The macro- and micro-instabilities in the pedestal region of the Tokamak

In this paper, we present the theoretical and numerical studies of the linear characteristics and nonlinear transport features of the instabilities driven by the steep profile gradient and edge current in the pedestal region of the tokamak. Two important instabilities, the peeling-ballooning (P-B) modes (macro-instability) and the drift-Alfven modes (micro-instability), are studied using the fluid analysis and the BOUT++ codes. In particular, the edge-localized modes (ELMs), which appear to be the energy burst in the nonlinear stage of the peeling-ballooning mode, are numerically studied and the results are compared with the experimental measurement. In addition, the features of the impurity transport in the edge region of the tokamak are theoretically analyzed. Firstly, we explore the fundamental characteristics of the P-B modes and the ELM bursts numerically using the three-field reduced MHD model under the BOUT++ framework, in the shifted-circular geometry, i.e. the limiter tokamak geometry. In the linear simulations, the growth rate and real frequency and the mode structure versus the toroidal mode number (n) are shown. The features of the ELM bursts are shown in the nonlinear simulations, including the time evolution of the relative energy loss (ELM size) and the pedestal profile. Secondly, two original research projects related to the P-B modes and the ELM burst are described. One is the study of the scaling law between the relative energy loss of ELMs and the edge collisionality. We generate a sequence of shifted-circular equilibria with different edge collisionality varying over four orders of magnitude using EFIT. The simulation results are in good agreement with the multi-tokamak experimental data. Another is the study of the differences of the linear behaviors of the P-B modes between the standard and snowflake divertor configurations. Using DIII-D H-mode ElMing equilibria, we found that the differences are due to the local magnetic shear change at the outboard midplane, which is the result of the realization of the snowflake configuration. Finally, the micro-instability, the drift-Alfven instability in the pedestal region of the DIII-D tokamak is studied. A modified six-field Landau fluid model under BOUT++ framework is used to study the linear characteristics and transport features of the drift-Alfven modes. Based on the DIII-D H-mode discharge, a sequence of divertor tokamak equilibria with different pedestal height is generated by the ’VARYPED’ tool for our studies. Qualitative agreement is obtained between theoretical analysis and the simulation results in the linear regime. Moreover, the heat transport induced by the drift-Alfven turbulence is explored and the convection level is estimated for both ions and electrons.