Parametric instabilities of plasmas in the frequency ranges ω approximately > ωsub(LH) and ω<ωsub(LH)

Most parametric instabilities considered up to date were discribed by three-wave resonant decay. The emphasis is laid here on parametric destabilization occurring in plasmon-particle-plasmon scattering (i.e. non-linear Landau interaction) in the frequency range Ωsub(i)<ω<ωsub(LH) and ω greater than or of the order of ωsub(LH) (Ωsub(i)=ion gyrofrequency; ωsub(LH)=lower hybrid frequency). More specifically, a non-linear theory of lower hybrid turbulence driven by a whistler pump wave has been developed leading to theoretical estimates of (i) the saturation level of the turbulence; (ii) the corresponding anomalous absorption rate of the pump wave; (iii) the plasma heating rate. Numerical evaluations are given for the parameter ranges which are relevant to the present generation of tokamaks and to reactors. The theoretical results are very promising; the technique apparently should only fail at high densities in very large machines [e.g. for N greater than or of the order of 3x1014 cm-3 if a (plasma radius) equals 200 cm, B=100 kG, T=5 keV. This result is, of course, explained by the poor tunnelling of the pump wave through the evanescent region between the plasma vacuum interface and the turning point under those conditions.] The relevance of ion Bernstein turbulence induced by a magneto-acoustic pump wave is also discussed; it is felt that this parametric instability should not be very effective in heating a tokamak plasma. (author)