BORAY-3D: A ray tracing code for three-dimensional magnetized plasma configurations

Abstract

Ray tracing codes are useful tools for studying electromagnetic wave propagation and absorption using the geometrical-optics approximation. Existing codes commonly provide either broad radio-frequency coverage in axisymmetric equilibria or three-dimensional capability specialized for electron-cyclotron (EC) applications. BORAY-3D integrates three desirable features in a single version. First, it has a broad frequency range of validity regime from ion-cyclotron, helicon and lower-hybrid waves to EC waves and emission. Second, it provides a unified treatment of arbitrary two- and three-dimensional magnetic-plasma configurations, including both closed and open field-line regions. Third, it incorporates fully relativistic Maxwellian EC absorption. The code extends the axisymmetric BORAY formulation by solving the ray equations in cylindrical coordinates $(r,ϕ,z)$ while allowing the toroidal mode number $n_ϕ$ to vary. Magnetic-field, density and temperature data are directly described in $(r,ϕ,z)$ coordinates without the restriction of flux functions, so that numerical equilibria and analytic field models can be handled in the same form. The non-relativistic hot-plasma model inherited from BORAY is used for lower-hybrid, ion-cyclotron and helicon absorption, whereas the relativistic model is coupled to reciprocal radiative transfer for electron cyclotron emission (ECE). Practical applications include 13.56 MHz helicon and 50 MHz fast waves, a 3.7 GHz lower-hybrid wave, and 115--220 GHz EC emission. BORAY-3D has been systematically benchmarked against GENRAY for tokamak toroidal-field ripple, Raytrax and TRAVIS for W7-X, as well as public HSX heating and W7-X ECE results.