Formation and sustainability of H-mode regime in tokamak plasma via sources perturbations based on two-field bifurcation concept

A set of coupled particle and thermal transport equations is used to study a formation and sustainability of an edge transport barrier (ETB) in tokamak plasmas based on two-field bifurcation. The two transport equations are numerically solved for spatio-temporal profiles of plasma pressure and density. The plasma core transport includes both neoclassical and turbulent effects, where the latter can be suppressed by flow shear mechanism. The flow shear, approximated from the force balance equation, is proportional to the product of pressure and density gradients, resulting in non-linearity behaviors in this calculation. The main thermal and particle sources are assumed to be localized near plasma center and edge, respectively. It is found that the fluxes versus gradients regime illustrates bifurcation nature of the plasma. This picture of the plasma implies hysteresis properties in fluxes versus gradients space. Hence, near marginal point, the perturbation in thermal or particle sources can trigger an L-H transition. Due to hysteresis, the triggered H-mode can be sustained and the central plasma pressure and density can be enhanced

Simulations of ITER in the presence of ITB using the NTV intrinsic toroidal rotation model

Abstract Simulations of a standard H-mode International Thermonuclear Experimental Reactor (ITER) scenario in the presence of internal transport barrier (ITB) are carried out using the 1.5D BALDUR integrated predictive modelling code. The intrinsic offset toroidal rotation, which can play an essential role in turbulent transport suppression that results in the ITB formation, is theoretically calculated using a model based on the neoclassical toroidal viscosity (NTV) concept. The core transport in this simulation is a combination of a mixed Bohm/gyro-Bohm anomalous transport model and an NCLASS neoclassical transport model. The boundary condition of the simulations is taken to be at the top of the pedestal where the pedestal value is calculated using the pedestal model based on a combination of pedestal width scaling determined by magnetic/flow shear stabilization and an infinite-n ballooning pressure gradient model. It is found that the predicted intrinsic rotation can result in the formation of ITB, locating mostly between r/a = 0.6 and 0.8 and having a strong impact on the plasma performance in ITER. It is also found that the variations of plasma density and heating power result in a minimal change in toroidal rotation; whereas the increase in plasma effective charge can considerably reduce the toroidal velocity peaking.</jats:p

Understanding roles of E × B flow and magnetic shear on the formation of internal and edge transport barriers using two-field bifurcation concept

Abstract A set of heat and particle transport equations with the inclusion of E  ×  B flow and magnetic shear is used to understand the formation and behaviors of edge transport barriers (ETBs) and internal transport barriers (ITBs) in tokamak plasmas based on two-field bifurcation concept. A simple model that can describe the E  ×  B flow shear and magnetic shear effect in tokamak plasma is used for anomalous transport suppression with the effect of bootstrap current included. Consequently, conditions and formations of ETB and ITB can be visualized and studied. It can be seen that the ETB formation depends sensitively on the E  ×  B flow shear suppression with small dependence on the magnetic shear suppression. However, the ITB formation depends sensitively on the magnetic shear suppression with a small dependence on the E  ×  B flow shear suppression. Once the H-mode is achieved, the s-curve bifurcation diagram is modified due to an increase of bootstrap current at the plasma edge, resulting in reductions of both L-H and H-L transition thresholds with stronger hysteresis effects. It is also found that both ITB and ETB widths appear to be governed by heat or particle sources and the location of the current peaking. In addition, at a marginal flux just below the L-H threshold, a small perturbation in terms of heat or density fluctuation can result in a transition, which can remain after the perturbation is removed due to the hysteresis effect.</jats:p

Roles of driven current locations on ETB and ITB based on three-field bifurcation concept

Abstract This work investigates the roles of external current source on the formation and effectiveness of an internal transport barrier (ITB) and an edge transport barrier (ETB) in fusion plasma using bifurcation approach. Thermal, particle and toroidal momentum transport equations are solved simultaneously for the spatiotemporal profiles of plasma pressure, density and toroidal velocity, respectively. The transport effects include neoclassical and turbulent terms with constant coefficients assumption. The turbulent suppression, leading to intrinsic formation of transport barriers, is driven by the magnetic shear and the flow shear. Residual stress effect is included in this work. Thermal, particle and torques sources are locally provided based on Gaussian shape distribution at plasma center, plasma edge and plasma center, respectively. The effects of off-axis driven current locations on ITB and ETB formations are investigated. In particular, width and height of ETB and ITB are shown to be affected by the source. It is found that off-axis of driven current can increase plasma temperature, density and toroidal velocity at its core because ITB is formed and expanded. However, size of ETB pedestal is slightly affected by the location of driven current. When the location of driven current is changed from r = 0.00 to 0.60, ITB width changes from r = 0.00 to 0.12 of plasma profile and ITB top formation location changes from r = 0.00 to 0.80.</jats:p

Model for toroidal velocity in H-mode plasmas in the presence of internal transport barriers

A model for predicting toroidal velocity in H-mode plasmas in the presence of internal transport barriers (ITBs) is developed using an empirical approach. In this model, it is assumed that the toroidal velocity is directly proportional to the local ion temperature. This model is implemented in the BALDUR integrated predictive modelling code so that simulations of ITB plasmas can be carried out self-consistently. In these simulations, a combination of a semi-empirical mixed Bohm/gyro-Bohm (mixed B/gB) core transport model that includes ITB effects and NCLASS neoclassical transport is used to compute a core transport. The boundary is taken to be at the top of the pedestal, where the pedestal values are described using a theory-based pedestal model based on a combination of magnetic and flow shear stabilization pedestal width scaling and an infinite-n ballooning pressure gradient model. The combination of the mixed B/gB core transport model with ITB effects, together with the pedestal and the toroidal velocity models, is used to simulate the time evolution of plasma current, temperature and density profiles of 10 JET optimized shear discharges. It is found that the simulations can reproduce an ITB formation in these discharges. Statistical analyses including root mean square error (RMSE) and offset are used to quantify the agreement. It is found that the averaged RMSE and offset among these discharges are about 24.59% and −0.14%, respectively.</jats:p