Absolute instability and transient growth near the band edges of a traveling wave tube

Abstract

An electron beam in the slow wave structure of a traveling wave tube may be subjected to absolute instability at the lower and upper band edges, where the group velocity is zero. From a careful re-examination of the immediate vicinity of these band edges, we use the Briggs-Bers criterion to show that, contrary to previous findings, an absolute instability may arise at the lower band edge if the beam current is sufficiently high, even if the beam mode intersects with the circuit mode with a positive group velocity. However, the upper band edge was found to be more susceptible to absolute instability than the lower band edge. The threshold condition for the onset of absolute instabilities is derived analytically at both band edges. The Green's function shows possible transient temporal growth with an exponentiation rate proportional to t1/3, whether or not the band edge is subject to an absolute instability.

Intrinsic resonance in gyrotron using non-resonant RF structure

“…Noteworthily, the absolute instability near the zero group velocity points, similar to the condition in the present study, has recently been carefully re-examined using the BBC, for the conventional traveling-wave tube cases. 50,51 On the other hand, it is important to clarify similarities and differences between the findings presented in this paper and the predictions of classical theories linked to the backward-wave oscillator (BWO) and the traveling-wave tube (TWT). During the linear and start-oscillation stages, as illustrated in Figs.…”

Time simulation of the nonlinear wave–particle interaction in meters-long traveling-wave tubes

“…pulse propagation 44 ) and include harmonics in nonlinear regimes. This advantage was used [45][46][47] to investigate instabilities [48][49][50] at cutoff (near the edge of the transmission band) of TWTs where frequency models have difficulties to describe the situation. Originally, the discrete model was developed to investigate those regimes, especially for coupled cavity TWTs.…”

Recent discrete model for small-signal analysis of traveling-wave tubes

“…Nevertheless, it still fails to describe the situation at the cutoff (near the edge of the transmission band) where Pierce's coupling impedance tends to infinity. This situation, widely studied [14][15][16][17][18], is critical since it generates unwanted oscillations for TWTs. We suggested elsewhere [19] that frequency domain envelope models (not only Pierce's), having the same issue, slightly violate Maxwell equations when coupling is strong.…”