Parametric Instabilities Due to Lower-Hybrid Radio Frequency Heating of Tokamak Plasmas

The linear theory of parametric instabilities relevant to radiofrequency heating near the lower‐hybrid frequency of tokamak‐type plasmas is presented. The dispersion relations are analyzed numerically to all orders of the ion Larmor radius. The complete range of unstable spectra is obtained for 1<ω0/ωlh<5, for both deuterium and hydrogen plasmas. As the pump wave propagates from the edge of the plasma toward its interior, the transition from resonant decay to decay into quasi‐modes is demonstrated. The effects of inhomogeneities upon the threshold for parametric decay, such as density gradients, finite pump width, and magnetic shear, are obtained. The relevance of these results to recent tokamak experiments is discussed briefly.

[1]  M. Porkolab,et al.  Observation of parametric instabilities in lower hybrid radio frequency heating of tokamaks , 1977 .

[2]  A. Hasegawa,et al.  Theory of plasma heating by nonlinear excitation of lower hybrid resonance , 1975 .

[3]  B. Coppi,et al.  Slide-away distributions and relevant collective modes in high-temperature plasmas , 1976 .

[4]  W. Manheimer,et al.  Nonlinear Development of the Beam-Cyclotron Instability , 1971 .

[5]  M. Porkolab,et al.  Propagation and mode conversion of lower-hybrid waves generated by a finite source , 1974 .

[6]  T. Moreno,et al.  Microwave Transmission Design Data , 1948 .

[7]  A. Rogister,et al.  Theory of parametric heating of plasma in the lower hybrid frequency range , 1976 .

[8]  I. Fidone,et al.  Anomalous absorption near the lower‐hybrid frequency , 1976 .

[9]  R. Chang,et al.  Nonlinear decay and instability of a nonuniform finite-amplitude plasma wave , 1970 .

[10]  W. Manheimer,et al.  Theory and simulation of the beam cyclotron instability. , 1972 .

[11]  G. Laval,et al.  Parametric Instabilities in Bounded Plasmas , 1973 .

[12]  C. Béghin,et al.  Electromagnetic and electrostatic wavesin a multi-component plasma near the lower hybrid frequency , 1976, Journal of Plasma Physics.

[13]  A. Rogister.  Anomalous Absorption of Electromagnetic Energy through Parametrically Induced Lower-Hybrid Turbulence , 1975 .

[14]  Miklos Porkolab,et al.  Theory of parametric instability near the lower‐hybrid frequency , 1974 .

[15]  M. Rosenbluth.  Parametric Instabilities in Inhomogeneous Media , 1972 .

[16]  M. Brambilla.  Propagation and absorption of waves at the lower hybrid resonance , 1976 .

[17]  V. Glagolev.  Propagation and absorption of ion hybrid waves in a weakly inhomogeneous plasma laser. I , 1972 .

[18]  C. T. Dum,et al.  SATURATION OF NONLINEAR EXPLOSIVE INSTABILITIES. , 1969 .

[19]  R. Berger,et al.  Thresholds of parametric instabilities near the lower‐hybrid frequency , 1976 .