1358 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



Over the range of w/wo for which the waves are attenuated {a j^ 0) 

 the net power flow in each of the modes is zero. The power flow in the 

 electron stream is equal and opposite to that in the circuit. Such behavior 

 is characteristic when two modes with power flows of opposite signs are 

 coupled. It is characteristic of the stop band of an electric wave filter. 



The curves of Fig. 11 exhibit the same behavior that has been found 

 by other means, although similar curves are sometimes plotted somewhat 

 differently. 



When an input signal is applied to the helix of a traveling-wave tube, 

 all three forward waves are set up. The increasing wave grows until it 

 predominates, and it forms the amplified output of the tube. 



The total ac power of the increasing wave is zero. How can we obtain 

 power from it? In the increasmg wave we have a positive electromagnetic 

 power flow in the circuit and an ec^ual negative power flow in the elec- 

 tron stream. If we terminate the helix we can draw off the electromag- 

 netic power; the electron stream is left with less power than it had on 

 entering the helix. 



DOUBLE-STREAM AMPLIFIERS 



A double-stream amplifier makes use of two streams of electrons which 

 have different velocities, as shown in Fig. 12. The behavior of a double- 

 stream amplifier is very similar to that of a tra\'eling-wave tube. In such 

 a device each electron stream supports a slow, negative-energy wave 

 and a fast, positive-energy wave. At a constant frequency w let the 

 velocity U]_ of one stream be kept constant and let the velocity Ui of the 

 other stream be varied. The behavior of the phase constants /3 of the 

 waves is shown quahtatively in Fig. 13. /3«i and jS/i are the phase con- 

 stants of the slow and fast waves of the constant-velocity stream, and 

 /3g2 and /3/2 are the phase constants of the slow and fast waves of the 

 stream whose velocity is changed. There are two ranges of velocity Ui for 

 which gam is obtained; for u-i a little larger or a httle smaller than Ux . 



INPUT I I I 



Fig. 12 — Two nearby electron streams of different velocities u\ and u-i consti- 

 tute a double-stream amplifier. 



