Citation
Lindgren, Robert Gary (1970) Theory of the Positive Column of a Gas Discharge. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/B4W0ST96. https://resolver.caltech.edu/CaltechTHESIS:08062015144055650
Abstract
An attempt is made to provide a theoretical explanation of the effect of the positive column on the voltagecurrent characteristic of a glow or an arc discharge. Such theories have been developed before, and all are based on balancing the production and loss of charged particles and accounting for the energy supplied to the plasma by the applied electric field. Differences among the theories arise from the approximations and omissions made in selecting processes that affect the particle and energy balances. This work is primarily concerned with the deviation from the ambipolar description of the positive column caused by space charge, electronion volume recombination, and temperature inhomogeneities.
The presentation is divided into three parts, the first of which involved the derivation of the final macroscopic equations from kinetic theory. The final equations are obtained by taking the first three moments of the Boltzmann equation for each of the three species in the plasma. Although the method used and the equations obtained are not novel, the derivation is carried out in detail in order to appraise the validity of numerous approximations and to justify the use of data from other sources. The equations are applied to a molecular hydrogen discharge contained between parallel walls. The applied electric field is parallel to the walls, and the dependent variables—electron and ion flux to the walls, electron and ion densities, transverse electric field, and gas temperature—vary only in the direction perpendicular to the walls. The mathematical description is given by a sixthorder nonlinear twopoint boundary value problem which contains the applied field as a parameter. The amount of neutral gas and its temperature at the walls are held fixed, and the relation between the applied field and the electron density at the center of the discharge is obtained in the process of solving the problem. This relation corresponds to that between current and voltage and is used to interpret the effect of space charge, recombination, and temperature inhomogeneities on the voltagecurrent characteristic of the discharge.
The complete solution of the equations is impractical both numerically and analytically, and in Part II the gas temperature is assumed uniform so as to focus on the combined effects of space charge and recombination. The terms representing these effects are treated as perturbations to equations that would otherwise describe the ambipolar situation. However, the term representing space charge is not negligible in a thin boundary layer or sheath near the walls, and consequently the perturbation problem is singular. Separate solutions must be obtained in the sheath and in the main region of the discharge, and the relation between the electron density and the applied field is not determined until these solutions are matched.
In Part III the electron and ion densities are assumed equal, and the complicated spacecharge calculation is thereby replaced by the ambipolar description. Recombination and temperature inhomogeneities are both important at high values of the electron density. However, the formulation of the problem permits a comparison of the relative effects, and temperature inhomogeneities are shown to be important at lower values of the electron density than recombination. The equations are solved by a direct numerical integration and by treating the term representing temperature inhomogeneities as a perturbation.
The conclusions reached in the study are primarily concerned with the association of the relation between electron density and axial field with the voltagecurrent characteristic. It is known that the effect of space charge can account for the subnormal glow discharge and that the normal glow corresponds to a close approach to an ambipolar situation. The effect of temperature inhomogeneities helps explain the decreasing characteristic of the arc, and the effect of recombination is not expected to appear except at very high electron densities.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  (Chemical Engineering and Applied Mathematics)  
Degree Grantor:  California Institute of Technology  
Division:  Chemistry and Chemical Engineering  
Major Option:  Chemical Engineering  
Minor Option:  Applied Mathematics  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  8 May 1970  
Additional Information:  Title varies in the 1970 Caltech commencement program: Theory of the Positive Column  
Funders: 
 
Record Number:  CaltechTHESIS:08062015144055650  
Persistent URL:  https://resolver.caltech.edu/CaltechTHESIS:08062015144055650  
DOI:  10.7907/B4W0ST96  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9081  
Collection:  CaltechTHESIS  
Deposited By:  INVALID USER  
Deposited On:  11 Aug 2015 16:41  
Last Modified:  16 May 2024 23:35 
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