Abstract

The exact small-signal hot-tube dispersion relation for a thin tape helix traveling-wave tube (TWT) is derived, based on the exact cold-tube dispersion relation by Chernin et al.1. This is an attempt to provide a reliable determination of Pierce's “AC space-charge” parameter $Q$ for a realistic TWT, for which there is no general formulation. We found that in addition to Q, another parameter, q, is necessary to account for the space-charge effects on the circuit mode. This $q$ modifies the circuit mode in Pierce's 3-wave theory of TWT. In a realistic example, the effect of $q$ is equivalent to a modification of the circuit phase velocity by as much as two percent. We will compare our results against commonly used models for Q2, 3.

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