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The principle of using a variable reactance in a circuit to produce gain can be applied to an electron beam. The beam is strongly modulated by an rf wave at a frequency equal to twice the signal frequency. In such a beam the two normal space charge waves at the signal frequency break into two partsÂ¿one grows exponentially with distance and the second is attenuated. Either the "slow" or the "fast" space charge wave can be amplified. When this beam, which has been previously modulated at the double frequency, is coupled to a slow wave circuit, growing waves are found and again the "fast" space charge wave can be amplified. We stress the amplification of the fast wave since the noise theorems which apply to previous microwave amplifiers and establish a lower limit to the noise figure do not apply. Thus, in principle, we should be able to obtain lower values for the noise figure.