482 BELL SYSTEM TECHNICAL JOURNAL 



For a linear potential variation in the drift space, at the optimum r-f gap 

 voltage, according to the approximate theory presented in Section III the 

 efficiency for a lossless resonator is 



r? = (.520)(/3F/Fo). (5.7) 



Comparing, we find an improvement in efficiency for the ideal drift tield in 

 the ratio 



■m/r) = 1.23, (5.8) 



or only about 20%. Thus, the linear drift field is quite effective. The 

 ideal drift field does have one advantage; the bunching is optimum for all 

 gap voltages or, for a given gap voltage, for all modulation coefficients since 

 ideallv an infinitesimal a-f voltage will change the transit time from tt to 27r 

 and completely bunch the beam. This should tend to make the efficiency 

 high despite variations in /3 over various parts of the electron flow. The 

 hmitation imposed by the fact that electrons cannot return across the gap 

 against a high voltage if they have been slowed up in their tirst transit across 

 the gap remains. ' 



This last mentioned limitation is subject to amelioration. In one type of 

 reflex oscillator which has been brought to our attention the electrons cross 

 the gap the first time in a region in which the modulation coefficient is small. 

 If the gap has mesh grids, a hole may be punched in the grids and a beam of 

 smaller diameter than the hole focussed through it. Then the beam may be 

 allowed to expand and recross a narrow portion of the gap, where the modula- 

 tion coefficient is large. Thus, in the first crossing no electrons lose much 

 energy (because /3 is small) and in the second crossing all can cross the gap 

 where /3F is large and hence can give up a large portion of their energy^ 



\T. Electronic Gap Loading; 



So far, attention has been concentrated largely on electronic phenomena 

 in the drift or repeller region. To the long transit time across the gap 

 there has been ascribed merely a reduction in the effect of the voltage on the 

 electron stream by the modulation coefficient /3. Actually, the long transit 

 across the gap can give rise to other effects. 



One of the most obvious of these other effects is the production of an elec- 

 tronic conductance across the gap. If it is positive, such a conductance 

 acts just as does the resonator loss conductance in reducing the power out- 

 put. Petrie, Strachey and Wallis of Standard Telephones and Cables have 

 treated this matter in an interesting and rather general way. Their work, 

 in a slightly modified form, ap])cars in Ajipcndix \'III, to wliicli the reader 

 is referred for details. 



