On the essential identity of the amplification of longitudinal plasma waves and the negative absorption of Čerenkov radiation in an electron stream

Abstract

It is shown that in certain conditions the negative Čerenkov absorption and building up of plasma waves obtained in the quantum treatment of the problem is identical with amplification effect and building up of these waves which is obtained as a result of classical considerations on the basis of the kinetic equation. In this connection the authors criticize the paper by Twiss (1963) in which a different opinion is expressed.