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Theory of runaway electrons

Abstract

This paper treats the problem of electrons moving through an infinite gas of positive ions under the influence of a static uniform electric field of arbitrary strength. In evaluating the electrical conductivity of such a gas the conventional treatment involves a perturbation solution of the time-independent Boltzmann equation, and results in the well-known (temperature){sup 3/2} law. Two assumptions are basic to these treatments: 1) that a steady state electron velocity distribution is attained several mean-free collision times after the electric field is applied, and 2) that the terminal electron drift velocity is small compared to the average random electron speed. Both assumptions are avoided in this paper. In the next section the problem is formulated starting with the Boltzmann equation and a review of approximate analytic solutions appropriate to the weak and strong electric field cases is presented. We then describe a time-dependent numerical solution to the Boltzmann equation and compare these results with the approximate solutions. All of these treatments lead to the conclusion that this problem does not admit a time-independent solution. Because of the strong energy dependence of the Rutherford scattering law, the electron drift velocity is not bounded by a terminal value, rather it grows monotonically  More>>
Authors:
Dreicer, H [1] 
  1. Los Alamos Scientific Laboratory, University of California, Los Alamos, NM (United States)
Publication Date:
Jul 01, 1958
Product Type:
Conference
Report Number:
INIS-XU-021; P-2292-USA
Resource Relation:
Conference: 2. United Nations international conference on the peaceful uses of atomic energy, Geneva (Switzerland), 1-13 Sep 1958; Other Information: 3 refs, 19 figs, 2 tabs; Related Information: In: Proceedings of the second United Nations international conference on the peaceful uses of atomic energy. V. 31. Theoretical and experimental aspects of controlled nuclear fusion, 400 pages.
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANALYTICAL SOLUTION; BOLTZMANN EQUATION; CATIONS; COLLISIONS; COMPARATIVE EVALUATIONS; DISTRIBUTION; ELECTRIC CONDUCTIVITY; ELECTRIC FIELDS; ELECTRON DRIFT; ENERGY DEPENDENCE; NUMERICAL SOLUTION; PERTURBATION THEORY; PLASMA WAVES; RUNAWAY ELECTRONS; RUTHERFORD SCATTERING; STEADY-STATE CONDITIONS; TIME DEPENDENCE; VELOCITY
OSTI ID:
21068298
Research Organizations:
United Nations, Geneva (Switzerland)
Country of Origin:
UN
Language:
English
Other Identifying Numbers:
TRN: XU0800008082390
Availability:
Available from INIS in electronic form
Submitting Site:
INIS
Size:
page(s) 57-64
Announcement Date:
Sep 13, 2008

Citation Formats

Dreicer, H. Theory of runaway electrons. UN: N. p., 1958. Web.
Dreicer, H. Theory of runaway electrons. UN.
Dreicer, H. 1958. "Theory of runaway electrons." UN.
@misc{etde_21068298,
title = {Theory of runaway electrons}
author = {Dreicer, H}
abstractNote = {This paper treats the problem of electrons moving through an infinite gas of positive ions under the influence of a static uniform electric field of arbitrary strength. In evaluating the electrical conductivity of such a gas the conventional treatment involves a perturbation solution of the time-independent Boltzmann equation, and results in the well-known (temperature){sup 3/2} law. Two assumptions are basic to these treatments: 1) that a steady state electron velocity distribution is attained several mean-free collision times after the electric field is applied, and 2) that the terminal electron drift velocity is small compared to the average random electron speed. Both assumptions are avoided in this paper. In the next section the problem is formulated starting with the Boltzmann equation and a review of approximate analytic solutions appropriate to the weak and strong electric field cases is presented. We then describe a time-dependent numerical solution to the Boltzmann equation and compare these results with the approximate solutions. All of these treatments lead to the conclusion that this problem does not admit a time-independent solution. Because of the strong energy dependence of the Rutherford scattering law, the electron drift velocity is not bounded by a terminal value, rather it grows monotonically with time. This is the so-called runaway effect predicted by Giovanelli. Collective effects, or plasma oscillations, are ignored in this work, although these undoubtedly play an important role in the conduction of electricity through the plasma.}
place = {UN}
year = {1958}
month = {Jul}
}