On mechanisms of impurity leakage and retention in the tokamak divertor

Impurity seeding into a tokamak divertor for radiative cooling is considered as a tool for achieving detached/semi-detached regimes required to meet the condition of acceptable heat loads on divertor plates. Experiments aimed at searching for an operational window with a significant reduction of poloidal heat fluxes due to the impurity radiation and without decrease of confinement are performed on many tokamaks. A critical issue in these experiments is how large a fraction of impurities is retained in the divertor region and how much is extracted upstream to the scrape-off layer. In the present paper a physical mechanism of impurity transport from a divertor towards upstream and back to the divertor is analyzed. It is demonstrated that the widespread concept that the impurity leaks if the parallel thermal force exceeds the friction due to main ions and is retained otherwise—is not correct. In this paper, we contend that the impurity leaks if it crosses the stagnation point of the impurity ion poloidal velocity profile before being ionized, and is retained if it ionizes closer to the target than the location of that stagnation point. Thus the leakage efficiency depends on the relative spatial positions of the impurity atom ionization source and the stagnation point of the impurity ion poloidal velocity profile. The impurity ion poloidal velocity is to large extent the sum of the poloidal projection of its parallel velocity and the E × B drift velocity, where the former is derived from the parallel impurity force balance equation. It is demonstrated that the solution of this equation may be approximated by the balance of friction and thermal forces in all regimes, while other terms are smaller. This allows for expressing the impurity parallel velocity through the main ion one and makes the distribution of the parallel (poloidal) fluxes of the main ions, including Pfirsch–Schlüter fluxes and E × B drift fluxes, to be an important element of the impurity transport. It is shown that the impurity distribution in the edge plasma is rather sensitive to the value of the impurity ion ionization rate. This analysis is supported by simulation results obtained for the ASDEX Upgrade tokamak with various seeding rates of N and Ne with the SOLPS-ITER code. The importance of the inclusion of self-consistent drift flows is demonstrated by comparison to results of corresponding simulations with the drifts turned off.