REFLEX OSCILLATORS 481 



modulated electron stream with the bunching effectiveness of a field with 

 the same drift angle 6 but with a linear variation of potential with distance. 

 Suppose, for instance, that the variation of transit time, r, with energy 

 gained in crossing the gap V is for a given field 



dr/dV (5.2) 



and for a linear potential variation and the same drift angle 



(dr/dV),. (5.3) 



Then the factor F is defined as 



F = (dT/dV)/(dT/dV),. (5.4) 



In appendix V, F is evaluated in terms of the variation of potential with 

 distance. 



The efficiency is dependent on the effectiveness of the drift action rather 

 than on the total number of cycles drift except of course for the phase re- 

 quirements. Thus, for a nonlinear potential variation in the drift space 

 we should have instead of (3.7) 



■n = H/FN. (5.5) 



In the investigation of drift action, one procedure is to assume a given 

 drift field and try to evaluate the drift action. Another is to try to find a 

 field which will produce some desirable kind of drift action. As a matter 

 of fact, it IS easy to find the best possible drift field (from the point of view 

 of efficiency) under certain assumptions. 



The derivation of the optimum drift field, which is given in appendix VH, 

 hinges on the fact that the time an electron takes to return depends only on 

 the speed with which it is injected into the drift field. Further, the varia- 

 tion in modulation coefficient for electrons returning with different speeds 

 is neglected. With these provisos, the optimum drift field is found to be 

 one in which electrons passing the gap when the gap voltage is decelerating 

 take IT radians to return, and electrons which pass the gap when the voltage 

 is accelerating take l-rr radians to return, as illustrated graphically in Fig. 

 136, Appendix VH. A graph of potential vs. distance from gap to achieve 

 such an ideal drift action is shown in Fig. 137 and the general appearance of 

 electrodes which would achieve such a potential distribution approximately 

 is shown in Fig. 138. 



With such an ideal drift field, the efficiency of an oscillator with a lossless 

 resonator is 



Vi = (2/7r)(/3F/Fo). (5.6) 



