Density-Function Calculations of Noise Propagation on an Accelerated Multivelocity Electron Beam

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Abstract
The propagation of noise current and voltage fluctuations through the multivelocity accelerating region immediately in front of the potential minimum has been calculated using the density-function method of analysis. Basic assumptions made include: (a) linearized one-dimensional analysis; (b) zero total ac current in the beam; (c) uncorrelated full shot noise in each velocity class at the minimum plane; (d) dc potential η(ξ) given by the Fry-Langmuir analysis. Starting at the minimum, the noise fluctuations were traced out towards positive ξ by a numerical forward-integration process using an IBM 650 electronic computer. Principal results of the computations are that Haus's noise parameters S and Π are found to vary significantly with distance between η=0 and η=4, contrary to previous assumption. The noise parameter S decreases to ∼0.7 of its initial value of kTc/2π, while the noise power Π rises from zero to ∼0.3 of the initial value of S. Exact results depend slightly on frequency. Beyond η=4 both noise parameters become invariant. The theoretical minimum noise figure of a beam type microwave amplifier, which is Fmin=1 +(2π/kT) (S-Π), is thus found to be reduced to ∼3½ db for a temperature-limited cathode instead of the commonly quoted value of 6½ db which is based on the values of S and Π at the cathode.