Impurity modelling for the study of start-up and burn-through phases in tokamaks with the 0d code

Plasma start-up in Tokamaks requires high loop voltage (energy source), induced using Ohmic coils, in the pre-filled gas inside the vacuum vessel. This energy needs to be driven through it as quickly as possible in order to minimize the energy loss and assure maximum ionization. Losses can occur in various ways such as transport driven heat and particle loss from plasma, Bremsstrahlung radiation, ionization, recombination and equilibration. Thus, in order to achieve a successful start-up, it is essential to maintain energy balance so that the radiation and ionization barrier is successfully overcome during the burn-through phase with minimum possible amount of energy. Start-up failures are mostly due to plasma contamination by impurities originating from first wall. Carbon (C) and Oxygen (O) are the major impurity constituents. Complete ionization of these impurities in the burn-through phase utilizes most of the input energy. A 0D code has been developed in-house at IPR to study plasma start-up and evolution in tokamaks. In this code, a dynamic evolution of impurities has been modeled. Previously, impurity content in the plasma was considered as a constant percentage of the electron density (n_e), irrespective of their ionization states, throughout the plasma evolution. This approximation may lead to serious over/under estimation of major plasma parameters during their evolution, especially in the burn-through phase. Now the 0D code is augmented with a detailed impurity model and it has rendered the impurity content of plasma to be dynamic, governed by the evolution of n_e, temperature (T_e) and the initial impurity influx considered. Evolution of C and O density and all of their charged states is interrelated and represented by coupled ordinary differential equations (ODEs). Rate of change of impurity densities in the model are coupled through three types of interactions viz. recombination, ionization and charge exchange. Reaction cross-sections depend on impurity densities, n_e and T_e. Solving the energy balance equations for each time step in the 0D code yields the temperature of ions and electrons for the next time step. These are used in the impurity model to calculate the coefficients of all the reactions and evolve data for the next step. Temporal profiles of n_e, T_e and current are compared with experimental profiles from the SST-1 tokamak and a better correlation is obtained with incorporation of the impurity model. Further, time evolution of various charged states of C and O will also be reported. (author)