Phase transition from eigenmodes to solitary perturbations in magnetized plasma boundary

Abstract

Mankind is expected to face a serious world energy problem where the energy demand exceeds the available energy due to the growth of world population and the economic growth of large nations. The promising alternative energy to solve the energy problem is fusion energy, which is high efficiency and environment friendly energy. Fusion energy is the enormous amount of energy produced by the reduction in total mass when light nuclei are fused into a heavy nucleus. In order to implement fusion energy on the earth, we need to develop a method to confine the fusion fuel. Therefore, a tokamak device was conceived to confine the nuclear fusion fuel in a doughnut shape using a magnetic field. Efforts to increase the efficiency of fusion energy have continued for several decades. In 1982, a new operating mode, high confinement mode (H-mode) which is characterized by drastically improved temperature, pressure and particle confinement, was developed. However, while the plasma confinement is improved more than twice in the H-mode plasmas, a steep pressure gradient (called as a pedestal) is formed near the plasma edge and periodic pedestal collapse occurs. The pedestal collapse results in the ejection of energy and particle from the plasma, causing severe damage at the strike points on the plasma facing components (PFCs). There has been an effort to understand and control the pedestal collapse, but the mechanism of pedestal collapse is not yet identified. The well-known theoretical model for describing edge perturbations and pedestal collapse is the peeling-ballooning (PB) model which is driven by the pressure gradient and current density at the edge of the plasmas. However, this model only describes some of the edge perturbations and it is not enough to explain all the phenomena that occur at the edge. The evolution of edge perturbation during the formation and collapse of the pedestal observed by the KSTAR electron cyclotron emission imaging (ECEI) system, which measures local electronic temperature fluctuations, is divided into four stages: the initial growth stage, the quasi-steady stage, the phase transition stage, and the collapse stage. After the eigenmode structure grows semi-exponentially at the edge of H-mode plasma, the amplitude and spatial structure of the perturbation are unchanged for a while (typically a few ms). Then, the pedestal collapse occurs after a phase transition from an eigenmode to a nonmodal structure. Because the saturation of mode amplitude and the generation of nonmodal perturbation structure are difficult to be explained by the linear PB model, it is important to establish a new theoretical model based on detailed phenomenon reports. One of the notable phenomena not described by existing edge theory is the structural change of quasi-stable eigenmode (QSM) during the inter-collapse period. The QSM, whose intensity is almost constant for few hundreds of µs to few tens of ms, is observed in quasi-steady stage. The structure of the QSM can be represented by a toroidal mode number n, which is a common parameter that distinguishes the mode structure, and it is generally unchanged until the pedestal collapses. However, the rapid structural change of the QSM is often observed in quasi steady stage. The abrupt structural transitions of QSM have been diverse including small and large increase (o rdecrease) in the mode number and multiple changes during a single inter-collapse period. Two classes of the structural change of QSM were identified: non-overlapping change and overlapping change. The former case is characterized by the absence of coherent filamentary structure during the transition and the latter case is characterized by co existence of two coherent filamentary structures with different mode numbers. Each transition process typically lasts a few hundreds to thousands of µs. Another notable phenomenon is the ocrrurrence of nonmodal solitary perturbation (SP) near the pedestal collapse. The SP localized both poloidally and radially is observed within ~ 100 µs before the pedestal collapse. It develops with a low toroidal mode number (typically unity) in the pedestal ingrained with QSM. The SPs have smaller mode pitch and different (often opposite) rotation velocity compared to the QSMs. The observed SPs may be compared to non-linear growth of a low-n mode reported in numerical simulations of the pedestal collapse phase and it is considered as a strong trigger of the pedestal collapse. These observations provide solid experimental data for the validation of theory and numerical simulations and pave a way to identify the governing equations for the edge perturbation and the collapse of edge pedestal. The rapid structural change of QSM and generation of SP at the plasma boundary layer may also be a general interest as a strong nonlinear boundary phenomenon. Therefore, this thesis points out the limitations of the existing edge theoretical model and suggests the development direction.