Analytical calculations for impurity seeded partially detached divertor conditions

A simple analytical formula for the impurity seeded partially detached divertor operational point has been developed using 1D modelling. The inclusion of charge exchange momentum loss terms improves the 1D modelling for ASDEX Upgrade conditions and its extrapolation to larger devices. The investigations are concentrated around a partially detached divertor working point of low heat flux and an electron temperature around 2.5 eV at the target which are required to maintain low sputtering rates at a tungsten target plate. An experimental formula for the onset of detachment by nitrogen seeding in ASDEX Upgrade is well reproduced, and predictions are given for N, Ne and Ar seeding for variable device size. Moderate deviations from a linear P-sep/R size dependence of the detachment threshold are seen in the modelling caused by upstream radiation at longer field line lengths. The presented formula allows the prediction of the neutral gas or seed impurity pressure which is required to achieve partial detachment for a given P-sep in devices with a closed divertor similar to the geometry in ASDEX Upgrade.