PART I — THE GROWING NOISE PHENOMENON 847 



and short space-charge wavelengths correspond to high frequencies, 

 where the former change very slowly with frequency. 



(b) Second stage 



When noise power over this large band has been amplified sufficiently, 

 electron bunching becomes non-sinusoidal, and the beam becomes non- 

 linear. Harmonics and beat-frequencies^ of the fundamentals, and pos- 

 sibly sub-harmonics, are excited. As the beat-frequencies are excited 

 by a continuum of pairs of frequencies, their standing-wave patterns 

 overlap one another, resulting in a "wash-out" of the noise minima, and 

 a smooth growing-noise pattern. Eventually, the same non-linear proc- 

 esses take place within this subsidiary band, leading to a gradual leveling 

 of the entire noise spectrum. The initial rates of rise of the intermodula- 

 tion products, however, should take place closer to the gun and be 

 greater, for a lower freciuency. They will depend on both the spectrum 

 of noise power in the primary band and, so to speak, the spectrum of 

 "beam non-linearity" within that band. 



To simulate this intermodulation process, two low-level klystron sig- 

 nals (9,050 and 12,275 mc, respectively) were simultaneously permitted 

 to modulate the electron beam as it entered the drift tube, by means of 

 a short length of lossy helix. The magnetic fields at the cathode and in 

 the drift space were adjusted to produce a beam ripple which amplified 

 both of these signals simultaneously over most of the drift space, as 

 shown in Fig. 8 (a, b, c).* Noise-power records were then made at the 

 difference-frequency, in the presence of the two modulation signals. 

 Fig. 8(d), and in their absence, Fig. 8(e). The difference between the 

 noise levels in the latter two records increases with distance, as both 

 parent space-charge waves grow in amplitude, and the degree of beam 

 non-linearity increases. Naturally, the contribution to 3,295-mc noise 

 in the absence of modulating signals is far greater than that of the latter 

 two alone, as the primary bandwidth of noise amplified is very great, 

 and that of the signals very small. 



There are several reasons why exponentially-growing noise should 

 stop growing and level off, and sometimes even decrease .slightly: 



(1) depletion of dc kinetic energy in the beam ripples; 



(2) de-amplification in the fundamental band, due to departure from 

 the proper phase relation for gain between standing wave and ripple, 

 if only over part of the band (Fig. 3); 



* The fine ac detail superimposed on the pattern of Fig. 8(b) is due to inter- 

 ference between the waves traveling along the beam and that propagating as a 

 waveguide mode in the drift space. 



