PART I — THE GROWING NOISE PHENOMENON 851 



is simultaneously modulated as before with two klystron signals (8,400 

 and 11, 590 mc, respectively), but now at fairly high level; and the fo- 

 cusing field is made large. The interference dips in the pattern of 3,120-mc 

 noise are quite deep, and are spaced irregularly and farther apart than 

 the space-charge wavelength of any of the three frequencies involved. 

 The third dip is shallower than the previous two because of the growth 

 of 3,120-mc noise other than that due to the signals, as shown in Fig. 

 9(c). The latter pattern of noise in the absence of the two high-level, 

 high-frequency signals suggests that the characteristic first gentle dip 

 following the growing-noise region is indeed of the same nature as the 

 artificially-produced interference dips, and has nearly the same cjuasi- 

 period. 



The pattern of dips agrees with simple calculations, based on this 

 model, in which the amplitude of the difference-frequency intermodula- 

 tion product, excited at any plane f , is assumed proportional to the prod- 

 uct of the amplitudes of the two high-frequency space-charge standing 

 waves, as follows: 



\di,\ oc |ti(f)-z2(r)(^rl, (7) 



where 



in = In sin p„l3p^- sin co„(^ - t/u), (n = 1,2). 



The total current at f = ^ is the sum of contributions from all the stand- 

 ing waves excited to the left of it : 



1 f^ 



I t3 I cc -/1/2 / COS P3(3p(2 - f)[C0S (pi - 7)2)i3pf 



4 Jo (8) 



- cos (pi -{- P2)0p^] f/f . 

 This expression is readily integrated and evaluated. 



VI CONCLUSIONS 



Synchronized measurements of electron-current density and noise 

 currents at several microwave frequencies have shown that the "growing 

 noise" pattern in drifting cylindrical beams is the result of a two-stage 

 process. In the first stage, rippled-beam amplification of noise fluctua- 

 tions takes place over a very broad band of microwave frequencies, 

 much higher than the usual observation frequency. In the second, noise 

 energy is transferred to lower frec^uencies by intermodulation and other 

 non-linear processes within this band. The element of non-linearity is 

 supplied when primary noise gain is sufficient to make electron bunching 



