Interaction between static magnetic islands and interchange modes in heliotron plasmas ヘリオトロン配位での静的磁気島と交換型モードとの相互作用
Interaction between static magnetic islands and interchange modes in heliotron plasmas
Nonlinear interaction between static magnetic islands generated by an xternal fieldand a resistive interchange mode driven by pressure gradient is investigated in straightheliotron configurations by means of a numerical method based on the reduced magnetohydrodynamics(MHD) equations. For the comprehensive understanding of the interaction, two aspects are studied by utilizing different MHD equilibria. One is effects of the interchange mode on the change of the static island and the other is effects of the static island on the growth of the interchange mode. Firstly, the former interaction aspect is studied with an equilibrium correspondingto nested magnetic surfaces. In this case, the interchange mode grows in spite ofexistence of a static magnetic island. The island width is changed in the nonlinear saturation phase of the interchange mode. The situation of the increase or decrease of the width depends on whether the diffusion of the equilibrium pressure in the direction parallel to the magnetic field is taken into account or not. In the case without the effect of the diffusion of the equilibrium pressure, there exist two solutions corresponding to the increase and the decrease of the island width. In this case, in spite of the nonlinear interaction, the total poloidal flux is approximately given by the linear sum of the poloidal flux generated by the interchange mode without a static island and the external poloidal flux for the generation of the static island. In the case with the effect of the diffusion of the equilibrium pressure, there exists only one solution corresponding to the increase of the width. This is due to the fact the parallel diffusion term generates a pressure term corresponding to the increase of the island width. Next, the latter interaction aspect is studied. For this study, equilibria includingstatic magnetic islands are necessary because the equilibrium pressure profile consistentwith the magnetic islands has possibility to affect the stability of the interchange mode.We have developed a numerical code (FLEC) to calculate the equilibria and found thatthere exist two kinds of solutions. One is the equilibrium of which the pressure profile is flat at not only the O-point but also the X-point. In this case, the pressure gradient is continuous at the separatrix. The other is the equilibrium of which the pressure profile is flat at the O-point and steep at the X-point. In this case, the pressure gradient is iscontinuous at the separatrix of the magnetic island. The finite beta has a contribution to increase the island width. Since it is known that the pressure profile with annular local flat structure aroundthe resonant surface have a stabilizing contribution to the interchange mode, effects of the static island on the interchange mode is studied for the equilibrium with the steep gradient at the X-point. The linear growth rate of the interchange mode is decreased and the saturation level is reduced as the island width is increased. The mode is completely stabilized when the width exceeds threshold value. In the case that interchange modes are unstable in an equilibrium with a thin island width, there are two cases of the increase and the decrease of the island width in the nonlinear saturation of interchange modes as obtained in the study for the former interaction aspect.