A full wave description of the accessibility of the lower‐hybrid resonance to the slow wave in tokamaks

Mode conversion between the fast and slow electromagnetic waves in the lower‐hybrid frequency range is considered. This phenomenon determines the accessibility of the lower‐hybrid resonance to the slow wave, and is also of theoretical interest because the mode coupling differs in certain aspects from cases previously investigated by the authors and others. A second‐order approximation is used in the mode conversion region leading to Weber’s equation from which transmission coefficients are then obtained in various cases. Ray‐tracing results are recovered for a plasma with a linear density profile in a uniform magnetic field. The effect of including a magnetic field gradient is to move the mode conversion region to the plasma edge. The second part of the paper provides justification for the use of Weber’s equation. The exact fourth‐order system of ordinary differential equations for the problem is set down and a linear transformation, which is an extension of that given by Heading, reveals the second‐order nature of the coupling process. Numerical solutions of the fourth‐order system yield transmission coefficients in excellent agreement with the second‐order theory, and also demonstrate that the electric field variation across the mode conversion region is well approximated, via the above transformation, by the second‐order theory.