Time-dependent shell model for spreading of impurities locally injected into hot plasmas

Abstract

The spreading of impurities locally injected into hot magnetized plasmas is modelled on the basis of a fluid description for electrons, impurity neutrals and ions in low charge states in the vicinity of the injection position. The elaborated model takes into account that impurity particles of different charges are localized predominantly inside the nested shells whose extensions along and across the magnetic field increase with the charge. By integrating fluid equations for particle, parallel momentum and heat transfer, ordinary differential equations for the time evolution of characteristic shell dimensions, densities and temperatures of impurity ion species are deduced. The proposed approach is applicable under conditions where the local impurity density can noticeably exceed the density of the background plasma ions, but the effects of plasma cooling due to the presence of impurity are negligible. The results of calculations for plasma conditions typical in experiments with impurity seeding in tokamaks are presented.