Instability of coupled longitudinal and transverse electromagnetic modes of wave-propagation in bounded streaming plasmas

Abstract

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k²)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<150.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k³)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k²)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.