Nonlinear dynamics of frequency sweeping energetic particle modes in tokamaks

Abstract: In a burning plasma, such as the next generation tokamak experiment ITER, significant numbers of highly energetic particles will be produced via nuclear reactions. The presence of energetic particles, be it fusion born alpha particles or ions accelerated by auxiliary heating schemes, may excite kinetic instabilities and thereby affect the heating and transport of all particles in the plasma. Of particular interest is the toroidal Alfvén eigenmode (TAE), a cavity mode that can be excited by super Alfvénic ions as they slow down due to friction-like collisions with the background plasma and eventually hit the wave-particle resonances. Such modes have attracted much attention during almost 30 years, since their detection provides diagnostic opportunities to probe the plasma core. However, their presence and long-term behavior are still far from understood. They may have detrimental effects on the plasma confinement and heating, but can potentially also be utilized as a collisionless way to channel power from the fast ions to the bulk plasma. In this thesis we employ linear and nonlinear analysis to study fast particle driven TAEs whose signals exhibit frequency sweeping. Their existence is tied to the formation and evolution of phase space structures known as holes and clumps in the non-thermal fast particle distribution. A one-dimensional ``bump-on-tail'' model is employed and used to investigate the stability of a phase space plateau that emerges early in the mode evolution cycle. Fast particle collisions and sources are included in the analysis in order to substantiate the role of the plateau as a hole/clump breeding ground from which the frequency sweeping initiates. Furthermore, the ideas of phase-locking of fast ions orbits in the wave-particle resonances is used to calculate the radial motion of already established hole/clump modes during the frequency sweeping for the ideal cases of deeply trapped and well passing particles, and it is proposed that the intensity of the sweeping signals correlates with the fast ion environment through which the hole/clump moves.