DOUBLE-STREAM AMPUFIERS 661 



By this sort of interaction, a traveling wave which increases as it travels, 

 i.e., a traveling wave of negative attenuation, may be produced. To start 

 such a wave, the electron flow may be made to pass through a resonator or a 

 short length of helix excited by the input signal. Once initiated, the wave 

 grows exponentially in amplitude until the electron flow is terminated or 

 until non-linearities limit the amplitude. An amplified output can be ob- 

 tained by allowing the electron flow to act on a resonantor, helix or other 

 output circuit at a point far enough removed from the input circuit to give 

 the desired gain. 



In general, for a given geometry there is a limiting value of current below 

 which there is no increasing wave. For completely intermingled electron 

 streams, the gain rises toward an asymptotic hmit as the current is increased 

 beyond this value. The ordinate of Fig. 16.3 is proportional to gain and the 

 abscissa to current. 



When the electron streams are separated, the gain first rises and then falls 

 as the current is increased. This effect, and also the magnitude of the in- 

 creasing wave set up by velocity modulating the electron streams, have been 

 discussed in the Hterature.® 



Double-stream amplifiers have several advantages. Because the electrons 

 interact with one another, the electron flow need not pass extremely close to 

 complicated circuit elements. This is particularly advantageous at very 

 short wavelengths. Further, if we make the distance of electron flow between 

 the input and output circuits long enough, amplification can be obtained 

 even though the input and output circuits have very low impedance or poor 

 coupling to the electron flow. Even though the region of amplification is 

 long, there is no need to maintain a close synchronism between an electron 

 velocity and a circuit wave velocity, as there is in the usual traveling- 

 wave tube. 



16.1 Simple Theory of Double-Stream Amplifiers 



For simplicity we will assume that the flow consists of coincident streams 

 of electrons of d-c velocities % and U2 in the z direction. It will be assumed 

 that there is no electron motion normal to the z direction. M.K.S. units will 

 be used. 



It turns out to be convenient to express variation in the z direction as 



exp -j^z 



rather than as 



exp —Vz 



6 J. R. Pierce, "Double-Stream Amplifiers," Proc. I.R.E., Vol. 37, pp. 980-985, Sept. 

 1949. 



