Trivelpiece A W & Gould R W. Space charge waves in cylindrical plasma columns. J. Appl. Phys. 30:1784-93, 1959

“This paper had its origins in a summer of 1956 project to build 1,420 mc low noise traveling wave tubes for use as preamplifiers in the Caltech radio telescope. The tubes that I built had measured noise figures that were much worse than the predicted theoretical minimum of six db. I used the standard low noise tube design formulae, which had been previously demonstrated to result in tubes that could achieve the six db minimum, albeit at higher frequencies. These low noise design formulae are based on the one dimensional Lewellyn-Peterson equations. To explore the possibility that the design formulae needed to be modified for tubes in this lower frequency range, I used the HahnRamo equations for space charge waves on electron beams to analyze how three dimensional effects might influence the propagation of velocity and current noise disturbances on a drifting electron beam. “In the course of this work, the case of a nondrifting electron beam was explored. The dispersion relation derived for zero drift velocity predicted that slow (phase velocity much less than c) space charge waves could propagate below the plasma frequency on an electron beam (plasma) filling a conducting tube that would otherwise not support any propagating electromagnetic Trivelpiece A W & Gould R W. Space charge waves in cylindrical plasma columns. J. Appl. Phys. 30:1784-93, 1959. [California Institute of Technology, Pasadena, CA]