WAVES IN ELECTRON STREAMS AND CIRCUITS 



637 



Another way of putting this is to say 



r.+ F(o,,|3) = 

 From (2.13) and (2.7) we obUin 



j3 = j3o ± ft 



./_m_a 



/3) 



(2.13) 



(2.14) 



ELECTRON 

 STREAM 



■RESONATORS 



Fig. 2.2 — An electron stream passing through a series of resonators, as in a multireson- 

 ator klystron. 



Suppose, for instance, that the circuit admittance is capacitive and is 

 equal to that for a longitudinal electric field in vacuum of area equal to 

 the beam area a. Then 



F(w, j8) = jwe(T mho meter 



and we have two unattenuated waves 



/3 = /3o ± jSp 



We see that whenever (1) the circuit admittance is inductive or (2) the 

 circuit admittance has a dissipative component, jS will be complex, and 

 there will be increasing and decreasing waves. Either of these conditions 

 can be achieved, for instance, by surrounding the electron stream by a suc- 

 cession of essentially uncoupled resonators, tuned to be inductive, or with 

 dissipation, as shown in Fig. 2.2. This is merely a continuous multi-resonator 

 klystron. 



In a transmission-line type of circuit such as we have considered and 

 such as is used in the traveUng-wave tube, for instance, the circuit admit- 

 tance depends strongly on the phase constant /3, and in solving (2.14) for 

 ^ we must take cognizance of this fact. 



We can, for instance, derive the circuit admittance from (1.12). We 

 can use 



E = j^V 



