160 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1956 



0.5 



1.0 



1.5 



2.0 



2.5 3.0 



/3o a COT j^. 



3.5 



4.0 



4.5 



5.0 



Fig. 3.1 — The radius r at which the longitudinal field is zero for transversely 

 excited coupled coaxial helices. 



is by using a dispersive circuit, (i.e. one in which the phase velocity varies 

 significantly with frequency). Thus, we obtain an amplifier that can be 

 limed by varying the beam voltage; being dispersive we should also 

 expect a low group velocity and therefore higher circuit impedance. 



Calculations of the phase velocities of the normal modes of coupled 

 concentric helices presented in the appendix show that the fast, longitu- 

 dinal or (+ + ) mode is highly dispersive. Given the geometry of two 

 such coupled helices and the relevant data on an electron beam, namely 

 current, voltage and beam radius, it is possible to arrive at an estimate 

 of the dependence of gain on frecjuency. 



Experiments with such a tube showed a Ijandwidth 3.8 times larger 

 than the simple estimate would show. This we ascribe to the presence 



