A Contemporary Study in the Theory of Traveling-Wave Tubes

Abstract

The traveling-wave tube (TWT) is a widely used amplifier in satellite communications and radar. An electromagnetic signal is fed into one end of the device and is amplified over a distance until it is extracted downstream at the output. The physics behind this spatial amplification of an electromagnetic wave is predicated on the interaction of a linear DC electron beam with the surrounding circuit structure. J. R. Pierce, known as the “father of communications satellites,” was the first to formulate the theory for this beam-circuit interaction, which was since used in other electronic devices such as free-electron lasers, gyrotrons, and Smith-Purcell radiators. In this thesis, we extend the classic Pierce theory in two directions: harmonic generation and the effect of high beam current on both the beam mode and circuit mode. The classical Pierce theory was formulated for a single (fundamental) frequency, same as the input signal. However, in a TWT with an octave bandwidth or greater, in particular the widely used helix TWT, the second harmonic of the input signal may also be within the amplification band and thus may also be generated and amplified. There is no input at this second harmonic frequency. An extension to the Pierce formulation that incorporates the generation of harmonics, including non-uniform taper, will be presented. We show that the second harmonic arises mostly from a newly discovered dynamic synchronous interaction instead of by the kinematic orbital crowding mechanism that is the most dominant harmonic generation mechanism in a klystron. The methodology provided may be applicable to the bi-frequency recirculating planar magnetron and other high-power microwave sources. In beam-circuit interactions, the space-charge effect of the beam is important at high beam currents. In Pierce's TWT theory, this space-charge effect is modeled by the parameter which he called Q in the beam mode. A reliable determination of Q remains elusive for a realistic TWT. In this thesis, the author constructed the first exact small-signal theory of the beam-circuit interaction for the tape helix TWT, from which Q may be unambiguously determined. In the process of doing so, it was discovered that the circuit mode in Pierce's theory must also be modified at high beam current, an aspect overlooked in Pierce’s original analysis. We quantify this circuit mode modification by an entirely new parameter that we call q, introduced here for the first time in TWT theory. For the example using a realistic tape helix TWT, we find that the effect of q is equivalent to a modification of the circuit phase velocity by as much as two percent, which is a significant effect equivalent to a detune of two percent. Lastly, we apply the theory developed for Q and q to a high-power TWT amplifier of current interest, the disk-on-rod TWT. For this configuration, the exact analytical forms of these parameters are extracted from the exact dispersion relation, which the author has also constructed. Comparisons of the numerical solutions to the analytic results to simulations done in ANSYS HFSS, ICEPIC, and MAGIC are made.