Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-20T08:14:28.096Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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