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Particle simulations of mm-wavelength magnetrons with cold secondary-emission cathodes show that such important practical characteristics as the output power, efficiency, and operation current are dependent on secondary-emission properties of the cold cathode used in such magnetrons. However, in some cases, the enhancement of the magnetron characteristics can be achieved with a relatively low secondary-emission yield of the cold cathode. This opens a way for using of pure inexpensive metals for the cathode production. The interplay between the secondary-emission yield and the magnetron performance is studied to realize this approach.