334 



BELL SYSTEM TECHNICAL JOURNAL 



case, as shown in Fig. 2, is simply, /? = — -—. For future reference we will 



6/2, 



write the loss expression for this case as 



J{d) = 2 (1 - cos 6) - 6 sin 6. 



Drift Space Analysis 



Now let us consider the conversion region in a typical velocity-variation 

 tube. Figure 3 is a drawing of several such devices with the conversion 



O 



2IT an 4TT 



TRANSIT ANGLE (9) 



Fig. 1 — The energy transfer between an initially uniform electron stream and a longitudi- 

 nal electromagnetic field as a function of transit angle. 



regions indicated. We will assume for the moment that the electrons enter 

 this region with a small variation in velocity and at a perfectly uniform rate. 

 Since the total number of electrons entering the region must be equal to the 

 number of electrons leaving the region we may write 



or 



ii dti 



ti 



iodto 

 dh' 



