Diffusion theory of the low-pressure positive column with two-step ionization from a metastable state. I

Abstract

We present a self-consistent theory of a low-pressure positive column with two-step ionization from a metastable state in which the coupling between the continuity equations for the electrons and the metastables is appropriately taken into account. The corresponding boundary value problem is solved numerically for both cylindrical and planar geometries and vanishing electron and metastable densities at the boundary, for a wide range of the two parameters on which the problem is shown to depend. Curves of the electron and metastable density profiles, of the eigenvalues, and of conveniently defined generalized diffusion lengths for both types of particles are presented. We also show that the eigenvalues together with Boltzmann calculations of the electron rate coefficients and transport parameters provide similarity laws for a steady-state positive column with radius R: ratio of the electric field to the gas density, E/N vs NR for I/R=const and ratio of the metastable density to the gas density, nM(0)/N vs I/R for NR=const, where I is the discharge current. An application to argon is discussed.