Description
It is well known that the measured propagation and absorption profiles of RF wave beams in laboratory torus plasmas tend to be spatially broader than those predicted by numerical simulations. We have approached resolving this discrepancy by improving the accuracy of the theoretical models used in numerical calculations. The wave beam propagation in inhomogeneous plasmas has conventionally been described using geometrical-optics or quasi-optical ray-tracing methods. In this study, we re-consider ray tracing not only in real space {x} but in the phase space {x, k}, which combines real space with its dual Fourier wave vector space. To reconstruct the ray model in phase space, we employed the mathematical techniques developed in quantum theory, specifically the Wigner–Weyl–Moyal formalism. A general linear wave equation defined in Hilbert space is reduced to a Liouville equation that describes the evolution of the wave-energy spectrum in phase space. We found that the Lagrange-solution of this equation can be interpreted as a phase-space extension of the conventional family of rays model restricted to real space. Since this method does not assume a specific central ray, it is applicable to the description of global and in-coherent wave fields. Based on this Lagrange-type Liouville model, we newly developed the family of phase-space rays tracing code FARANKS. Comparisons with the quasi-optical code PARADE demonstrated that diffraction is correctly incorporated in FARANKS, and that FARANKS can additionally capture other broadening effects that quasi-optics cannot represent, such as lensing, beam splitting, scattering, and interference.