PART I — THE GROWIXG NOISE PHENOMENON 841 



near 10.69 knic, is shown in Fig. 6. The significant features of both sets 

 of records can be summarized as follows: 



(1) In both cases, the beam-ripple periods are equal to the RF scallop 

 periods; i.e., the half-wavelengths of the space-charge standing waves. 

 The noise minima tend to occur at planes where the collector currents 

 are at their average values and decreasing; i.e., where the beam diame- 

 ters are at their average values and increasing. The noise-current maxima 

 occur where the beam diameters are about to decrease. These are the 

 classical conditions for rippled-beam amplification. ' ' 



(2) In Fig. 5, the ripple amplitudes and peak values of all three col- 

 lector-current curves decline appreciably with distance, the rate of de- 

 cline being greatest for the smallest aperture. (Similar curves, not shown 

 here, have displayed little or no such decline in the absence of noise 

 growth.) This suggests that the RF noise power is amplified at the ex- 

 pense of do energy associated with radially-directed electron velocities. 



(3) In Fig. 6, the disparity among rates of decline of current-ripple 

 amplitudes and their peak values, for the three aperture sizes, is even 

 more pronounced. In addition, the ripple wavelength barely changes 

 for the^ 0.100-inch aperture, but increases with drift distance for the 

 smaller apertures, resulting in an increasing "phase shift" among them. 

 Thus the current-density variations at different radii in the beam can 

 contribute unequally to space-charge wave amplification, depending ori 

 their local ripple amplitude and phase. In this instance, the variations 

 in current density along the beam are initially greatest near the axis, 

 and suffer the greatest reduction there. It is worth noting that this 

 "inner rippling" would be missed entirely in beam-size measurements 

 with a large aperture.* 



The decrease of beam ripple and the increase in average beam diame- 

 ter, shown in Figs. 5 and 6, has been found to accompany rippled-beam 

 amplification of impressed signals by T. G. Mihran. Another corrobora- 

 tion of the identity of this gain mechanism can be obtained by comparing 

 the measured noise gain per scallop with that predicted by theory for 

 idealized conditions. ' For a beam with stepwise alternations of maxi- 

 mum and minimum beam diameters (ratio r2/ri), and with noise maxima 

 and beam-diameter maxima coinciding, the gain per scallop is as follows: 



Gr,. = {;^ - ^. (1) 



Here, V is the beam potential, and p the reduction factor w^/ajp . Al- 

 though the actual rippled beam is far removed from either Brillouin or 



* More information about "inner rippling" will be presented in Part II. 



