A quasi-optical description of the propagation and damping of the slowly varying wave amplitude across an arbitrary electron cyclotron wave beam is presented. This model goes well beyond those implemented in existing beam tracing codes, which typically require the spatial inhomogeneity across the wave beam to be small. The present model allows an accurate description of the wave beam evolution in the region of electron cyclotron power deposition, where the latter condition is quite generally broken. The additional physical effects from spatial inhomogeneity and dispersion included in the quasi-optical model are discussed in relation to their consequences for the power deposition profile. Quite generally, a broader power deposition profile is obtained in the quasi-optical calculations. The importance of these effects is analysed in a number of scans varying the injection geometry for typical conditions in both the ITER and the TEXTOR tokamak. Optimization of the power deposition profile towards a minimal width is found to require a focused wave beam with a waist of typically 2 cm width localized near the electron cyclotron resonance region. Calculations are also presented for beams injected from the ITER Upper Port electron cyclotron resonance heating (ECRH) launcher as it is currently being designed. These show that the additional power deposition profile broadening from quasi-optical effects may result in a drop in the predicted efficiency for neoclassical tearing mode or sawtooth control by up to a factor of 2.

The quasi-optical description of wave beams is extended to smoothly inhomogeneous anisotropic and/or gyrotropic media. A method of deriving quasi-optical equations for a slow-varied scalar beam amplitude from Maxwellian equations is proposed. Transversal localization of the beam near the central ray allows one to separate and sequentially derive the refractional, focusing (or defocusing) and aberrational terms. The correct relationship between the scalar beam amplitude and the vector electric field is conserved for every order. For simplicity, a cold collisionless magnetized plasma is considered. However, all basic results are valid, with minor amendments, for media with spatial dispersion. The aberration-free parabolic-like equation for a complex beam envelope is considered in detail. Its physical properties are investigated and a general solution is found.

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