Mode crossing effects at electron beam–plasma interaction and related phenomena

Mode crossing points are shown to play an important role in interpreting the spatio-temporal plasma wave spectra from satellite and laboratory measurements. Here, the Langmuir wave near the electron plasma frequency is considered and from linear dispersion curve analysis it may cross the whistler wave, the L-wave or the electron-acoustic mode depending on plasma conditions. An essential parameter is the electron cyclotron frequency to plasma frequency ratio, G = Ωe/ωe. The crossing point exists for wave propagation slightly oblique to a background magnetic field and we find that for a broad spectrum of waves excited by an instability, via an energetic beam or background plasma temperature anisotropy, the maximum amplitude of the wave activity appears at the crossing points which can be well separated from the region of maximum linear growth. Within this process the saturated waves act as an 'antenna' for other wave modes in the same wave number range. Linear and kinetic simulation analysis are used to demonstrate the frequency splitting at mode crossing points in two relevant examples; unmagnetized beam–plasma instability with Langmuir and electron-acoustic mode crossing in the presence of electron plateau distribution, and beam-excited Langmuir waves in overdense (G < 1) and underdense plasmas (G > 1) with background magnetic field. It is shown that the appearance of amplitude modulations associated with double-peak spectra of the electric field is directly related to the frequency splitting and coupling at mode crossing points. The importance of transitions between quasi-longitudinal wave modes at oblique propagation to transverse modes for the interpretation of beam–plasma interaction phenomena, such as type III radiation, and laboratory experiments is discussed.