PART I — THE GROWING NOISE PHENOMENON 



843 



Table I — Measured Versus Calculated Maximum Noise Gain 



confined flow, the published values of reduction factor for both extremes 

 can be used as first approximations. ' ' The ratio ri/ri can be estimated 

 by assuming the current density to be uniform over the beam cross- 

 section near the middle of the drift region, for each of the three apertures 

 used. The potential variations can be neglected. The results of such cal- 

 culations are given in Table I. 



As the computed gains are expected to be somewhat greater than those 

 measured, because of the optimum conditions assumed, the best cor- 

 respondence between measured and computed gain rates appears to be 

 for the ripple data taken with the 0.050-inch iris at 3,990 mc, and that 

 with the 0.020-inch iris at 10,690 mc. This distinction is in accord with 

 previous qualitative comparison of Figs. 5 and 6, showing that most of 

 the beam cooperates in the ripples of the former, but that "inner rip- 

 pling" characterizes the latter. 



Another calculation that reveals which part of the beam is interacting 

 with the RF noise field in each case is that of the space-charge half- 

 wavelength, as follows: 



2 



where 



/3p6 



17^I"'/V"\ 



(2) 



(3) 



Here ^p is the plasma wave number, b the beam radius, and p the reduc- 

 tion factor, which can be evaluated as previously for the smooth beam 

 in either ideal Brillouin or confined flow. For the gun used here, the 

 square root of the perveance is 



or 



X»/2 ^ 29.8 h/p. (4) 



