## Citation

Rollins, David Kenneth
(1986)
*Diffusion with Varying Drag; the Runaway Problem.*
Dissertation (Ph.D.), California Institute of Technology.
http://resolver.caltech.edu/CaltechETD:etd-03192008-095816

## 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 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.)) | ||||||
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Subject Keywords: | Applied Mathematics | ||||||

Degree Grantor: | California Institute of Technology | ||||||

Division: | Physics, Mathematics and Astronomy | ||||||

Major Option: | Applied Mathematics | ||||||

Thesis Availability: | Restricted to Caltech community only | ||||||

Research Advisor(s): | - Corngold, Noel Robert
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Thesis Committee: | - Corngold, Noel Robert (chair)
- Lorenz, Jens
- Meiron, Daniel I.
- Gavalas, George R.
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Defense Date: | 2 September 1985 | ||||||

Funders: |
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Record Number: | CaltechETD:etd-03192008-095816 | ||||||

Persistent URL: | http://resolver.caltech.edu/CaltechETD:etd-03192008-095816 | ||||||

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 ETD-db | ||||||

Deposited On: | 27 Mar 2008 | ||||||

Last Modified: | 23 May 2019 22:05 |

## Thesis Files

PDF (Rollins_dk_1986.pdf)
- Final Version
Restricted to Caltech community only See Usage Policy. 2940Kb |

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