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A Theorem Concerning Noise in Electron Streams

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1 Author(s)
Pierce, J.R. ; Bell Telephone Laboratories, Murray Hill, New Jersey

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It is proposed that if Imax and Imin are the maximum and minimum noise currents in a noise standing wave on an electron stream, then the product of their magnitudes cannot be smaller than

|Imax||Imin|=αeI0B
 ω 
 ωq 
 kTc 
 eV0 
. Various assumptions lead to a factor α ranging between 0.8 and 1. I0 is beam current, B is band width, ω is frequency, ωq is effective plasma frequency, Tc is cathode temperature, and V0 is the voltage specifying the velocity of the electrons.

Published in:

Journal of Applied Physics  (Volume:25 ,  Issue: 8 )