The Theory of the Low‐Pressure, High‐Current Discharge Column: The Influence of the Degree of Ionization and of the Neutral Gas Temperature on the Radial Profiles of the Charged Particle Density, the Neutral Gas Density, and on the Electron Temperature

Abstract

AbstractTo give a theoretical description of the low‐pressure positive column at high degrees of ionization under ambipolar and under free‐fall conditions, the differential equations for the first two and the first three moments of the velocity distribution functions of the atoms, the ions, and the electrons are derived. In particular, to close the set of the equations in a physically reasonable manner, typical features of the discharge in the free‐fall regime are taken into consideration by the statements for the heat flux tensors of the ion gas and of the neutral gas. Numerical solutions are given for the radial profiles of the number density, of the radial drift velocities, and of the radial and the azimuthal temperatures in the ion gas and in the neutral gas. The charged particle density profile is broadened under diffusion conditions, if the electron temperature and the degree of ionization increase. In the free‐fall regime the charged particle density profile depends only weakly on the electron temperature and is slightly constricted if the degree of ionization increases. The degree of ionization affects the density profiles of the charged particles and the neutral gas under ambipolar diffusion conditions more than under free‐fall conditions. Rising neutral gas temperature leads to a weak narrowing of the charged particle density in both regions. The electron temperature depends only weakly on the forms of the density profiles of the charged particles and of the neutral gas. Furthermore, the ion flux density to the wall and the wall potential are calculated in dependence on the degree of ionization and on the neutral gas temperature.