34 BELL SYSTEM TECHNICAL JOURNAL 



The important factors in the interaction are the electric tield, which stores 

 energy and acts on the electrons, and the electrons themselves. The charge 

 of the electrons produces the electric field; the mass of the electrons, and 

 their kinetic energy, serve much as do inductance and stored magnetic 

 energy in electromagnetic propagation. 



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 resonator, helix or other 

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

 the desired gain. 



There are several advantages of such an amplifier. 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 imped- 

 ance 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. 



A companion paper by Dr. A. V. Hollenberg of these laboratories describes 

 an experimental "double stream" amplifier tube consisting of two cathodes 

 which produce concentric electron streams of somewhat different average 

 velocity, and short helices serving as input and output circuits. No further 

 physical description of double stream amplifiers will be given in this paper. 

 Rather, a theoretical treatment of such devices will be presented. 



2. Simple Theory 



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

 of electrons of d-c. velocities Ui and «2 in the .v direction. It will be assumed 

 that there is no electron motion normal to the x direction. The treatment 

 will be a small-signal or perturbation theory, in which products of a-c. 

 quantities are neglected. M.K.S. units will be used. All quantities will 

 be assumed to vary with time and distance expj{ul — )3.v). The wavelength 

 in the stream, Xg , is then related to /3 by 



/3 = 2t/X. (1) 



