1354 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



part of a wave approaching it. In other terms, each capacitance acts to 

 couple one mode or wave (say the forward wave) to another (say, the 

 backward wave). When the distance between the capacitances is such 

 that the couplings reinforce, that is, near a half wavelength in this case, 

 the system is a filter in its stop band ; it does not transmit traveling waves, 

 but supports rather a wave which increases exponentially with distance 

 and a wave which decays exponentially with distance. Neither of these 

 waves alone carries any power. 



The space-charge waves of an electron stream can be coupled to one 

 another, to a space-charge wave of another stream, or to an electromag- 

 netic A\ave. In any of these cases we can have increasing waves. 



THE SPACE-CHARGE-WAVE AMPLIFIER 



Consider an electron beam surrounded by a series of metallic tubes 

 A, B, A, B ■ • • , alternately at different potentials with respect to the 

 cathode from which the electrons come, as shown in Fig. 7. The impe- 

 dances of the space-charge waves will be different in tuloes ^4 from what 

 they are in tubes B. The behavior of this system is much like that for the 

 transmission line system shown in Fig. 8, in which we have alternate line 

 sections of different characteristic impedances Ka and Kb. We know that 

 such a series of line sections forms a filter ^vith stop bands. 



Fig. 7 • — The impedances of waves in an electron beam passing through elec- 

 trodes at alternate!}' higher and lower potentials differ in regions of different po- 

 tentials. This can result in stop bands characterized by growing and decaying 

 waves. Such a device is a space-charge-wave amplifier. 



Fig. 8 — A transmission line with alternating sections of impedances K^ and 

 Kb is somewhat analogous to the space-charge-wave amplifier. 



