The noise figure of a microwave beam amplifier has a lower limit that depends entirely upon the noise process in the electron gun near the potential minimum. This paper is chiefly concerned with the theory and experimental results of a new method of measuring the noise parameters of the electron beam, especially the correlation between its velocity and current fluctuations, by using a "selective beam coupler" that has properties similar to the conventional microwave directional coupler. An appreciable value for the real part of the correlation coefficient between the velocity and current fluctuations was found in the space-charge-limited region. This value went to zero, or slightly negative, in the temperature-limited region. The probable error in the noise measurements is discussed by taking account of the residual selectivity of the selective beam coupler, the effect of the pickup cavities upon the beam, the thermal noise from the pickup cavities, and the higher-order modes in the beam. Measurements of

, the real part of the correlation coefficient between velocity and current fluctuations, have been made on a number of guns. Under space-charge-limited conditions, the observed values were approximately 0.2 to 0.3. Under temperature-limited conditions,

.