Calculation of a wave field from ray tracing

Radio frequency heating and current drive are important features of many tokamaks. In order to predict the efficiency of the current drive and where it takes place in the tokamak profile, computational techniques which couple calculations of the wave field to Fokker-Planck solutions of the electron distribution function have been developed. In the electron cyclotron and lower hybrid (LH) frequency ranges the wave field is often calculated using ray tracing techniques, though more recently some full wave calculations have been done. Ray tracing provides a simpler way of proceeding, but the problem arises of dealing with the situation in which there is not a single well defined beam and diffraction and beam divergence are important. Since an LH antenna produces a complicated spectrum, launching waves in a range of directions, the problem is particularly acute there. In this paper we suggest a way of calculating the wave field from tracing of multiple rays using a technique based on the stationary phase approximation. We demonstrate how it can be used and its effectiveness through a number of simple examples.