When an electron beam is passed through a plasma and modulated by a high frequency signal, there will be modes of propagation along the beam plasma system which have large growth rates. This phenomenon was first demonstrated by Boyd, Field, and Gould . Since that time, the modes of a finite beam passing through a finite plasma column in the presence of a finite magnetic field have been analysed by Bogdanov et al  and Allen et al [3, 4].
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- Normal mode theory for electron-beam plasma amplification
J. C. Eidson
G. S. Kino
- Macmillan Education UK