## 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
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Dreicer, H

^{[1] }- Los Alamos Scientific Laboratory, University of California, Los Alamos, NM (United States)

## 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}

}

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}

}