The Calculations of the Concentrations,of the Radial Distributions,and of the Radial Particle Currents of Excited and of Doubly Charged Ions in Low Pressure Discharges

A system of differential equations describing the radial profiles of the number densities and of the radial drift velocities of the ions and of the electrons in positive columns at low pressure containing several species of ions is derived. Excited ions and doubly charged ions, generated in two-step processes by electron impacts, the inertia of the ions and space charge effects are taken into account. For the excited ions de-excitation processes by electron collisions and by spontaneous emission are regarded. A set of nonlinear equations to determine the population densities and the initial values of the differential equations and corresponding boundary conditions are put up. Numerical solutions are given for discharges in argon under free-fall conditions similiar to argon ion lasers. One notices that without stepwise processes via excited ion levels the concentration of double charged ions remains small. In some cases the radial drift of the ions considerably reduces the population of the metastable ion levels. The radial density profiles of the double charged ions and of long-living excited ions considerably deviate from the squared radial profile of the electron density. In addition, for low degrees of ionization the theory of the free-fall column given by Tonks and Langmuir is extended to plasmas containing two species of ions.