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(ωωq)(kTceV0). 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.
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John R. Pierce (1954) studied this question.
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