TRAVELING-WAVE TUBES 47 



Then, approximately 



(3.76) 



Let us assume that AF- is very small and retains terms up to the first 

 power of AF- 



h = ^l 4- ^ (3 77) 



Fx "^^ ^ 2{XBu + BXu) ^ ^ 



Let 



Fo = - XB (3.78) 



K?=±i_ ^rg/ro (379) 



Let us now interpret (3.79). This says that if AFo is zero, that is, if XiBi = 

 X2B2 exactly, there will be two modes of transmission, a longitudinal mode 

 in which F2/F1 = +1 and a transverse mode in which V2/V1 = — L If 

 we excite the transverse mode it will persist. However, if AFo 9^ 0, there 

 will be two modes, one for which V2 > W and the other for which F2 < Fi; 

 in other words, as AF5 is increased, we approach a condition in which one 

 mode is nearly propagated on one helix only and the other mode nearly 

 propagated on the other helix only. Then if we drive the pair with a trans- 

 verse field we will excite both modes, and they will travel with different 

 speeds down the system. 



We see that to get a good transverse field we must make 



AFo 



-F « 2(Bn/B + Xn/X) (3.80) 



1 



In other words, the stronger the coupling (^12, X12) the more the helices 

 can afford to differ (perhaps accidentally) in propagation constant and the 

 pair still give a distinct transverse wave. 



Thus, it seems desirable to couple the helices together as tightly as pos- 

 sible and especially to see that Bn and .Y12 have the same signs. 



Let us consider two concentric helices wound in opposite directions, as in 

 Fig. 3.17. A positive voltage Vi will put a positive charge on helix 1 while a 

 positive voltage F2 will put a negative charge on helix 1. Thus, Bn/B is 

 negative. It is also clear that the positive current I2. will produce flux link- 

 ing helix 1 in the opposite direction from the positive current 7i, thus mak- 

 I ing Xii/X negative. This makes it clear that to get a good transverse field 

 between concentric helices, the helices should be wound in opposite direg- 



