Simulation Of Interaction Between Energetic Particles And Internal Kink Modes In Tokamaks

As a result of the exhaustion of traditional energy sources, the development and utilization of new energy sources is the inevitable choice for sustainable progress and development of humanity. Fusion is the most promising source of energy for human development in the future as it is safe and clean with abundant fuel. The tokamak is the most promising magnetic fusion device for re-alizing controllable nuclear fusion energy. The interaction between energetic particles and internal kink modes is an important research topic in the tokamak physics because the sawtooth oscillations caused by internal kinks can drive large energetic particle transport. On the other hand, energetic particles can stabilize the internal kink mode, lengthen the period of sawtooth oscillations, eventu-ally leading to "Monster Sawteeth". Large sawteeth can trigger neoclassical tearing mode, degrade plasma confinement, and even lead to plasma disruption.In this dissertation the magnetohydrodynamic (MHD)-kinetic hybrid code M3D-K has been used to simulate the interaction between energetic particles and internal kink modes, including energetic particle transport due to a sawtooth crash in tokamak plasmas, and the linear stability and nonlinear dynamics of the n=1 internal kink mode. This dissertation contains six chapter-s, of which chapter 1 presents an introduction to the dissertation, chapter 2 reviews the physics background of energetic particles and internal kink modes in tokamaks, chapter 3 describes the MHD-kinetic hybrid model used in the M3D/M3D-K code and the related numerical simulation methods in detail, chapter 4 and chapter 5 present the main research results in the dissertation from two specific aspects, and finally in chapter 6 conclusions are summarized and suggestions for possible future work are given. The specific content of this dissertation is as follows:In chapter 4, we present nonlinear simulation results of sawtooth cycles and energetic particle transport due to a sawtooth crash in tokamak plasmas. MHD simulations show repeated sawtooth cycles similar to the Kadomtsev model. Furthermore, test particle simulations are carried out to study the energetic particle transport due to a sawtooth crash. The results show redistribution of energetic particles in the plasma core inside the sawtooth region. The results also show transport of particles from inside the q=1 surface to outside of the q=1 surface due to magnetic reconnection. In addition, the redistribution level of energetic particles depends on particle pitch angle and energy. For trapped particles, there exists a critical energy above which particles are weakly redistributed. The critical energy is approximately inversely proportional to the crash time and is independent of the particle mass. For passing particles, the redistribution of co-passing particles is strong and is approximately independent of particle energy. In contrast, the redistribution level of the counter-passing particles decreases with increasing particle energy. The difference between redistribution behaviors of the co-passing and counter-passing particles is due to the difference in their precession frequencies. The precession frequency of the counter-passing particles is substantially larger than that of the co-passing particles, leading to a stronger energy dependence of particle transport. Besides, we have studied the effects of magnetic field perturbation and mode rotation on particle redistribution. It is shown that the effect of magnetic field perturbation is important only for the redistribution of co-passing particles at sufficiently high energy, and the mode rotation changes the critical energy. Finally, we have estimated the critical energy of energetic particles in tokamak devices such as Dâ…¢-D and ITER. The trapped particles are expected to be weakly redistributed while the redistribution of both co-passing and counter-particles is expected to be strong.In chapter 5, the linear stability and nonlinear dynamics of the n=1 internal kink mode are simulated. There are two types of m=n=1 oscillations between sawtooth crashes in a DIII-D plasma discharge, including a fishbone-like mode with higher frequency and frequency chirping, and a constant and lower frequency oscillation which emerges when the beam ion distribution becomes broader. When the beam ions are described by the MHD model, linear simulation results show that the n=1 internal kink mode is unstable, and nonlinear simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. Moreover, when the perpendicular thermal conductivity decreases below a critical value, the nonlinear evolution of the internal kink mode transits from the quasi-steady saturation state to sawtooth cycles. When the kinetic effects of energetic beam ions are considered, linear simulations show that an=1 mode is excited with mode frequency around a few kHz, and the mode frequency is larger with higher beam ion pressure or narrower radial profile of the beam pressure. Nonlinear simulation results show that the n=1 mode transits to a saturated kink mode with finite mode frequency. For a broader beam ion profile, the mode frequency in the nonlinear phase is almost the same with the initial linear frequency. However, for a narrower beam ion profile, the mode frequency chirps down significantly in the nonlinear phase. In addition, Our analysis has shown that the MHD nonlinearity is the dominant mechanism for mode saturation and mode rotation. Finally, we have discussed the effects of the n=1 mode on the beam ion profile. After the sawtooth crash, beam ions are strongly redistributed radially inside the sawtooth region. Then, during the nonlinear saturation of the kink mode, the distribution of the beam ions becomes flatter inside the q=1 surface. These results are consistent with the experimental observation of saturated kink modes between sawtooth crashes.