Stability and properties of electron-driven fishbones in tokamaks

In tokamaks, the stability of magneto-hydrodynamic modes can be modified by populations of energetic particles. In ITER-type fusion reactors, such populations can be generated by fusion reactions or auxiliary heating. The electron-driven fishbone mode belongs to this category of instabilities. It results from the resonant interaction of the internal kink mode with the slow toroidal precessional motion of energetic electrons and is frequently observed in present-day tokamaks with Electron Cyclotron Resonance Heating or Lower Hybrid Current Drive. These modes provide a good test bed for the linear theory of fast-particle driven instabilities as they exhibit a very high sensitivity to the details of both the equilibrium and the electronic distribution function. In Tore Supra, electron-driven fishbones are observed during LHCD-powered discharges in which a high-energy tail of the electronic distribution function is created. Although the destabilization of those modes is related to the existence of a fast particle population, the modes are observed at a frequency that is lower than expected. Indeed, the corresponding energy assuming resonance with the toroidal precession frequency of barely trapped electrons falls in the thermal range. The linear stability analysis of electron-driven fishbone modes is the main focus of this thesis. The fishbone dispersion relation is derived in a form that accounts for the contribution of the parallel motion of passing particles to the resonance condition. The MIKE code is developed to compute and solve the dispersion relation of electron-driven fishbones. The code is successfully benchmarked against theory using simple analytical distributions. When coupled to the relativistic Fokker-Planck code LUKE and to the integrated modeling platform CRONOS, it is used to compute the stability of electron-driven fishbones using reconstructed data from tokamak experiments. Using the code MIKE with parametric distributions and equilibria, we show that both barely trapped and barely passing electrons resonate with the mode and can drive it unstable. More deeply trapped and passing electrons have a non-resonant effect on the mode that is, respectively, stabilizing and destabilizing. MIKE simulations using complete ECRH-like distribution functions show that energetic barely passing electrons can contribute to drive a mode unstable at a relatively low frequency. This observation could provide some insight to the understanding of Tore Supra experiments. (author)