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.
