

868 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1956 



focusing field need not be considered. The electron beam was produced 

 in a gridded gun and is thus near to the ideal confined flow, which is the 

 only focusing arrangement which is known to determine a reasonably- 

 uniform boundary to the beam. The beam size and straightness was 

 checked using a fluorescent screen at the collector end. \ 



NORMALIZING FACTORS 



The measurements described are expressed relative to the linear 

 theory, in Pierce's' notation, which are generally used in the design of 

 traveling wave tubes. Thus, instead of being presented in the terms of 

 measurement or simply normalized to efficiency, perveance, impedance, 

 etc., they are expressed in terms of C, QC, yro , etc., with normalized 

 fields, currents and velocities. In this way the results become adjuncts 

 to the linear theory and are more easily applied to tube design. Electron 

 velocity is plotted on the same scale as the relative velocity parameters 

 b and yi used in low level theory, (i.e., normalized to AV/2VoC). Effi- 

 ciency is normalized as r]/C, which for C less than 0.1 is relatively inde- 

 pendent of C. Field strength in the linear region is proportional to 



v't 



{ri being efficiency measured at the appropriate signal level). Solving 

 the equation for C , 



>3 E lo 



^ ~WP2Vo ^^^^ 



gives us 



V 



^ (13) 



C /3C2F, 



which we use as the normalizing parameter for electric field. Circuit po- 

 tential is the integral of circuit field over a quarter period, giving a 

 normalized parameter V/VoC . For convenience in the use of common 

 coordinates, circuit potential was plotted as —V/2VoC^ in Figure 7. 



The other curves are plotted as values relative to dc quantities or to 

 saturation level. 



Strictly speaking, the results hold only for tubes having the same pro- 

 portions as the model. Practically, however, as long as the helix imped- 

 ance and radius {ka or ya) are not different by orders of magnitude from 

 the values used, and as long as the perveance is low (below 2 X 10~^ for 



