Numerical Simulations Of Micro-turbulence In Tokamak Edge

As a magnetic confinement device, the tokamak is one of the most promising approaches to enable controlled fusion, which can solve the energy problem ultimately. The high confinement mode (H-mode) can make it much easier to achieve ignition. Thus the H-mode becomes a baseline operation scenario for the International Thermonuclear Experimental Reactor (ITER). In the past three decades, many physical issues about the H-mode, such as micro-instabilities and turbulent transport in the edge, as well as the mechanism of L-H transition, are still not well understood.After twenty years of development, first-principle gyrokinetic simulation has become a major tool to study turbulent transport in tokamaks. In this thesis, we carried out gyrokinetic simulations using GTC code for several recent shots of HL-2A tokamak in H-mode. The major electrostatic instability with experimental parameters is identified by the GTC simulation to be trapped electron mode (TEM), with good agreement in both nonlinear frequency and poloidal mode number. At the linear stage, the electrostatic modes driven by steep grdient with the H-mode edge parameters show un-conventional mode structures, which are not localized at the outboard mid-plane of the poloidal cross section, while the conventional ballooning mode structures are linked with L-mode parameters. This un-conventional structures can peak at any poloidal angle between 0 and 2π and can also have multi-peaks. The linear mode frequency is observed to jump to another branch when the gradient exceeds a critical value. The poloidal mode spectrum cascades inversely into longer wavelength region during the nonlinear saturation of turbulence, which are found more likely to come from the nonlinear evolution of each single mode instead of the mode-mode coupling pro-cess. The instability problem is mimicked by a model equation where a series of unstable eigen solutions are found. Under weak gradient, the most unstable modes are found to be in the ground state, which shows the conventional ballooning structure. However, under strong gradient, the most unstable solution jumps into the non-ground state, which shows aforementioned un-conventional mode structure. Thus, the L-H transition could be analogous to the transition between eigenstates. By nonlinear gyrokinetic simulations, we found that zonal flow would be less important to sup- press turbulent transport in the strong gradient regime. More interestingly, we discovered that the turbulent transport coefficient would decrease with the gradient increasing when the gradient ex-ceed a critical value. This provide a new route for the L to H transition without invoking shear flow or zonal flow. Physically, we would argue that the change of linear eigenmode structure leads to change of transport characteristics for the H-mode edge plasma, e.g., the reduction of radial correlation length, or change from diffusion and convection mixed transport to mainly diffusion transport.The electromagnetic effects should be included for a completely study of the edge mirco-instabilities. However, these studies are still less successful after more than one decade of effort, even reach agreement on the linear frequency among different codes or between code and experi-ment. Theoretically, the most important electromagnetic mode in H-mode edge is considered to be kinetic ballooning mode (KBM). We find that this mode is very sensitive to the magnetic equilib-rium implementation in the numerical code, although the TEM and ITG (ion-temperature gradient mode) modes are found not to be sensitive. This could explain why the codes tend to differ from experimental observations on KBM mode while tend to agree on ITG/TEM.