Paradoxical Nonmonotonic Behavior of Excitation-Rate Spatial Profiles in Bounded Plasmas

Abstract

Paradoxical nonmonotonic behavior of spatial profiles of excitation rates in bounded plasmas have been analyzed. It is shown that the effect is related to the nonlocal character of the electron distribution function.

Nonlocal Behavior of Electron Fluxes and Excitation Rates for “Local” EEDF in Moderate and High Pressures DC Positive Column Plasmas

“…Recall that electron spatial flows redistribute particles and energy in the plasma volume and form a plasma density profile [1]- [3]. These electron energy distribution function (EEDF) forming flows bear information about the fine characteristics of the discharge, such as generation and loss of charges, components and mechanisms of the electron energy balance, etc.…”

“…The left-hand side of (1) is the divergence of differential electron flows [1]- [3] with respect to energy and coordinate, i.e.,…”

“…I N VARIABLES of coordinate r and total electron energy ε, the Boltzmann kinetic equation for electrons represents an equation of 2-D diffusion with coefficients D r = vλ/3 and D E = (eE) 2 D r and the "velocity" of energy loss in elastic collisions V ε = δνw (see, for details, [1]- [3]), i.e.,…”

“…On the other hand, in the elastic region of energy (lower excitation level: for argon, 11.55 eV), radial and energy fluxes (2) can be comparable. In addition, different energy dependence of D E and V ε (their ratio can be increasing or decreasing depending on the behavior of σ el (w)) results to directions of the electron flux being different in various regions of the phase plane.The model used for these simulations consists of a series of linked modules that are iterated to a converged solution [1]. The modules are as follows: 1) the kinetic module (for calculation of the electron spatial energy distribution function; it is a 2-D (r, ε) cylindrically symmetric simulation) and 2) the fluid module (for solving all neutral and charged particle densities and Poisson's equation for the electric potential; it is a 1-D simulation for the radial distribution of parameters).…”

“…The model used for these simulations consists of a series of linked modules that are iterated to a converged solution [1]. The modules are as follows: 1) the kinetic module (for calculation of the electron spatial energy distribution function; it is a 2-D (r, ε) cylindrically symmetric simulation) and 2) the fluid module (for solving all neutral and charged particle densities and Poisson's equation for the electric potential; it is a 1-D simulation for the radial distribution of parameters).…”