WAVE ENERGY FLUX AND ABSORPTION OF ELECTRON CYCLOTRON GAUSSIAN BEAMS IN TOKAMAK PLASMAS

In this thesis some theoretical problems related to the propagation and absorption of Electron Cyclotron Gaussian beams in tokamak plasmas of interest for nuclear fusion applications are investigated. To account for diffraction effects, beam propagation is analyzed in the framework of the complex eikonal method, a generalization of geometrical optics in which the phase function is assumed to be complex valued, with the non-negative imaginary part accounting for the finite width of the beam cross section. Within this framework, the solution at the dominant order in the expansion parameter is well-known, and the wave beam is modeled as a bundle of “extended rays”. The derivation of the transport equation for the field amplitude is much more complicated with respect to the standard geometrical optics one, hampering the derivation of the wave energy flux. In this work, an argument is proposed that greatly simplifies the analysis of the transport equation allowing us to derive the wave energy flux. This result, not available in the literature in the case of beam propagation in anisotropic media like magnetized plasmas, has been obtained in collaboration with O. Maj (IPP, Garching, Germany), and published on Physics of Plasmas. The effects of the finite beam width on the Electron Cyclotron resonant interaction have been described with a model that takes into account the transverse wave vector spectrum width and the non-uniformity of the equilibrium magnetic field. The model has been implemented in a modified version of the GRAY code [D. Farina, Fusion Sci. Technol. 52, 154 (2007)]. The differences between the power absorption profi les obtained using this model and the “plane wave” one are illustrated numerically in ITER conditions and are found to be small for realistic cases, thus justifying the use of the usual model for practical purposes.