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A statistical theory of cascade multiplication*

Published online by Cambridge University Press:  24 October 2008

P. M. Woodward
P. M. Woodward
Affiliation:
Telecommunications Research EstablishmentMinistry of SupplyMalvern
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Extract

The secondary emission electron multiplier is chosen to illustrate the phenomenon of ‘cascade multiplication’. A method is given for deriving the semi-invariants of the probability distribution for the number of output electrons after any number of identical stages of multiplication, in terms of the corresponding semi-invariants for a single stage. The output distribution is not, in general, either of the Poisson or Gaussian types, though it tends to a limiting shape as the number of stages becomes very large. The special case in which each stage replaces a single primary electron by a Poisson distribution of secondaries is considered. The overall output distribution after many stages is still not Gaussian unless the mean amplification per stage is large compared with unity.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 3 , July 1948 , pp. 404 - 412
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

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