DOUBLE-STREAM AMPLIFIERS 



665 



the 



s a^ IS a factor greater than unity, which merely expresses the fact that 

 charge density corresponding to a given voltage is somewhat greater 



man if there were field in the z direction only for which equation (16.12) is 



valid. Combining (16.14) with (16.11) we obtain 



(-(-0-)"(-(-O-) 



^eU- 



(16.15) 



Fig. 16.2 — This shows a circuit curve, 3, and two electronic curves which give the 

 sum of the charge densities of the two streams divided by the voltage which bunches them. 

 With curve 2, there will be four unattenuated waves. With curve 1, which is for a higher 

 current density than curve 2, there are two unattenuated waves, an increasing wave and 

 a decreasing wave. 



where 



W = 



/o 



2a ejSeWoFo' 



(16.16) 



In solving (16.15) it is most convenient to represent (i in terms of )3« and 

 a new variable h 



^ = /3,(1 + h) 



Thus, (16.15) becomes 



i'-th'i) 



1^ 



(16.17) 

 (16.18) 



