Non-resonant Internal Kink Mode Interaction With Energetic Particles

One of major issues facing human beings is the energy crisis, and to avoid it many possible schemes have been proposed. Among them magnetic confinement fusion is considered to be the most promising ultimate solution to the energy demand of human beings as it has inexhaustible fuel, and is mainly controllable and clean. However, after over fifty years’efforts, magnetic confinement fusion still has many fundamental technological and engineering issues waiting for solutions. The tokamak is regarded as the most promising device to provide mankind with economically viable nuclear energy. The main thrust of this dissertation is to study unclear but important physical phenomena observed in tokamak experiments by means of numerical simulation.Experimental results show that in spherical tokamaks such as the National Spherical Torus Experiment (NSTX) and the Mega-Ampere Spherical Tokamak (MAST), with neutral beam injection (NBI) heating, high β, and a safety factor (q) above unity and weakly reversed magnetic shear, plasmas could easily be unstable to an ideal, non-resonant internal kink mode (NRK). In MAST, this mode can saturate and persist nonlinearly, and it was termed "long-lived mode"(LLM). It can also induce a strong damping of the core plasma rotation. And plasmas usually experience a phase of strong frequency sweeping fishbone activity before the mode appears. In NSTX, experimental results show that the mode has strong interaction with energetic particles, which induces redistribution of neutral beam inj ection current drive, and further modify q profile.This dissertation focuses on studying the NRK in spherical tokamaks, in which a3-D ex-tended MHD model was used to describe the thermal plasma, and a kinetic model was used to describe the energetic particles injected by the neutral beam injection (NBI). A massively par-allel kinetic/MHD hybrid code M3D-K was used to simulate the plasma with realistic plasma parameters and geometric parameters of spherical tokamak NSTX with NBI injection. The dissertation contains six chapters, of which the first chapter presents an introduction to the dis-sertation, and the second chapter describes the physical model and numerical methods; in the following three chapters, it presents the research results on the NRK interaction with energetic particles from three specific aspects.Chapter3centers on the NRK mode linear stability and nonlinear dynamics using the ex-tended MHD model without considering energetic particles. Simulation results show that the NRK mode is an ideal and pressure driven MHD mode, dominated by toroidal mode number n=1harmonic component; the mode can induce m/n=2/1island nonlinearly, which could be the seeding of neoclassical tearing modes (NTMs). The nonlinear evolution of the LLM is reproduced numerically, and the corresponding simulation results agree with experimental and theoretical results well. In particular, the plasma toroidal rotation effects on the NRK mode are taken into account, including rotation effects on plasma equilibrium, linear stability and nonlinear evolution. Simulation results show that the plasma toroidal rotation with a velocity at experimental level has weak effects on equilibrium and the NRK mode linear growth rate, while the plasma rotation at a high velocity has significant stabilizing effects on the NRK mode. Non-linearly, the plasma rotation has significant effects on (m/n=1/1) component evolution, and can reduce(m/n=2/1) island width markedly, even at a low rotation velocity, which agrees with experimental observation:plasma rotation can increase the beta threshold of NTMs.In chapter4, a test particle method is used to analyze the NRK mode effects on the motion of energetic particles. In these simulations, a fixed MHD perturbation from previous nonlinear MHD simulations is considered, and drift-kinetic equations are used to describe energetic par-ticle orbits. Simulation results show that perturbation from the NRK mode breaks the plasma toroidal symmetry, and destroys the invariance toroidal angular momentum (Pφ). And results also show that the NRK perturbation effects on passing particles and trapped particles are very different:for passing particles, particles around (m/n=1/1) and (m/n=2/1) components can be disturbed respectively; for trapped particles, with finite banana orbits, particles in a wide region are disturbed by (m/n=1/1) perturbation, while the (m/n=2/1) island has a weak effect on trapped particles. We also consider energetic particles with slowing down distribution function. Results show that the NRK mode redistributes energetic particles significantly, and it can also induce neutral beam injection current drive anomaly, which agrees with experimental results.In chapter5, a self-consistent model was used to study energetic particle interaction with the NRK mode. Linear simulation results show that at a low β of energetic particles, trapped particles have strong stabilizing effects on the NRK mode, especially at high energy; on the other hand, passing particles increase the NRK linear growth rate. With high energetic particles pressure, trapped particles can excite an energetic particle mode which is similar to fishbone in conventional tokamaks with q=1resonant surface. The mode frequency is close to trapped particle precessional drift frequency, and it behaves nonlinearly fast frequency chirping. The fishbone is more unstable at higher qmin, in contrast, the NRK mode is stable at high qmin.In tokamaks, usually, the qmin decreases with the discharge evolution, which is the reason why the fishbone mode always appears before the LLM in the MAST.In the final chapter, the conclusions from the study are summarized and the future work is outlined.