TWO-DIMENSIONAL AND RELATIVISTIC EFFECTS IN LOWER-HYBRID CURRENT DRIWE*

We present new numerical and analytic solutions of the two-dimensional Fokker-Planck equation supplemented by a parallel quasilinear diffusion term. The results show a large enhancement of the perpendicular temperature of both the electrons resonant with the applied RF fields and the more energetic electrons in the tail. Both the RF generated current and power dissipated are substantially increased by the perpendicular energy broadening in the resonant region. In the presence of a small DC electric field the RF current generated is very much enhanced, much more than in a simple additive fashion. In addition we present a relativistic formulation of the two-dimensional Fokker-Planck quasilinear equation. From conservation equations, based upon this formulation, we derive the characteristics of RF current drive with energetic electrons. These show how the RF driven current and its figure of merit (I/Pd) increase with the energy of the current-carrying electrons, and that their perpendicular, random momentum must also increase. The results are relevant to recent experiments of lower-hybrid current drive on Alcator C and PLT in which the applied RF spectra are resonant with very energetic electrons, and in which large perpendicular temperatures of the energetic electrons have been observed. It is pointed out that substantial improvements in the figure of merit, (I/P), of present experiments may be achieved by current drive with fast-waves in the lower-hybrid frequency range. The ultimate limitation in this type of current drive is likely to be the confinement of the very energetic electrons. * Work supported by DOE Contract No. DE-AC02-78ET-51013. Duplicat