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A two-port magnetron model is discussed whose opposing cavities are coupled by an external wave channel with a common load. The resonance frequencies of equivalent circuit are calculated and analysis is made of the effect of impedance properties of the load on the mode spectrum, that is, frequency pulling and occurrence of hysteresis instability.Generating electronic devices of the microwave range have space-developed cavity systems and are characterized by a set of natural oscillations, that is, modes with a fairly dense frequency spectrum. The transitions between competing oscillation modes are the strongest factors of spectral and time instability of the generation process and result in a low radiation quality. However, the problem of mode and spectral stability is very topical for short-pulse high-power relativistic oscillators operating in the conditions of nonstationary emission processes [1,2]. An effective way taking advantage of the distributed character of high-frequency fields was proposed for stabilizing and controlling the generation processes [3,4]. This method is based on the possibility of separating out oscillating subsystems within the space-developed cavity system of the device and introducing external controlled couplings between them. Constructivism of the approach is due to the fact that the system, phenomenologically, becomes similar to a coherent system of self-excited oscillators with intrinsic (by means of electron flow) and external interconnection. The methods of theory of mutual synchronization can be applied to theoretical investigations into such systems with external couplings [5][6][7][8]. The external coupling, as our experience suggests, significantly affects spectral characteristics of radiation of the relativistic magnetron [9, 10].The aim of the work is to analyze the effect of impedance properties of the coupling channel with a common load on the magnetron mode spectrum: frequency pulling and occurrence of hysteresis instability. RESONANCE FREQUENCIES OF A MAGNETRON WITH EXTERNAL CAVITY COUPLINGNatural frequencies of a magnetron cavity system correspond to a certain azimuthal distribution of high-frequency fields -oscillation modes. A priori knowledge of these fields allows us to separate out fragments of a single electromagnetic process and construct a multipole oscillator model [7,8]. Figure 1 shows an equivalent circuit of a six-cavity magnetron whose opposing resonators are coupled by a wave channel with a common load: ρ and L are the wave impedance and length of a transmission-line section and l R is the common load. The magnetron is presented by the parallel resonance circuits and capacities separating them. Assuming the system to be azimuthally-symmetrical, we consider the inductions 0 L , capacities 0 C , conductivities 0 G , and capacities 1 C (capacities between the anode vanes and cathode) to be similar. It should be noted that the poles of coupling channel are parallelly connected to the cavities. In fact, the cavity system of the magnetron is connected to the ex...

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