ISSN 1063-7842, Technical Physics, 2013, Vol. 58, No. 7, pp. 1056–1060. © Pleiades Publishing, Ltd., 2013. Original Russian Text © V.V. Emel’yanov, A.V. Yakovlev, N.M. Ryskin, 2013, published in Zhurnal Tekhnicheskoi Fiziki, 2013, Vol. 83, No. 7, pp. 129–134. 1056 Much efforts have been made in the last few years to develop and fabricate small-size millimeter- and submillimeter-wave oscillators using advanced tech- nologies of vacuum microelectronics (see, e.g., reviews [1–3]). Recent advances in this area of research have opened the way to creating miniature analogues of “classical” vacuum electron devices, among which are reflex klystrons, traveling-wave and backward-wave oscillators, distributed interaction klystrons, etc. These devices will be of great signifi- cance for the evolution of communications, radar, spectroscopy, materials processing, and other applica- tions. A typical problem arising in the design of vacuum microelectronic devices is the need to use electron beams with small cross-sectional sizes and, accord- ingly, with an extremely high current density. A natural way to overcome this difficulty is to apply multibeam structures. In [4, 5], the design of a two-stage klystron oscillator consisting of two floating-drift-tube dual- cavity klystrons was suggested. In this design, the out- put cavity of one klystron is connected to the input cavity of the other and vice versa (Fig. 1). The feasibil- ity of an oscillator with a larger number of stages was discussed. In [6], an elementary mathematical model of an oscillator in the form of a set of differential equa- tions with a delayed argument was developed and ana- lyzed and the numerical simulation of dynamic modes arising when the electron beam current is increased was performed. However, the model developed in [6] is approximate and ignores several important factors, such as space charge forces and the nonlinearity of the electron velocity modulation in the cavities. It gives an adequate qualitative description of the oscillator’s behavior, but more rigorous mathematical models should be employed to quantitatively characterize the practically important parameters of the device (output power, efficiency, etc.). These models are usually based on large-particle methods commonly used in microwave electronics. In this work, the nonlinear dynamics of a two-stage klystron oscillator is simulated in terms of the Vainsh- tein nonstationary theory of cavity excitation [7]. In this theory, the high-frequency field in the cavity gap is given by (1) Here, j, k = 1 or 2; A jk are the slowly varying complex amplitudes; x jk are the coordinates of the centers of the respective gaps; and ω 0 is the resonance frequency, which is assumed to be the same for both cavities. Sub- script jk refers to the k th cavity of the j th klystron E jk Re A jk t () E s x x jk – ( ) e i ω 0 t [ ] . = Computer Simulation of a Two-Stage Millimeter-Wave Klystron Oscillator V. V. Emel’yanov, A. V. Yakovlev, and N. M. Ryskin* Chernyshevsky State University, Astrakhanskaya ul. 83, Saratov, 410012 Russia *e-mail: RyskinNM@info.sgu.ru Received July 3, 2012 Abstract—The results of computer simulation of a two-stage millimeter-wave klystron oscillator are reported. The oscillator consists of two closed-loop floating-drift-tube klystrons with the output cavity of one klystron connected to the input cavity of the other and vice versa. It is shown that 200-W oscillations at a fre- quency of 95 GHz can be reached by optimizing the coupling coefficient between the cavities and the loaded Q factor. DOI: 10.1134/S1063784213070062 RADIOPHYSICS V 0 E 11 E 12 E 21 E 22 1 V 0 4 2 2 1 3 3 Fig. 1. Two-stage klystron oscillator: (1) electron guns, (2) electron beams, (3) coupled cavities, and (4) collectors. 4