Simulation of 650 GHz Backward Wave Oscillators

Similar to travelling wave tubes a backward wave oscillator (BWO) is a device for converting DC power into RF power. Furthermore, it uses also the same working principle, namely the application of DC power to an electron gun resulting in a steady electron beam. This electron beam interacts with a slow wave structure to excite RF power. While the backward wave (the wave travelling in the opposite direction as the electrons) in a travelling wave tube is a limiting factor, it is exactly this wave which is used in backward wave oscillators. The intensity of the backward wave is dependent on the beam current level, the slow wave geometry, focusing and the transition regions to absorb the final RF wave. The frequency of the backward wave is determined by the transit time or velocity of the particles and therefore simultaneously by the initially applied DC power. More information can be found in [1].

The design of the backward wave oscillators was invented and published by Carol L. Kory and James A. Dayton Jr., Teraphysics Corporation, USA [2]. One device (shown in figure 1 left) is based on a biplanar interdigital slow wave structure, where the beam moves between the opposing fingers.

The other device (shown in figure 1 right) is realized by a helical structure, where the beam moves outside of the helix.

Both backward wave oscillators are designed to provide an output power at a frequency of 650 GHz. The beam profiles of the new designs are represented by the emission surfaces shown in figure 2. The beam voltage is in both cases 12kV. The current is 2mA in the interdigital and 10mA in the helical case, respectively.

The time signal of the output power is directly recorded with waveguide ports known also from CST MICROWAVE STUDIO® (CST MWS). The waveguide ports are positioned according to figure 3.

Figure 4 shows on the left hand side the signal received at the waveguide port for the interdigital BWO including conductor losses. Obviously, the steady state condition has been reached. Since the signal is recorded in terms of wave amplitudes, the resulting output power can be easily determined by taking the square of the time signal. The spectrum of the signal, evaluated with the template based postprocessing, shows nicely the peak at 650 GHz for which the BWO was designed.

The time dependent particle trajectory of the beam is shown in figure 5 from initial to steady state condition. The color indicates the velocity of the particles. Thus, the modulation of the particle velocity due to the interaction of beam and slow wave structure can be seen.

The phase space plot for an instance of time, where the steady state condition is reached, is shown in figure 6.  The aforementioned modulation of the particles becomes again obvious. Furthermore, the energy transfer between particles and RF wave is demonstrated by the decreasing average energy.

So far only the results of the interdigital BWO including conductor losses have been demonstrated. The time signal and spectrum of the lossless interdigital BWO, the lossless helical BWO and the helical BWO with conductor losses are quite similar. They of course differ in the steady state amplitude.  The table below gives an overview of the different output powers obtained with the classical analysis (see [2] and references [3,4]),  MAFIA and CST PS. The results are courtesy of Teraphysics Corporation, USA. 

The results of CST PS show excellent agreement with classical analysis. The lossless simulations can already in principle be perfomed within MAFIA, the predecessor of CST PS. However, the lossy simulations need either additional approximations or are even impossible. Since CST PS benefits from many features initially developed for CST MWS as for example waveguide ports, lossy metal models and PERFECT BOUNDARY APPROXIMATION (PBA)®, such a simulation can conveniently be performed with CST PS.

References:

[1] A. S. Gilmour Jr., "Principles of Travelling Wave Tubes", Artech House, Inc, Norwood, MA, USA, 1994.

[2] C. L. Kory and J. A. Dayton, Jr., "Interaction Simulations of Two 650 GHz BWOs Using MAFIA", Proceedings of the IVEC 2008, Monterey, USA, April 22-24, p. 390-391, 2008.

[3] J. W. Gewartowski, H. A. Watson, "Principles of Electron Tubes", D. Van Nostrand Company, Inc, New York, 1965.

[4] R. Grow, D. Gunderson, "Starting Conditions for Backward Wave Oscillators with Large Loss and Large Space Charge", IEEE Trans. ED, Vol. ED-17, No. 12, 1970.