Electrons space-dependent plasmas

Furthermore, the detailed procedure ultimately used to determine the velocity distribution sensitively depends on the type of plasma and is quite different when studying the electron kinetics in steady-state, time-dependent, or space-dependent plasmas. 

Equations (12), simplified by the assumption of isotropic scattering in exciting and dissociating collisions, represent the basic equations for studying many quite different problems in electron kinetics. In particular, the additional simplification to steady-state, purely time-dependent, or purely space-dependent plasma conditions allows a detailed microphysical analysis of various electron kinetic problems related to each of these plasma conditions. 

In purely space-dependent plasmas, the consistent particle, power, and momentum balance equations of the electrons, Eqs. (31) to (33), have the simplified representation (Sigeneger and Winkler, 1997a Sigeneger and Winkler, 1996)... 

In contrast to the situation in plasmas in steady state or in time-dependent plasmas, the electron density n z) in space-dependent plasmas always depends on the z coordinate, and this happens already if only conservative inelastic collisions are considered. As an immediate consequence, it no longer makes sense to separate the density from the isotropic and anisotropic distribution of the electrons. 

By the preceding representations, an attempt has been made to give, on the basis of the electron Boltzmann equation, an introduction to the kinetic treatment of the electron component in steady-state, time-dependent, and space-dependent plasmas and to illustrate by selected examples the large variety of electron kinetics in anisothermal weakly ionized plasmas. 

As a consequence, for different plasma conditions—for instance, steady-state, time-dependent, or space-dependent problems—different solution approaches and numerical techniques have been developed and applied. In addition, the specific structure of the electric field acting upon the electrons is of particular importance for the establishment of a special symmetry in the velocity distribution and thus for a specific simplification of the solution approach. 

A quite different situation with respect to the spatial behavior of the electron component arises if the inhomogeneity of the plasma is caused by a plasma confinement. The electron kinetics established in the radial direction of the positive column of dc glow discharges, which usually operates in a cylindrical discharge tube with an isolated wall, presents a representative example (Kortsha-gen, 1995 Uhrlandt and Winkler, 1996 Pfau et al, 1996 Alves et al, 1997) of such a condition. From the point of the electron kinetics, this space-dependent problem is somewhat more complex than those considered above. 

The voltage drop at the anode is a result of negative space charge produced by the flow of electrons from the plasma to the anode in the absence of positive ions. Normally, the anode is not a somce of positive ions and the potential gradient in the positive coliutm tends to drive the positive ions away from the anode. The magnitude of the anode fall of potential will depend on the arc current. Once the anode is heated to its vaporization point, positive ions will form in this space and the potential drops drastically. 

As shown by Eq. (4), the rate of reactions involving electrons depends on the EVDF, /(r, V, f). Determination of the distribution function is one of the central problems in understanding plasma chemistry. The EVDF is defined in the phase-space element dydr such that /(r, v, f) dy dx is the number of electrons dn at time t located between r and r + dr which have velocities between v and v -I- d. When normalized by the total number of electrons n, it is a probability density function. The EVDF is obtained by solving the Boltzmann transport equation [42, 43, 48, 49]... 

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