Analysis of Non-Uniform Cathode Emission and Backward Wave Oscillations in a Traveling Wave Tube

Abstract

The traveling wave tube (TWT) is a vacuum electronic device that provides wide bandwidth and high gain amplification of radio-frequency signals for applications in radar, electronic warfare, and satellite communications. The TWT operates by transferring the kinetic energy of an electron beam to the input signal via synchronous interaction with a periodic circuit structure. In this thesis, we theoretically analyze various realistic effects that are of contemporary interest.

The classical theory describing TWTs was developed by J. R. Pierce some 70 years ago. A recent exact theory on a tape-helix TWT concluded that Pierce’s theory omitted the potentially important detuning effect on the circuit mode at high beam currents. However, this exact theory excluded ohmic losses in the circuit, which are always present in a realistic TWT. This thesis included circuit loss in the exact theory. We find that the exact and Pierce’s classical theories agree well only in a restricted frequency range. The discrepancies are due to the effect of higher order circuit modes and their space harmonics, included in the exact theory but neglected in Pierce’s classical theory. Backward wave oscillations (BWOs) pose a threat to the stable operation of TWTs. They are caused by the interaction of the electron beam with the backward propagating wave on the circuit. The threshold condition for BWO excitation was formulated by H. R. Johnson. This thesis extends Johnson’s theory to include the effects of random manufacturing errors on the circuit, motivated by recent attempts to operate TWT in the terahertz regime. At such high frequencies, the circuit size is substantially reduced, making manufacturing errors proportionally much more significant. We showed that, surprisingly, Johnson’s threshold beam current required for BWO excitation is insensitive to the effect of random manufacturing errors whose presence could alter the delicate synchronous interaction between the electron beam and the circuit’s backward wave. An interpretation of this unexpected result is given. We found, however, that the threshold conditions for BWO excitation depend sensitively on the phase and magnitude of the reflection coefficients at the ends of the TWT.

Lastly, we consider thermionic cathodes used in TWTs. To preserve cathode life, and therefore the life of the TWT and the satellite carrying it, it is imperative to operate the cathode at the lowest possible temperature that provides sufficiently high current. Thus, thermionic cathodes are typically operated near the transition between thermionic emission and space-charge-limited emission. In the plot of anode current vs cathode temperature (Miram curve), this transition is smooth and broad in experiments, a feature no physical theory can replicate to date. A sharp and abrupt transition is highly desirable, usually simulated but difficult to achieve in practice. This thesis made an attempt to solve this outstanding puzzle. An analytic theory is formulated to show how non-uniform emission arising from 2-dimensional work function variations on the cathode surface can affect the shape and location of this transition. Also addressed are various factors which could affect the Miram curve, such as strongly-emitting local spots, various non-emitting regions, and the emission feature size. We show that the anode current is still governed by the 1-dimensional Child-Langmuir law, as if the entire cathode was emitting despite the existence of significant non-emitting areas. The analytical theory is in excellent agreement with particle-in-cell simulation.