A LARGE SIGNAL THEORY OF TRAVELING- WAVE AMPLIFIERS 361 



equipment. The problem was programmed by Miss D. C. Legaus. The 

 cases computed are listed in Table I in which m and m2 are respectively 

 Pierce's .xi and iji , and A,(d — iny) and tj at saturation will be discussed 

 later. All the cases were computed with A^ = 0.2 using a model based 

 on 24 electron discs per electronic wavelength. To estimate the error 

 involved in the numerical work, Case (10) has been repeated for 48 elec- 

 trons and Cases (10) and (19) for Ay = 0.1. The results obtained by 

 using different numbers of electrons are almost identical and those ob- 

 tained by varying the inter\'al A// indicate a difference in A (y) less than 

 1 per cent for Case (10) and about 6 per cent for Case (19). As error 

 generally increases with QC and C the cases listed in this paper are 

 limited to QC = 0.4 and C = 0.15. For larger QC or C, a model of more 

 electrons or a smaller interval of integration, or both should be used. 



7. POWER OUTPUT AND EFFICIENCY 



Define 



A(ij) = HVa,(yy + aM' 



-0(y)=i^n-'^-^ + by ^^^^ 



aiiy) 



We have then 



F{z,t) = ^A{y) cos 



^ -^t- e{y) 



Uo 



(22) 



The power carried by the forward wave is therefore 



2CA'hVo (23) 



(f) = 



\Z/o/ average 



and the efficiency is 



Eff. = ?£^^ = 2CA' or ^ = 2CA' (24) 



In Table I, the values of A(y), 6{y) and y at the saturation level are 

 listed for every case computed. We mean by the saturation level, the 

 distance along the tube or the value of y at which the voltage of the 

 forward wave or the forward traveling power reaches its first peak. 

 The Eff./C at the saturation level is plotted in Fig. 1 versus QC, for 

 k = 2.5, h for maximum small-signal gain and C = small, 0.05, 0.1, 0.15 

 and 2. It is also plotted versus h in Fig. 2 for QC = 0.2, k = 2.5 and 

 C = small, 0.1 and0.15, and in Fig. 3 for QC = 0.2, C = 0.1 and k = 1.25 

 and 2.50. In Fig. 2 the dotted curves indicate the values of h at Avhich 



