Simulation of a 95 GHz Two-Stage Three-Cavity Klystron Oscillator Valeriy V. Emelyanov 1, Yulia P. Emelianova 2, Anton V. Yakovlev 1, and Nikita M. Ryskin 1 1 2 Saratov State University, Saratov, 410012 Russia Yuri Gagarin State Technical University of Saratov, Saratov, 410054 Russia Abstract—A two-stage oscillator consisting of two coupled three cavity klystrons is studied. A small-signal theory of this oscillator is developed, which predicts start-oscillation current and oscillation frequency. Results of 1-D particle-in-cell simulation of the W-band oscillator are presented. The numerical results are in good agreement with the small-signal theory. The simulations predict over 400 W output power with nearly 400 mA beam current. M I. INTRODUCTION ICROFABRICATED vacuum-tube THz sources are of great interest for numerous applications [1]. In particular, a two-stage klystron oscillator was proposed [2,3], which consists of two klystron amplifiers with counter-streaming electron beams. The output cavity of one klystron is coupled through coupling slots with the input cavity of another one and vice versa. The idler cavities are not coupled to each other. RF oscillation excited in the output cavity of one klystron is transmitted through the coupling slot to the input cavity of its counterpart, thus forming a feedback loop. The results of theoretical analysis [4] and numerical simulation of the two-stage double-cavity oscillator [5] have shown that self-excitation of oscillator occurs at nearly 180 mA and output power over 200 W is attained. However, for such values of power rather high values of the beam current (600-700 mA) are required which are hardly feasible in a miniaturized device. To reduce the beam current, we propose the two-stage multiple-cavity oscillator, since a multiple-cavity klystron usually provides significantly higher gain than a double-cavity one. In this paper, we study the W-band oscillator consisting of two coupled three-cavity klystrons. Schematic of the modified three cavity oscillator is presented in Fig. 1. Fig. 1. Schematic of the oscillator. 1 − cathodes; 2 − electron beams; 3 – coupled cavities; 4 – collectors; 5 – idler cavities. TABLE PARAMETERS OF THE TWO-STAGE KLYSTRON OSCILLATOR Resonance frequency (GHz) Shunt impedance (Ohm) Gap width (mm) Distance between the cavities (mm) Unloaded Q-factor Loaded Q-factor Beam tunnel size (mm) 95 35.5 0.3 5 800 550 0.6×0.6 II. RESULTS We developed a small-signal theory of the two-stage three cavity oscillator allowing to calculate start-oscillation current and frequency. In Fig. 2, generation zones in the beam voltage-beam current plane are presented for oscillator with parameters summarized in Table. The results of small-signal theory and numerical simulation are in good agreement with each other. For the simulations we use a 1-D time-domain particle-in-cell (PIC) code recently developed in [5,6]. From Fig. 2 one can see, that adding the idler cavities results in significant reduce of the start-oscillation current. In the threecavity oscillator the start-oscillation current is about 100 mA, while in the two-cavity one it was no less than 180 mA [5]. We performed calculations of output power, efficiency, and oscillation frequency in a wide range of control parameters. In particular, loaded Q-factor and coupling coefficient between the cavities were optimized in order to achieve maximal Fig. 2. Generation zones in the beam voltage-beam current plane. Small-signal theory and numerical results are shown with solid lines and circles, respectively. At higher values of the current, there appear non-stationary self-modulation regimes. A complicated sequence of bifurcations resulting in transition to chaos takes place with the increase of the current (see [4,5] for details). In such regimes, the strong modulation of the output power is observed, and the averaged power decreases significantly. In Fig. 3(b) and (c) output power for two neighboring generation zones ( V0  17.7 kV and 15.1 kV) are plotted. For these zones, self-modulation arises at significantly smaller currents. As a result, peak output power is 2–2.5 times smaller. However, the parameters were optimized for 16.4 kV beam voltage. Adjusting coupling between the cavities and loaded Q-factor, one can enhance the self-modulation threshold current. Consequently, the output power will increase. III. CONCLUSION In conclusion, we propose a two-stage klystron oscillator consisting of two chained three-cavity klystrons. Output characteristics of the W-band oscillator are calculated. The start oscillation current for the three cavity oscillator is nearly twice less than for the double-cavity klystrons [5]. The output power may be raised above 400 W by optimizing the coupling coefficient and loaded Q-factor. In addition, this value of power is attained at smaller currents than for the double-cavity oscillator (400 mA versus 600 mA). The main factor, which restricts the output power, is the appearance of selfmodulation with the increase of the beam current. Our further study will be aimed at investigation of the generator consisting of larger number of klystrons, as well as with larger number of cavities. IV. ACKNOWLEDGMENT This work is supported by Russian Foundation for Basic Research, Grants 14-02-31410 and 14-02-00976a. Fig. 3. Output power of two partial klystrons (triangles, squares) and total power (circles) versus beam current: (a) V0  16.4 kV; (b) 17.7 kV; REFERENCES [1] (c) 15.1 kV. Domains of self-modulation are shaded. output power. Fig. 3(a) shows the total output power (i.e. sum of the output powers of the two cascades) vs. the dc beam current at V0  16.4 kV in the center of the generation zone (see Fig. 2). In this simulation, the loaded Q-factor is reduced to 300 in order to maximize the output power. When the beam current exceeds the self-excitation threshold value a symmetric steady-state generation regime is observed. In this regime, output powers of the both klystrons are equal. The increase of beam current results in gradual increase of the output power. When the beam current exceeds 390 mA symmetry-breaking bifurcation takes place and non-symmetric regime with non-equal amplitudes arises [Fig. 2(a)]. Maximal power of 410 W is attained at beam current 420 mA. View publication stats [2] [3] [4] [5] [6] J.H. Booske, R.J. Dobbs, C.D. Joye, et al., “Vacuum electronic high power terahertz sources”, IEEE Trans. Terahertz Sci. Technol., vol. 1, no. 1, pp. 54-75, September 2011. Y.M. Shin, S.T. Han, S.G. 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