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Diffusion with Varying Drag; the Runaway Problem


Rollins, David Kenneth (1986) Diffusion with Varying Drag; the Runaway Problem. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/mwvx-6b36.


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 Fokker-Planck 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 one-dimensional problem and determine the runaway current as a function of the field strength. Diffusion coefficients, non-zero on a finite interval are examined. Some non-trivial 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 Schrödinger 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 three-dimensional problem.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Corngold, Noel Robert
Thesis Committee:
  • Corngold, Noel Robert (chair)
  • Lorenz, Jens
  • Meiron, Daniel I.
  • Gavalas, George R.
Defense Date:2 September 1985
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Record Number:CaltechETD:etd-03192008-095816
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1016
Deposited By: Imported from ETD-db
Deposited On:27 Mar 2008
Last Modified:19 Apr 2021 22:33

Thesis Files

PDF (Rollins_dk_1986.pdf) - Final Version
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