Abstract
Most recently, Wong et al. derived an exact hot tube dispersion relation for a tape helix TWT l, based on the exact cold tube dispersion relation obtained by Chernin et al.2 for the same tape helix model. It was found that Pierce's classical 3-wave TWT dispersion relation needs to be modified, in particular the circuit mode is modified by a new term, which they call q. This q for the modification of circuit mode at high beam currents is entirely analogous to Pierce's space charge parameter, Q, for the modification of the beam mode. For forward wave amplification, q may lead to a detune in the circuit mode phase velocity by as much as two percent in a realistic example1. Since Johnson's theory of backward wave oscillation (BWO) in a TWT3 was based solely on Pierce's 3-wave dispersion relation, we analyze the effect of q on Johnson's threshold condition for BWO. The value of q, together with of the values of the Pierce parameters C and Q, will be determined for the backward wave mode using the exact hot-tube dispersion relation1.
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