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

Abstract

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 mediaHere the momentum operatoris defined as the differentiation operator in the coordinate space normalized on the vacuum wave number k 0 = Ȧ/c. The simplification of this equation is possible for paraxial wave beams (broad in the wavelength scale) with parameters varying slowly along some curve r 0 (the reference ray). One can associate a curvilinear coordinate system r = (ȟ,IJ) and canonically conjugate momenta ( ) IJ p , =q p with the reference ray. Here IJ is the evolutionary coordinate along the reference ray, ȟ are two curvilinear coordinates orthogonal to the reference ray, 0