Theorie der nichtkontrahierten positiven Säule unter dem Einfluß negativer Ionen

Abstract

We consider a cylindrical positive column of a collision dominated plasma consisting of electrons, positive and negative ions and neutral particles. The qualities of such a column are deduced from an eigenvalue problem which follows from the application of the basic transport equations for such a plasma. The problem presents itself in the form of three simultaneous differential equations with boundary conditions. Applying a procedure which is known from nuclear physics as “Center-Wall-Approximation” we are able to reduce these three differential equations to three simultaneous algebraic equations. The numerical evaluation with the help of a digital computer produces the particle densities in the center of the discharge and the electric field as functions of the total current. The results are particularly interesting in the “subnormal” region of the discharge. With increasing current the subnormal decrease of the electric field is first interrupted due to the build up of the negative ion component which stops the formation of the ambipolar field. The subnormal field-decrease continues only at higher currents when the recombination of negative ions and positive ions remove the influence of the negative ion component. Due to these phenomena the subnormal features appear in two steps. The second one is delayed due to the described influence of the negative ions.