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Quasi-optical approach for inhomogeneous dissipative media with high-order spatial dispersion

Despite the development of codes for the electromagnetic wave propagation based on a numerical solution of the complete system of Maxwell's equations, asymptotic methods describing wave fields in smoothly inhomogeneous media with complex dielectric response still remain the main instrument of interpretation and optimization of experiments on microwave heating and current drive in magnetic confinement systems, in problems of signal generation in the Earth ionosphere and many other fields of physics and astrophysics. The main and most studied asymptotic approach is based on calculating the geometric-optics ray and absorption along them [1]. However, geometric optics can only qualitatively describe wave propagation and diffraction of the beam in more complex media with strong spatial dispersion and absorption, like, the vicinity of the electron cyclotron resonance in warm plasmas. The quasi-optical approach is a more accurate asymptotic method, which reduce Maxwell's equations to the evolution equation for the smooth envelope of the wave beam. Such a description allows one to consistently take into account the media anisotropy, spatial inhomogeneity, dispersion, and resonance dissipation within the framework of a unified approach [2]. Its generalization to the case of anisotropic and gyrotropic media with spatial dispersion and dissipation [3] was used to simulate the propagation of quasi-optical wave beams in tokamaks and showed much higher accuracy for resonance absorption in comparison to the previously used approaches [4]. In this paper, we discuss the further generalization of the quasi-optical approach [5] and the features of its application in media of a special kind. A quasi-optical equation [3] is the equation for the scalar complex amplitude U of the wave beam corresponding to selected electromagnetic mode in smoothly inhomogeneous media ( ) ( ) [ ] 0. ˆ , = r U H p r (1)