Citation
Rollins, David Kenneth (1986) Diffusion with varying drag; the runaway problem. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd03192008095816
Abstract
We study the motion of electrons in an ionized plasma of electrons and ions in an external electric field. A probability distribution function describes the electron motion and is a solution of a FokkerPlanck equation. In zero field, the solution approaches an equilibrium Maxwellian. For arbitrarily small field, electrons overcome the diffusive effects and are freely accelerated by the field. This is the electron runaway phenomenon.
We treat the electric field as a small perturbation. We consider various diffusion coefficients for the onedimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, nonzero on a finite interval are examined. Some nontrivial cases of these can be solved exactly in terms of known special functions. The more realistic case where the diffusion coefficient decays with velocity is then considered. To determine the runaway current, the equivalent Schrodinger eigenvalue problem is analyzed. The smallest eigenvalue is shown to be equal to the runaway current. Using asymptotic matching a solution can be constructed which is then used to evaluate the runaway current. The runaway current is exponentially small as a function of field strength. This method is used to extract results from the threedimensional problem.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied And Computational Mathematics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  2 September 1985 
Record Number:  CaltechETD:etd03192008095816 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd03192008095816 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1016 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  27 Mar 2008 
Last Modified:  26 Dec 2012 02:34 
Thesis Files
PDF (Rollins_dk_1986.pdf)
 Final Version
Restricted to Caltech community only See Usage Policy. 2940Kb 
Repository Staff Only: item control page