Harmonic Langmuir waves. I. Nonlinear dispersion relation

Abstract

Generation of electrostatic multiple harmonic Langmuir modes during beam–plasma interaction process has been observed in laboratory and spaceborne active experiments, as well as in computer simulationexperiments. Despite earlier efforts, such a phenomenon has not been completely characterized both theoretically and in terms of numerical simulations. This paper is a first in a series of three papers in which analytic expressions for harmonic Langmuir mode dispersion relations are derived and compared against the numerical simulation result.