852 THE BELL SYSTEM TECHNICAL JOUKNAL, JULY 1957 



non-sinusoidal. Other sources of non-linearity are thermal velocities, 

 non-laminar beam flow, etc. As the beat-frequency noise increments at 

 any plane are produced by continuous arrays of freciuency pairs, in- 

 creasing in numbers and amplitude in various ways as primary amplifica- 

 tion proceeds, the multiple standing-wave patterns at the observation 

 frequency progressively overlap one another. This results in the smooth 

 steep rise of noise power usually observed. 



Phase correlation among the space-charge waves excited at succes- 

 sive planes on the beam by the same set of frequency pairs is indicated 

 by gentle dips, due to their destructive interference, in the plateau 

 following the initial noise rise. 



Rippled-beam amplification occurs whenever the ripple wavelength 

 and half the space-charge wavelength are nearly ecjual, and bear a 

 favorable spatial relation to each other. However, this "phase" relation 

 becomes less critical with an increase in either the number of ripple 

 Avavelengths over which synchronism persists, or the ripple amplitude, 

 or both. Noise amplification by this mechanism, therefore, is probably 

 present to some degree in all rippled streams, particularly at high fields. 

 The extreme difficulty encountered in focusing ripple-free beams from 

 convergent, shielded guns has to this date prevented the detection of 

 any other primary gain mechanism, which may conceivabh' co-exist in 

 such beams. 



A conspicuous feature of rippled-beam amplification is the decrease 

 in ripple amplitude due to conversion of dc into ac kinetic energy. Such 

 changes in beam structure emphasize the inadequacy of beam-flow com- 

 putations based entirely on dc force eciuations. A more detailed descrip- 

 tion of this dc-ac energy conversion is given in Part II. 



ACKNOWLEDGMENTS 



The experimental apparatus could not have been built without the 

 combined efforts of man}- associates of the writer, principally A. R. 

 Strnad, P. Hannes, J. S. Hasiak and J. AI. Dziedzic. The author is also 

 indebted to R. Kompfner, C. F. Hempstead and K. M. Poole for valuable 

 suggestions; and above all to C. F. Quate for constant encouragement 

 and advice. 



REFERENCES 



1. C. C. Cutler and C. F. Quate, Experimental Verification of Space-Charge and 



Transit Time Reduction of Noise in Electron Beams, Phys. Rev., 80, p. 875, 

 1950. 



2. L. D. Smullin and C. Fried, Microwave Noise Measurements on Electron 



Beams, Trans. I.R.E. ED-1, No. 4, p. 168, Dec, 1954. 



