Langmuir emissions generated by electron beams in space plasmas usually appear as chains of strongly modulated wave packets. In this paper, we present a quantitative analysis of three-wave interaction between Langmuir and lower hybrid waves, L1↔L2+LH, which explains many details of recent Freja observations in the topside ionosphere. The packet-like waveforms are generated as the beating of several Langmuir modes. The primary Langmuir mode (L1) is produced by beam-plasma instability, and the other modes are produced as a result of parametric decay to secondary Langmuir waves (L2) and lower hybrid modes (LH). We show that the decay instability has a very low threshold and high growth rate. The limited transverse dimensions of electron beams in the polar ionosphere cause radiation losses from the beam region which influence spectra of the beam-plasma and parametric instabilities. ¿ 2001 American Geophysical Union