This work opens a series of papers where we develop a general quasioptical theory for modeconverting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multi-component wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ ("quasioptical equation") in the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. We also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radiofrequency wave beams in magnetized plasma based on this theory.

This work continues a series of papers where we propose an algorithm for quasioptical modeling of electromagnetic beams with and without mode conversion. The general theory was reported in the first paper of this series, where a parabolic partial differential equation was derived for the field envelope that may contain one or multiple modes with close group velocities. Here, we present a corresponding code PARADE (PAraxial RAy DEscription) and its test applications to singlemode beams in vacuum and also in inhomogeneous magnetized plasma. The numerical results are compared, respectively, with analytic formulas from Gaussian-beam optics and also with coldplasma ray tracing. Quasioptical simulations of mode-converting beams are reported in the next, third paper of this series.

This work continues a series of papers where we propose an algorithm for quasioptical modeling of electromagnetic beams with and without mode conversion. The general theory was reported in the first paper of this series, where a parabolic partial differential equation was derived for the field envelope that may contain one or multiple modes with close group velocities. In the second paper, we presented a corresponding code PARADE (PAraxial RAy DEscription) and its test applications to single-mode beams. Here, we report quasioptical simulations of mode-converting beams for the first time. We also demonstrate that PARADE can model splitting of two-mode beams. The numerical results produced by PARADE show good agreement with those of one-dimensional fullwave simulations and also with conventional ray tracing (to the extent that one-dimensional and ray-tracing simulations are applicable).

We report the first quasi-optical simulations of wave beams in a hot plasma using the quasi-optical code PARADE (PAraxial RAy DEscription) [K. Yanagihara, I. Y. Dodin, and S. Kubo, Phys. Plasmas 26, 072112 (2019)]. This code is unique in that it accounts for inhomogeneity of the dissipation-rate across the beam and mode conversion simultaneously. We show that the dissipation-rate inhomogeneity shifts beams relative to their trajectories in cold plasma and that the two electromagnetic modes are coupled via this process, an effect that was ignored in the past. We also propose a simplified approach to account for the dissipation-rate inhomogeneity. This approach is computationally inexpensive and simplifies the analysis of actual experiments.

Electron-cyclotron resonance heating is an essential tool for manipulating fusion plasmas and has been diligently studied for decades through numerical simulations and experiments. Here, we report the first comparison of simulations using the quasioptical code PARADE (PAraxial RAy DEscription) with experiments using a target-plate system on the Large Helical Device. We find that the numerical and experimental results agree qualitatively, which makes PARADE a promising code for modeling of electron-cyclotron wave beams in future experiments. The signature advantage of PARADE is its ability to capture both mode conversion and inhomogeneity of the dissipation rate across the beam cross section. Accounting for these effects, which can noticeably affect the power deposition, significantly improves the agreement between numerical results and experimental data.