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This paper is based on a wartime requirement for a 25-watt, 4000-megacycle continuous-wave oscillator capable of electronic frequency modulation with a deviation of at least 2.5 megacycles. A satisfactory solution was found in the addition of frequency control to a continuous-wave magnetron by the introduction of electron beams into the magnetron cavities in a manner described by Smith and Shulman. This method is referred to as "spiral-beam" control. A brief account is given of the method of designing a continuouswave magnetron for the specified power and frequency. The problem of adding spiral-beam frequency control to this magnetron is considered in detail, and a procedure is presented for obtaining the optimum design consistent with negligible amplitude modulation and reasonable cathode-current densities. The unusual features of construction of this magnetron are described, including a method of mechanical tuning and the method of adding grid-controlled beams for frequency modulation. Performance data on the continuous-wave magnetron over a wide range of operating conditions indicate that the required 25 watts output can be attained at 850 volts with 50 per cent efficiency. Experimental results on "spiral-beam" frequency control demonstrate that the required 2.5-megacycle frequency deviation with no amplitude modulation can be achieved by electron beams introduced into two out of twelve cavities. A deviation of 4 megacycles is attained under conditions allowing some amplitude modulation. Still greater deviation is predicted by using more beams.