NUMERICAL TREATMENT OF THE POSITIVE COLUMN OF A GAS DISCHARGE WITH SLAB SYMMETRY FOR THE ENTIRE RANGE OF PLASMA DENSITIES.
Abstract
The positive column of a gas discharge is mathematically described by a system of four non-linear differential equations containing an adjustable parameter which plays the role of an eigenvalue. Some coefficients of the system contain a factor representing the ion density at the center of the slab, and this factor may assume extremely high values. In the present report a procedure is shown which makes it possible to solve this system of differential equations and to determine the 'eigenvalue' for any value of the ion density no matter how large. For high ion densities a straightforward approach will lead to a tremendous loss of accuracy, although the problem by itself is well posed. This difficulty is partially overcome by a method due to Guderley and Nikolai. But the resulting equations still contain particular solutions which decrease extremely rapidly; one obtains 'stiff' equations for which the usual integration techniques can proceed only in very small steps. In the present report the method of Guderley and Nikolai is still used in the vicinity of the wall. In the remaining portion of the flow field a transformation is carried out by which the particular solutions that cause stiffness are nearly decoupled from the rest of the system and can be dealt with by semianalytic means. The transformation of the differential equation requires considerable attention to analytic details otherwise inadvertent losses of accuracy may be encountered. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1969
- Accession Number
- AD0697032
Entities
People
- Emma M. Valentine
- Karl G. Guderley
Organizations
- Air Force Research Laboratory