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An analytical estimation has been performed to determine the optimal parameters of pulsed magnetrons, operating at a spatial harmonic at a frequency of 35 GHz and an anode voltage of 6.5 kV in the drift-resonance mode, with the main cathode being the cold secondary-emission one. A 3D simulation experiment on a magnetron with the analytically determined characteristics has been conducted to check its adequacy in providing the required energy parameters. The breadboard magnetrons have the number of vane-type resonators in the anode unit N = 20 and N = 16 , respectively. The both magnetrons have generated the electromagnetic radiation in the Ka range with the magnetic field being slightly above 0.4 Т. It was proven that it is possible to create a full-functional Ka -range magnetron with a relatively low anode voltage and such parameters that enable its wide applicability.