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内容記述 |
The ballooning mode is a magnetohydrodynamic (MHD) instability that is excited<br />in finite beta plasmas. The energy source of the ballooning mode originates<br />from the pressure gradient in a locally unfavorable magnetic curvature region, typically,<br />in the outboard of the torus. The proximity of the measured edge pressure gradient<br />in H-mode to the critical gradient for ideal ballooning instability has led to the<br />proposal that these instabilities might have a role in triggering edge localized modes<br />(ELMs). New nonlinear theoretical models describe ELMs in terms of filaments that<br />erupt from the plasma. This is supported by strong experimental evidence from the<br />MAST tokamak[1, 2, 3] that the ELM does indeed exhibit a mode structure predicted<br />by the nonlinear ballooning mode theory. This thesis presents the nonlinear dynamics<br />of the ballooning mode and its relation with ELMs by means of numerical simulations<br />in spherical tokamak (ST) devices in the framework of MHD model and the drift<br />model. Our simulation reproduces the characteristic features of ELM crash phase.<br /> The nonlinear simulations using MHD model are executed in a three dimensional<br />full toroidal geometry. The initial MHD equilibrium for the simulation is given<br />as an axisymmetric numerical MHD equilibrium, which is obtained by solving the<br />Grad-Shafranov equation on the poloidal cross-section. The profiles are selected to be<br />moderately broad in the core region following the conventional experiments. During<br />the linear analysis, the intermediate-n modes (i.e., n = 5−9) have larger growth rates<br />than others, where n is the toroidal mode number. It is shown that these intermediate-n<br />modes have a ballooning mode nature in that the mode structures are poloidaly localized in the bad curvature region, and have a wide envelope consisting of several<br />poloidal components. In the nonlinear phase, the MHD ballooning modes evolve into<br />a nonlinear structure that results in the formation of a number of hot plasma filaments,<br />elongated along a magnetic field line, but localized about it. These filaments extend<br />out into the scrape-off layer on the outboard side but remain connected back into the<br />pedestal region on the inboard side. This filamentary structure is correspondent to the<br />convection motion of the plasma flows, which forms a twin-vortex flow pattern in such<br />a way that the plasma moves in outward direction, pushing the core plasma from inside<br />to outside of the torus. When the balloon structure is initially formed at the plasma<br />surface, the magnetic field lines on both sides of the separatrix are pushed against each<br />other by such perpendicular flows due to the spouting-out and the perfect conductor<br />conserving the poloidal flux. Under this situation, the reconnection of the field lines<br />can effectively occur by the driven reconnection mechanism. Once such reconnection<br />occur, the plasma rapidly flows out through the reconnected field lines due to the<br />parallel pressure gradient, leading to the filamentary structure. After the internal free<br />energy is partially lost by such convective processes, the system ceases to develop and<br />reaches a relaxed state. These results are compared qualitatively with the experimental<br />observation of the ELMs in MAST and NSTX experiments. Good agreement is<br />found in the following characteristics formation of filaments separating from the core,<br />non-uniform growth of filaments due to toroidal mode coupling, time scale of ELM<br />crash, triggering by the ideal ballooning mode, presence of intermediate-n precursors<br />and loss of plasma through convective process.<br /> Moreover the finite Larmor radius (FLR) effect is also addressed using the simplified drift model, where the ion diamagnetic drift effect is included in the advection<br />term of the equation of motion. This modification has been found to suppress the<br />higher-n components linearly, since the mode growth is suppressed by the sheared rotation flows. However, it has been also found that the filament separation from the core<br />can take place universally for FLR as well as the MHD case. |
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