Simulation study of energetic particle driven Alfvén eigenmodes and geodesic acoustic modes in toroidal plasmas 環状プラズマにおいて高エネルギー粒子が励起するアルヴェン固有モードと測地線音響モードに関するシミュレーション研究

博士論文

Energetic particle driven instabilities are important issues for fusion plasmas because they lead to energetic particle transport and losses. Especially for fusion burning plasmas, where the getic alpha particles play the leading role in the fuel plasma heating, the energetic particle driven instabilities should be suppressed or mitigated for the better confinement of the energetic alpha particles. Then, the understanding of the fundamental properties of energetic particle driven instabilities will contribute to the successful operation of the future fusion reactors. In this dissertation, the linear properties and the nonlinear evolution of energetic particle driven Alfvén eigenmodes and geodesic acoustic modes (GAM) are investigated using a hybrid simulation code for magnetohydrodynamics (MHD) and energetic particles. The interaction between energetic particles and Alfvén eigenmodes in reversed shear tokamak plasmas are investigated for different minimum safety-factor values. When the energetic particle distribution is isotropic in velocity space, it is demonstrated that the transition from low-frequency reversed shear Alfvén eigenmode (RSAE mode) to toroidal Alfvén eigenmode (TAE mode) takes place as the minimum safety-factor value decreases. The frequency rises up from a level above the GAM frequency to the TAE frequency. It is found that the energetic particles both co- and counter-going to the plasma current are transported by the TAE mode, whereas the co-going particles are primarily transported by the low-frequency RSAE mode. When only the co-passing particles are retained, the low-frequency RSAE modes are primarily destabilized. On the other hand, the high-frequency RSAE modes are destabilized when only the counter-passing particles are retained. The linear properties and the nonlinear evolution of energetic particle driven GAM (EGAM) are explored for the Large Helical Device (LHD) plasmas. Since the kinetic GAM frequency in LHD is close to that in tokamaks, tokamak type equilibria are examined with concentric magnetic surfaces, and with the safety factor profiles and the aspect ratio similar to the LHD plasmas. For the linear properties, it is found that the EGAM is a global mode because the fluctuation frequency is spatially constant, whereas the conventional local GAM frequency constitutes a continuous spectrum that varies depending on the plasma temperature and the safety-factor. The frequency of the EGAM intersects with the GAM continuous spectrum. The EGAM frequency is lower for the higher energetic particle pressure. The poloidal mode numbers of poloidal velocity fluctuation, plasma density fluctuation, and magnetic fluctuation are m=0, 1, and 2, respectively. Good agreement is found between the LHD experiment and the simulation result in the EGAM frequency and the mode numbers. The EGAM spatial profile depends on the energetic particle spatial distribution and the equilibrium magnetic shear. The wider energetic particle spatial profile broadens the EGAM spatial profile. The EGAM spatial profile is wider for the reversed magnetic shear than for the normal shear. The nonlinear evolution of EGAM is studied using the hybrid simulation code. The frequency chirping of EGAM has been observed in LHD and tokamaks. The frequency chirping up and down is found to take place in the simulation results. In order to understand the physics mechanism of the frequency chirping, the energetic particle distribution function and the energy transfer rate from the particles to the wave are analyzed in 2-dimensional velocity space of energy and pitch angle variable. In the linearly growing phase of the instability, two resonant regions, one destabilizing and the other stabilizing the EGAM, are found in the velocity space. In the nonlinearly frequency chirping phase, a pair of hole and clump is created at each resonant region. A hole and a clump correspond to negative and positive fluctuation, respectively in the distribution function. Then, two pairs of hole and clump are created, one at the destabilizing region and the other at the stabilizing region. The transit frequencies of the holes and clumps are compared with the EGAM frequency. The transit frequencies of the holes and clumps are in good agreement with the two branches of the EGAM frequency, one chirping up and the other chirping down. This indicates that the holes and clumps are kept resonant with the EGAM and the frequency chirping can be attributed to the hole-clump pair creation. The hole-clump pair creation and the associated frequency chirping are known to take place when the system is close to the instability threshold for the inverse Landau damping. However, the direct numerical simulations have so far been limited to the hole-clump pair creation at the destabilizing region in 1-dimensional velocity space. The result presented in this dissertation is the first numerical demonstration of a) hole-clump pair creation and frequency chirping for EGAM, b) two pairs creation at the destabilizing and the stabilizing regions, and c) hole-clump pairs in 2-dimensional velocity space. For the linear properties, it is found that the EGAM is a global mode because the fluctuation frequency is spatially constant, whereas the conventional local GAM frequency constitutes a continuous spectrum that varies depending on the plasma temperature and the safety-factor. The frequency of the EGAM intersects with the GAM continuous spectrum. The EGAM frequency is lower for the higher energetic particle pressure. The poloidal mode numbers of poloidal velocity fluctuation, plasma density fluctuation, and magnetic fluctuation are m=0, 1, and 2, respectively. Good greement is found between the LHD experiment and the simulation result in the EGAM frequency and the mode numbers. The EGAM spatial profile depends on the energetic particle spatial distribution and the equilibrium magnetic shear. The wider energetic particle spatial profile broadens the EGAM spatial profile. The EGAM spatial profile is wider for the reversed magnetic shear than for the normal shear. The nonlinear evolution of EGAM is studied using the hybrid simulation code. The frequency chirping of EGAM has been observed in LHD and tokamaks. The frequency chirping up and down is found to take place in the simulation results. In order to understand the physics mechanism of the frequency chirping, the energetic particle distribution function and the energy transfer rate from the particles to the wave are analyzed in 2-dimensional velocity space of energy and pitch angle variable. In the linearly growing phase of the instability, two resonant regions, one destabilizing and the other stabilizing the EGAM, are found in the velocity space. In the nonlinearly frequency chirping phase, a pair of hole and clump is created at each resonant region. A hole and a clump correspond to negative and positive fluctuation, respectively in the distribution function. Then, two pairs of hole and clump are created, one at the destabilizing region and the other at the stabilizing region. The transit frequencies of the holes and clumps are compared with the EGAM frequency. The transit frequencies of the holes and clumps are in good agreement with the two branches of the EGAM frequency, one chirping up and the other chirping down. This indicates that the holes and clumps are kept resonant with the EGAM and the frequency chirping can be attributed to the hole-clump pair creation. The hole-clump pair creation and the associated frequency chirping are known to take place when the system is close to the instability threshold for the inverse Landau damping. However, the direct numerical simulations have so far been limited to the hole-clump pair creation at the destabilizing region in 1-dimensional velocity space. The result presented in this dissertation is the first numerical demonstration of a) hole-clump pair creation and frequency chirping for EGAM, b) two pairs creation at the destabilizing and the stabilizing regions, and c) hole-clump pairs in 2-dimensional velocity space.

総研大甲第1545号