HIGH-FREQUENCY A MPUI'IER 



43 



Here F{W/Wm)- is the function plotted in Fig. 3. If (. is the total length 

 of the tlow, the total gain in db, G, will thus be 



As 



(30) 



We will now express (W/IVm)' in such a form as to indicate its dependence 

 on wavelength in the beam, X^ . We can write from (27) 



11' = 



X? 



Here K is a "plasma wavelength," defined by the relation 



Wo 



X« = 



(coe/27r) 



We further have 



Wl = PH(a/\s) 



Here H(a/\s) is the function of (a/Xs) which is plotted in Fig. 5. 



(31) 

 (32) 



25 



^ 20 



^ 





10 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 



bcy/oje 



Fig. 5 — In these curves the total gain in db, G, divided by the ratio of the length / to 

 the plasma wavelength \e , is plotted vs. bco/ue, which is proportional to frequency, for 

 several values of the parameter {a/bXe)^- Changing b, the velocity seperation, changes 

 both the parameter and the frequency scale. 



Now, from (26), (27), and (29) we can write 



G -(-)( — I ( ;■ ) /' 



kJ \ a 



bXeJ Hia/\s)_ 



(34) 



For a given tube the parameters {(/\e) and (a/b\e) do not vary with fre- 

 quency, while (a/Xs) is proportional to frequency. Hence, we can construct 

 universal frequency curves by plotting G/{C/Xe) vs. (a/Xs) for various values 

 of the parameter (a/bXe). It is more convenient, however, to use as an 

 abscissa bXg/Xs — bu/wg , and this has been done in^Fig. 5. 



