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Avalanches of electrons in a gas

Published online by Cambridge University Press:  24 August 2016

F. W. Steutel
F. W. Steutel*
Affiliation:
Eindhoven University of Technology
*
∗Postal address: Department of Mathematics and Computing Science, Eindhoven University of Technology, Den Dolech 2, P.O. Box 513, 5600MB Eindhoven, the Netherlands.
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Abstract

The motion of electrons through a gas of particles is modelled as a two-state process: an electron is alternatingly moving and being held captive by a non-moving particle, during exponentially distributed periods.

The model contains a parameter p, the probability that collision of an electron with a gas particle does not lead to its capture but produces an extra electron.

The quantity of interest is the current C(t) produced by the moving electrons, as a function of time.

Keywords

TWO-STATE MARKOV BRANCHING PROCESSBESSEL FUNCTIONASYMPTOTIC NORMALITY
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 867 - 879
Copyright
Copyright © Applied Probability Trust 1986 

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References

[1] Athreya, K. B. and Ney, P. E. (1972) Branching Processes. Springer-Verlag, New York.Google Scholar
[2] Luke, Y. L. (1962) Integrals of Bessel Functions. McGraw-Hill, New York.Google Scholar
[3] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[4] Steutel, F. W. (1985) Poisson processes and a Bessel-function integral. SIAM Rev. 27, 73–77.Google Scholar
[5] Verhaart, H. F. A. and Van Der Laan, P. C. T. (1984) The influence of water vapour on avalanches in air. J. Appl. Phys. 55(9), 3286–3292.Google Scholar