Plasma oscillations are here treated for a frequency range having application not only to gaseous discharges but also to solids such as impurity semiconductors.Amplification of longitudinal electrostatic waves in a plasma may be achieved through energy exchange with a synchronously traveling electron beam, this being the same mechanism which underlies amplification in the traveling‐wave tube. The dispersion equation describing this beam‐plasma interaction, first derived by Bohm and Gross, is studied systematically to obtain the characteristics of the growth‐in‐time, &ohgr;vs&kgr;, of standing plasma waves and the complex propagation constant &kgr;vs&ohgr; for traveling plasma waves, at extremely high frequencies (high plasma densities). The problem of collision damping is also discussed. The possible application of plasma oscillations to the solution of the problem of the generation of millimeter wave power is considered, both for plasmas in gaseous discharges and for the thermally generated plasmas in impurity semiconductors.