Effect of dissipation on the propagation of wave beams in inhomogeneous anisotropic and gyrotropic media
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Effect of Dissipation on the Propagation of Wave Beams in Inhomogeneous Anisotropic and Gyrotropic Media A. A. Balakin, M. A. Balakina, G. V. Permitin, and A. I. Smirnov Institute of Applied Physics, Russian Academy of Sciences, ul. Ul’yanova 46, Nizhni Novgorod, 603950 Russia Received July 31, 2007; in final form, October 29, 2007
Abstract—For wave beams propagating in inhomogeneous anisotropic absorbing media with spatial dispersion, a quasi-optical approximation is developed that makes it possible to account for the combined influence of the refraction, diffraction, and dissipation effects. It is shown that, in the aberration-free approximation, the problem of calculating the beam structure is reduced to that of solving a set of ordinary differential equations for the parameters of the kernel of an integral transformation and calculating the convolution with the spatial Fourier spectrum of the initial field distribution. In particular, the case of a Gaussian beam is analyzed. The applicability limits of the aberration-free solution, which are especially relevant to the ECR absorption regime, are discussed. The effect of aberrations associated with the Hermitian and anti-Hermitian parts of the dielectric tensor of the medium is considered. It is found that the beam deviates toward the region of weaker absorption and that, during the deviation, the beam may become wider or narrower, depending on the type of the inhomogeneity. It is demonstrated that, when absorption is taken into account correctly, the width of the power deposition region during plasma heating in controlled fusion devices can turn out to be substantially larger than that given by the existing estimates. PACS numbers: 41.20.Jb, 42.25.Bs, 42.15.Fr, 42.25.Fx DOI: 10.1134/S1063780X08060056
1. INTRODUCTION The propagation of wave beams in absorbing media is among those few issues in the physics of linear wave processes that have received insufficient study. Yet, this problem is very important for a number of practical applications, in particular, for such a challenging problem in controlled nuclear fusion as localization of the power deposition region during additional microwave plasma heating. The existing numerical methods for simulating the propagation of microwaves in a plasma can at most compute a system of geometro-optical rays [1, 2] or the quasi-optics of Gaussian beams, with absorption being calculated along the central ray1 [5, 6]. In this way, either diffraction effects and the spatial dispersion of the medium are ignored, or the influence of the nonuniform and nonlocal nature of absorption on the spatial dynamics of the wave beam is excluded from consideration. In some cases, such simplifications are unjustified because they lead to numerical results that are inconsistent with the actual behavior of the wave field. For instance, even a seemingly insignificant difference in determining the position of the power deposition 1 Note
that diffraction can also be taken into account by means of complex geometrical optics (see, e.g., [
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