DOUBLE-STREAM AMPUFIERS 667 



The gain in db/wavelength is 



db/wavelength = 20(27r)logioe"'' 



= 54.6 1 h I (16.23) 



We see that, by means of (16.22) and (16.23), we can plot db/wavelength 

 per unit b vs. {U/U mY- This is plotted in Fig. 16.3. Because W is propor- 

 tional to current, the variable (U/UmY is the ratio of the actual current to 

 the current which will just give an increasing wave. If we know this ratio, 

 we can obtain the gain in db/wavelength by multiplying the corresponding 

 ordinate from Fig. 16.3 by b. 



We see that, as the current is increased, the gain per wavelength at first 

 rises rapidly and then rises more slowly, approaching a value 27.36 db/wave- 

 length for very large values of (U/UmY- 



We now have some idea of the variation of gain per wavelength with 

 velocity separation b and with current (U/UmY- A more complete theory 

 requires the evaluation of the lower limiting current for gain (or of Uu) in 

 terms of physical dimensions and an investigation of the boundary conditions 

 to show how strong an increasing wave is set up by a given input signal.^- ' 



16,2 Further Considerations 



There are a number of points to be brought out concerning double-stream 

 amplifiers. Analysis shows® that any physical separation of the electron 

 streams has a very serious effect in reducing gain. Thus, it is desirable to 

 intermingle the streams thoroughly if possible. 



If the electron streams have a fractional velocity spread due to space 

 charge which is comparable with the deliberately imposed spread b, we may 

 expect a reduction in gain. 



Haeff* describes a single-stream tube and attributes its gain to the space- 

 charge spread in velocities. In his analysis of this tube he divides the beam 

 into a high and a low velocity portion, and assigns the mean velocity to 

 each. This is not a valid approximation. 



Analysis indicates that a multiply-peaked distribution of current with 

 velocity is necessary for the existent increasing waves, and gain in a "single 

 stream" of electrons is still something of a mystery. 



