474 BELL SYSTEM TECHNICAL JOURNAL 



In the expression for the admittance, the drift angle, 6, appears as a fac- 

 tor. This factor plays a double role in that it determines the phase of the 

 admittance but also in a completely independent manner it determines, 

 in part, the magnitude of the admittance. 6 as it has appeared in the 

 foregoing analysis, which was developed on the basis of a linear retarding 

 field, is the actual drift angle in radians. As will be shown in a later section, 

 certain special repeller fields may give effective drift action for a given angle 

 greater than the same angle in a linear field. Such values of effective drift 

 angle may have fractional optimum values although the phase must still be 

 such as to give within the approximations we have been using a pure con- 

 ductance at optimum. In order to generalize the following work we will 

 speak of an effective drift time in cycles, N e = FN, where N is the actual 

 drift time in cycles, n -\- f , and F is the number of times this drift is more 

 effective than the drift in a linear field. 



Suppose we have a tube of given /3^, 7o , Fo and resonator loss Gr and wish 

 to find the optimum effective drift time, FN, and determine the effect on the 

 efl&ciency of varying FN. It will be recalled that for very low losses we may 

 expect more power output the fewer the number of cycles drift. How- 

 ever the resonator losses may cut heavily into the generated power, for 

 short drift angles. With short drift angles the optimum load conductance 

 becomes small compared to the loss conductance so that although the 

 generated power is high only a small fraction goes to the useful load. There 

 is, therefore, an optimum value which can be obtained using the data of 

 Fig. 7. We define a parameter 



K = |^«G. (3.9) 



which compares the resonator loss conductance with the small signal elec- 



C K 



tronic admittance per radian of driftan gle. Then in terms of A', — = -— . 



Je B 



Hence, for a fixed value of K, various values oi 6 = lirFN define values of 



/^ 



— . When one uses these values in connection with Fig. 7 he determines 



Je 



the corresponding values of //„, and hence the efficiency, r] = — ^ . These 



values of r] arc plotted against FN as in Fig. 8 with values of A' as a param- 

 eter. In this })lot A' is a measure of the lossiness of the tube. The opil- 

 mum drift angle for any degree of lossiness is evident as the maximum 

 of one of these curves. 



The maximum power outputs in various repeller modes, « = 0, 1 etc. 

 and the repeller voltages for these various power outputs correspond to 

 discrete values of n and FN lying along a curve for a particular value of A'. 



