Analytic Study of Density Limit Mechanism for Tokamak LowerHybrid Current Drive Experiments

The dispersion relation of the lower hybrid wave in the tokamak current drive regime (ω > 2ω_LH, where ω_LH is the lower hybrid frequency) is analysed. Toroidicity effects can shift the parallel refractive index upward or downward. The downward shift will lead to a mode conversion from the slow wave to the fast wave. It is indicated that this is the main mechanism limiting the effectiveness of tokamak lower hybrid current drive. Accordingly, a sufficient condition is obtained for the wave penetration, corresponding to a critical density, which is proportional to f^4/3B^2/3(A)^4/3, with f being the wave frequency, B the magnetic field strength and A the aspect ratio. Quantitative agreement with experiments is found.