IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 19, NO. 4, AUGUST 1991 Parametric Decay Instabilities of the Fast Wave in the Lower Hybrid Frequency Regime Atul Kumar, R. P. Sharma, Y.K. Tripathi, and A. Hadi Al-Janabi Abstract—This paper presents three possible decay instabili- ties of the fast wave in the lower hybrid frequency regime. It has been considered that a fast wave may decay into a high- frequency, lower hybrid wave and a low-frequency wave, either the ion-Bernstein wave, ion-acoustic wave, or kinetic Alfven wave. Explicit expressions for growth rates, homogeneous thresholds, and convective thresholds have been given. Applications have been pointed out in tokamak plasmas during current drive experiments and magnetospheric plasmas. For example, for PLT tokamak parameters, the convective threshold for the decay instability of the fast wave into lower hybrid and ion acoustic waves comes out to be ~18O W/cm 2 . I. INTRODUCTION M OST of the current drive experiments in tokamak [1], [2] have utilized lower hybrid waves, but so far they are successful only in the low-density region. The limitation in density is the so-called "density limit" [3], beyond which the current cannot be driven by slow waves. Since fast waves [4], [5] propagate at higher densities, they may serve better than lower hybrid waves in a tokamak reactor. Current drive by a fast wave has been performed in several toroidal devices [6], [7] and tokamaks [8]-[10]. The exper- iments on the tokamaks [8], however, have not conclusively shown that fast wave current drive can be achieved by means of electron Landau damping of the fast waves launched directly, possibly due to conversion of the fast waves to slow waves. In the JIPPT-IIU current drive experiment [8], the density limit for the fast wave current drive is also observed, contrary to the theoretical expectations based on their linear wave propagation. Here also the fast wave current drive disappears almost at the same density as the density limit for the slow wave current drive. The ion tail formation was also observed during operation. From the viewpoint of linear theory, fast waves with a small perpendicular refractive index (r/o±) cannot interact directly with the ions. Hence there exist some possibilities for the excitation of parametric decay by the generation of slow waves, even during fast wave injection and the correlation of parametric decay of the fast wave with the ion tail formation, as was also studied experimentally [8]. For this purpose RF spectra of the pump and lower sideband were monitored. With increasing density the spectrum of received high-frequency signals changes from Manuscript received July 24, 1990; revised January 22, 1991. This work was partially supported by the Department of Science and Technology, India, through the sponsored project, "Study of Waves and Instabilities in Ionosphere, Magnetosphere, and Laboratory Conditions." The authors are with the Centre of Energy Studies, Indian Institute of Technology, New Delhi-110016, India. IEEE Log Number 9101094. a monochromatic pump to a spectrum with pump broadening accompanied by a weak lower sideband. It was concluded that the occurrence of parametric decay correlates with the ion tail formation and results in the deposition of a part of the RF power at the peripheral region. In an other JIPPT-IIU experiment [9], density limit for the fast wave is also observed, but this density is two orders of magnitude higher than the density limit predicted for the slow wave current drive. Some mechanisms [11], [12] have been suggested for the generation of slow waves during fast wave current drive experiments. The possibility of parametric decay of the fast wave (whistler) by the ion-cyclotron wave has been studied theoretically by Tripathi [11]. But some other decay channels which may be even more important during fast wave current drive experiments have not been considered in that paper. The decay channels of fast waves (FW) considered in the present paper are as follows: i) Decay into the lower hybrid wave (LHW) and ion- Bernstein wave (IBW) ii) Decay into the LHW and ion-acoustic wave (IAW) iii) Decay into the LHW and kinetic Alfven wave (KAW). It has been demonstrated theoretically that a fast wave can, in fact, excite the slow (LHW) wave and a low-frequency ion-Bernstein or ion-acoustic wave for JIPPT-II-U or PLT parameters. Application of the parametric decay instability of the FW into LHW and KAW (for (3 < m e /mi) has also been pointed out to Earth's magnetospheric plasma. II. BASIC THEORY A. High-Frequency Wave Dynamics The fast and slow waves are represented [4], [5] by so- lutions of the cold plasma wave dispersion relation. They can be distinguished by their polarization and different wave vectors. Considering static magnetic field along the z-axis (B 0 = B o z), the dispersion relation [5], [13] for slow and fast waves in the lower hybrid frequency regime is given by: Po = P2 = Pi = PiVo- (e ± + H P 2Vo + Po = £ 2 s II ~ 6± 0 ) + - 4 a) (2)