are equivalent to those that would exist in equilibrium with a hypothetical surface at 7 and emitting a neutral plasma. 

Semiempirical Approximation. The method that adopts a semiempirical approximation to a uses the Andersen-Hinthome local thermodynamic equilibrium (LTE) model [185] for estimating the degree of ionization. The model does not take account of any details of individual ionization processes but assumes that the region at and near the surface involved in sputtering can be approximated by a dense plasma in local thermodynamic equilibrium. The plasma has an associated temperature T. The ratio of the concentrations of two elements X and Y in a matrix B, if sufficiently dilute, can then be written as... 

Secondary Ion Yields. The most successful calculations of secondary in yields are based on the local thermal equilibrium (LTE) model of Andersen and Hinthorne (1973), which assumes that a plasma in thermodynamic equilibrium is generated locally in the solid by ion bombardment. Assuming equilibrium, the law of mass action can be applied to find the ratio of ions, neutrals and electrons, and the Saha-Eggert equation is derived ... 

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