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.