If correct, the Lengyel model offers a simple and powerful tool to predict the conditions required for detachment onset in future fusion reactors. We assess its validity against a comprehensive SOLPS-4.3 simulation database of ITER baseline (Q = 10) neon-seeded plasmas (Pacher et al 2015 J. Nucl. Mater. 463 591). In absolute terms, the Lengyel Model is found to significantly overpredict the simulated impurity concentration required in the ITER outer divertor for outer target ion flux rollover (by a factor ∼4.3 in this particular case). Importantly though, at detachment onset, and even beyond onset, the Lengyel model does give a remarkably accurate prediction of the scaling interdependencies between the electron density at the outer divertor entrance, the parallel energy flux density at the outer divertor entrance, and the impurity concentration in the outer divertor. However, the generalisation of these two key results to other machines, and in the presence of additional physics not included in these simulations, requires further studies. The analysis techniques described here provide a framework for such studies. Regarding the factor ∼4.3 overprediction of the simulated outer divertor impurity concentration, the main contributors to the disagreement are found to be other energy loss mechanisms besides impurity cooling (primarily neutral losses and radial transport) combined with convective energy fluxes near the target, as well as non-constant electron static pressure due to poloidally variable Ti/Te. None of these are included in the Lengyel model. By themselves, these do not strongly influence the scaling interdependencies of the main Lengyel parameters over the explored parameter range. The impurity residence time τ is observed to increase with density, which tends to flatten out the impurity concentration scaling at low density, relative to the Lengyel model (which usually assumes constant τ). In these simulations, however, this flattening out was cancelled by an accumulation of other effects, so that the scaling prediction of the Lengyel model was still well met. A simple physics model is derived for neτ that matches the simulation data well. Neon is found to migrate from the inner divertor to the outer divertor with increased puffing, thereby increasing the outer divertor neon enrichment. At outer target ion flux rollover, though, the enrichment is approximately independent of the upstream concentration, so that the Lengyel model predicts well the scaling dependency between the upstream impurity concentration and the upstream electron density, both key quantities dictating the operational range of a tokamak.
Three-dimensional impurity transport modeling of neon-seeded and nitrogen-seeded LHD plasmas