WAVE PICTURE OF MICROWAVE TUBES 



1351 



The impedance an electron beam sees in traveling through free space 

 or in a concentric lossless tube is capacitive. In section 1 the space-charge 

 waves were described as in\'olving the stored energy of the electric field, 

 capacitive in nature, and the kinetic energy of the electrons, which has 

 an inductive effect. We might liken the beam and its capacitive circuit 

 to the ladder network of Fig. 5. We know that such a network supports 

 waves. 



When the charge of the beam sees a negative susceptance, the be- 

 havior is much as if the capacitances in the ladder network of Fig. 5 were 

 negative.* In this case the waves characteristic of the circuit are not 

 traveling waves, but are a pair of waves, one of which decays with dis- 

 tance and one of which increases with distance. Neither has any net 

 stored energy. 



We can express the propagation constants of the waves much as in the 

 section on, ''Space-Charge Waves," but the effective plasma frequency 

 cog is now imagmary; we will call it jbiq . The phase constants j8i and ^2 



ARRAY OF RESONATORS 



^ 



Mm 



Fig. 4 — In the easitron, resonators surrounding the beam change the suscep- 

 tance the electrons see from positive to negative. The system, no longer supports 

 two traveling waves, but rather, a growing and a decaying wave. 



.^-rw^ 



■^Wo 



rmp' 



Fig. 5 — If the capacitances in this ladder network were negative it would sup- 

 port growing and decaying waves rather than traveling waves. 



* Some care must be used in arriving at proper equivalent circuits. For instance, 

 neither of the electric waves on a ladder network has negative energy if the net- 

 work is set in motion, but we have seen that one of the longitudinal space-charge 

 waves does have negative energj'. If both the capacitances and the inductances 

 of a ladder network are negative, the waves on the network will have negative 

 energies. 



