Analytic study of lower hybrid wave propagation in tokamak LHCD experiments

General but simplified dispersion relation for the lower hybrid wave in low hybrid current drive (LHCD) regime is derived by expanding technique through the small parameter δ = (ωpe2/ω2)-1. The upward and the downward shifts of the parallel refractive index, and the relevant mode conversion due to toroidal effects (such as the R-1 dependence of the toroidal magnetic field and the Shafnanov shift of magnetic surfaces) are discussed. A sufficient condition for the wave that is possible to penetrate into the inner region of the plasma column is obtained, which has a relationship with the experimentally observed LHCD density limit. A scaling about the critical density is found to be nec ∝f4/3B2/3A4/3, with f, B, A being the wave frequency, the magnetic field and the aspect ratio, respectively. There exists a quite good agreement between theory and experiments. The simplified equations for wave propagation can be used as a subroutine in a complete LHCD code