A computational model describing confinement and performance of circular and D-shaped Tokamak plasmas

Abstract

A combined one-dimensional and two-dimensional (“ 1 1 2 D ”) description of toroidal and axisymmetric plasmas is presented which is based essentially on an equilibrium solver resorting to the fast Buneman invertor (“equilibrium module”) and two one-dimensional transport codes describing the protium, deuterium, tritium, and plasma energy inventory (“plasma module”) and accounting for three impurity species (“impurity module”); it is employed to compute the time evolution of Tokamak plasmas. The attempt was made to achieve a consistent modelling of the transport and equilibrium phenomena in a plasma which interacts with the peripheral devices for, e.g., confinement, plasma heating, and limitation of the plasma aperture. The equilibrium solver is connected to a coil submodule computing the poloidal field coil currents maintaining the designed plasma shape approximately. A surface current density accounting for the magnetization of the iron core and the yokes is calculated by means of the module for the transformer iron. This module is linked to the equilibrium solver as well so that consistency between the coil currents, the plasma current distribution, and the magnetization of the transformer iron is achieved. The “scrape-off module” resorts to a radial model for the limiters. The modules for additional heating account for a full beam geometry within a simple approach for the RF-heating. The neutral atomic and molecular hydrogen species are described by a multidimensional Monte Carlo code or, alternatively, by the fast 1D-code SPUDNUT (“neutral gas module”). The MHD behaviour is estimated by evaluating the time evolution of the Mercier and the resistive interchange criteria (“stability module”). The calculations which are based on TEXTOR, JET, and INTOR data resort preferentially to the equilibrium, the coil, and the transformer module. It is shown that, e.g., in case of a specific shot, the measured-time evolution of the currents in the poloidal field coils of TEXTOR can be reproduced within an accuracy of 8 %, only if the nonsaturated transformer iron is accounted for. The main results concerning JET and INTOR are: The performance of the JET-plasma is strongly influenced by the impurities essentially due to sputtering at the (noncarbonized) linear material (iron). The radiate 50% of the input power. These losses and the conduction losses limit the maximum plasma temperature at around 10 keV. Around the end of the discharge the transformer core is almost saturated and the nonsaturated yokes are important for the flux function distribution. The analysis of the INTOR-plasma shows that at a burn temperature T b = 10 keV the fusion power (122 MW) exceeds the line radiation, ionization, conduction, and convection losses by 11 MW. Due to the high pressure gradient, the plasma turns out to be diamagnetic in the total cross section; the toroidal field, however, is reduced at the magnetic axis by 4% of the vacuum value only.