DOI: 10.14457/tu.the.2015.39
title: Study of formation and dynamics of internal and external transport barriers based on bifurcation concepts

description: The formation and dynamics of both Edge Transport Barriers (ETB) and Internal Transport Barriers (ITB) are analyzed based on bifurcation concepts. In this thesis, one-field (thermal) and two-field (coupled thermal and particle) transport equations are solved analytically and numerically for the profiles of pressure and density gradients as functions of heat and particle fluxes, respectively. The transport effect includes a combination of neoclassical transport and anomalous transport. The transport suppression mechanisms based on flow shear and magnetic shear are assumed to be only in the anomalous channel. It is found that plasmas can exhibit bifurcation where a sudden jump in plasma gradients can be achieved at the transition point corresponding to the critical flux. Local stability analysis shows that the transition occurs at a threshold flux and exhibits hysteresis only if the ratio of anomalous to neoclassical transport exceeds a critical value. The depth of the hysteresis loop depends on both neoclassical and anomalous transport, as well as the suppression strength. Dynamically, it is found that an ETB expands inward, in which the radial growth of the pedestal initially appears to be super-diffusive but later slows down and stops. In addition, the time of barrier expansion is found to be much longer than the time plasma takes to evolve from L-mode to H-mode. Evidently, an ETB can form only when the local flux (heat/particle) surpasses the critical value. The ITB formation is possible only with a presence of reverse q profile. The location and width of ITB are found to be correlated with the plasma current profile. Particularly, the top of ITB is found near the location of off-axis maximum current density and zero magnetic shear. Both ITB and ETB widths appear to be governed by the heat source, off-axis current drive position and transport strengths. In the second part of the thesis, a 1.5D BALDUR integrated predictive modeling code, with inclusion of toroidal velocity models, is used to simulate plasma profiles. The predictive toroidal velocity models are based on neoclassical toroidal viscosity (NTV) and toroidal current density effects. It is found that the predicted intrinsic rotation can result in the formation of an ITB, located mostly between r/a = 0.6 to 0.8 and having a strong impact on plasma performance. It is also found that plasma density and heating power affect minimally the toroidal rotation, whereas the increase of plasma effective charge can considerably reduce the toroidal velocity peaking. In the last part, the impacts of toroidal flow on the L-H¬ transition phenomenon are investigated based on bifurcation concepts. It is found that inclusion of toroidal velocity can substantially increase the plasma pressure and density, mainly due to an increase of the pedestal width.  In addition, the pedestal for pressure tends to form shortly before that of density. After the pedestal forms, it expands inwards super-diffusively in the initial state and sub-diffusively in the final state before reaching a steady state. The expansion speed is sensitive to the flow shear strength. The time required for the plasma to reach a steady state in H-mode is much longer than the transition time.