Interaction between energetic particles and axisymmetric modes in magnetically confined fusion plasmas

The most promising path towards controlled thermonuclear fusion as a new source of energy makes use of devices, called tokamaks, for the confinement of high temperature hydrogen plasma by means of intense magnetic fields in toroidal configurations. The deuterium-tritium reactions in fusion reactors generate alpha particles with 3.5 MeV energy. These particles are supposed to transfer their energy to the plasma in order to self-sustain the conditions required for thermonuclear burn. Therefore, in order to realize such a fusion burning plasma, alpha particles in the MeV range must also be magnetically confined. However, under these circumstances, instabilities related to resonant interactions between the periodic motions of energetic particles and normal mode fluctuations of the thermal plasma may be excited. Of particular interest in this thesis are toroidally axisymmetric normal modes of the thermal plasma that arise spontaneously in a confinement configuration where the plasma cross-section is non-circular. Indeed, so-called magnetic divertor configurations and plasma shaping are common features in modern-day tokamak experiments. The elongation of the plasma cross section is linked to axisymmetric movements of the toroidal plasma column, associated with so-called vertical displacement events (VDE). These are related to normal modes, which conserve toroidal symmetry, i.e. with toroidal wave number n = 0, resulting in a rigid shift of the plasma column. This kind of vertical instability can lead to a termination of the plasma discharge on a characteristic Alfven time scale, which is typically of the order of micro-seconds, with consequent large electromagnetic stresses on the confinement device. Hence, external feedback currents are used in tokamak experiments to avoid the occurrence of VDEs, which result in characteristic stable plasma oscillations with a frequency close to the characteristic Alfven frequency. On the other hand, orbits of energetic particles are periodic and exhibit a characteristic frequency called transit frequency. When the energy of energetic ions is of the order of 1 MeV, this frequency can become comparable with the oscillation frequency of n=0 axisymmetric vertical displacements, giving rise to a resonant interaction. This resonance leads to a collisionless transfer of energy between the plasma wave and the particles. Depending on the fast particles distribution function, this can result into either damping of the wave and consequent particle acceleration, or growth of the wave amplitude together with particle deceleration. The latter is clearly a dangerous unstable situation, as a growing vertical displacement may reach amplitudes that are no longer controllable by the external feedback system, giving rise to uncontrolled VDEs. This resonant interaction must be studied using a hybrid kinetic-MHD (Magneto Hydro Dynamic) model, in which the energetic particles are treated using kinetic plasma theory and the thermal plasma is modelled according to MHD. The subject of this work is a first study of the resonant interaction between the oscillating n=0 vertical displacement modes and energetic particles at their transit frequency. Thresholds for the resonant excitation of these modes are obtained. As far as we are aware, this is the first theoretical study of this interaction.