844 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



Two kinds of measurements are described. First, the efficiency and 

 power output are determined for various conditions of operation, and 

 second the spent beam ac velocity and current are measured. The prin- 

 cipal results are shown in Figs. 2 to 4 which give the obtainable effi- 

 ciencies, and in Figs. 7 to 10 which show some of the factors which con- 

 tribute to power saturation. These figures are discussed in detail later. 

 The most significant phenomenon is the early formation of an out-of- 

 phase bunch of electrons which have been violentl}^ thrown back from 

 the initial bunch, absorbing energy from the circuit wave, and inhibiting 

 its growth. The final velocity of most of the electrons is near to that of 

 the circuit wave which would lead to a value of 



limiting efficiency t] = —2yiC (6) 



if the wave velocity maintained its small signal value. Actually the wave 

 slows down, under the most favorable conditions giving rise to a some- 

 what higher efficiency. For other conditions, space charge, excess elec- 

 tron velocity, or nonuniformity of the circuit field enter in various ways 

 to prevent the desired grouping of electrons and result in lower effi- 

 ciencies. 



The observed efficiencies are a rather complicated function of QC, 

 yvo and C. To compare with efficiencies obtained from practical tubes one 

 must account for circuit attenuation and be sure that some uncontrolled 

 factor such as helix non-uniformity and secondary emission is not seri- 

 ously affecting the tubes' performance. Measured efficiencies of several 

 carefully designed tubes have been assembled and are compared with 

 the results of this paper in Table I. 



The results of these measurements compare fa^'orably with the com- 

 putations of Tien, Walker and Wolontis , and of Tien . There are, how- 

 ever some important differences which are discussed in a later section. 



TRAVELING WAVE TUBE EFFICIENCY MEASUREMENTS 



Reasoning from low level theory, efficiency should be a function of the 

 gain parameter, "C," the space charge parameter "QC," the circuit, 

 attenuation, and (for large beam sizes), the relative beam radius "yro ." 

 It was soon found that efficiency is a much more complicated function of 

 y)\i than expected. The iiiilial ()l)jecti\-e was to detoiniine the effect of 

 QC, C, and yr^ separately on efficiency, but it A\'as necessary to gi^'e a 

 much more general coverage of these parameters, not assuming an>' of 

 them to be small. 



Most of the measurements ha\^e been made with small \alues of loss 



