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THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1957 



Table II — Measured VERstJs Calculated Space-Charge 

 Half-Wavelengths 



Thus, agreement between this expression and the measured value 

 requires the correct choice of the effective beam radius, h. It turns out 

 that the suitable value for Fig. 5 (3,990 mc) is the average beam radius 

 obtained from ripple data taken with the 0.050-inch iris, and that for 

 Fig. 6 (10,690 mc) is obtained with data taken with the 0.020-inch iris. 

 The results are summarized in Table II. 



With this mechanism as the primary source of the noise gain, it be- 

 comes clear why nearly equal noise maxima were found, with some 

 values of the main focusing field, B, for two values of cathode flux den- 

 sity Be of opposite polarity. From approximate analyses of beam ripples 

 when flux threads the cathode, such as those provided by McDowell^^ 

 and others, it is found that the ripple wavelength depends nearly alto- 

 gether on B. Its amplitude and spatial phase, however, depend on Be , 

 as this affects the beam geometry at the drift-space entrance. For a 

 sufficiently wide range of variation of 5c , the spatial phase of the ripples 

 can be varied from the proper relation wdth the space-charge standing 

 wave for gain, through the positions for de-amplification, and back to 

 gain again. 



I 



V THE GROWING-NOISE MECHANISM 



Although many earlier noise records can be understood in the light of 

 the rippled-beam amplification (RBA) process, this is not yet true of 

 the smooth, steep noise growth usually observed, as in Figs. 2 and 3. 

 The simple theory predicts that a space-charge wave will be amplified 

 when, for small ripples, a "resonance" condition exists between the rip- 

 ple wavelength, L, and the space-chai'ge half-wavelength 



L ^ nXs/2, 



(5) 



where n is an integer, usually unity. In addition, as mentioned earlier, 

 there is an optimum phase relation between ripple and standing wave 

 for maximum gain. These conditions are not satisfied by the records of 



