A simple analytic model of impurity leakage from the divertor and accumulation in the main scrape-off layer

Edge codes such as SOLPS-ITER find distributions of impurity ions, e.g. of C, N, Ne and Ar, in the divertor and SOL which are quite non-uniform spatially, both poloidally and radially. Poloidally, impurity ion density distributions often have strong peaks near the targets as well as a peak on/near the separatrix in the main SOL near the outside midplane. A high density of low-Z impurities near the targets is quite desirable since cold, dense divertor plasma conditions there result in very efficient radiative dissipation of power. By contrast, impurity concentration near the outside midplane separatrix is often quite undesirable since the impurity density there is essentially the boundary value for impurity levels in the confined plasma. In order to better understand the poloidal distribution of impurities in the edge plasma, a simple analytic 1D impurity fluid model, 1DImpFM, has been developed for the transport along open field lines of impurity ions in a specified fuel-plasma background. Often, the strongest parallel forces acting on impurity ions in the edge plasma are (i) FiG, the (fuel) ion temperature parallel-gradient force ('thermal force'), and (ii) FF, the friction force between fuel and impurity ions ('friction force'). Recently, Senichenkov et al (2019 Plasma Phys. Control. Fusion61 045013) reported the extremely useful and informative result that the impurity ion parallel velocity calculated by the SOLPS-ITER code can be remarkably well reproduced by assuming the simple force balance FF + FiG = 0. In the present paper the basis for, and a number of basic predictions of, the 1DImpFM are reported including an assessment of the circumstances under which FF + FiG = 0 can be expected to be a good approximation. The 1DImpFM is used to elucidate the competing roles of thermal and friction forces, as they control three key features of edge impurity behavior: (a) leakage of impurity ions from the divertor, (b) the peaking of impurity density near the targets, and (c) impurity ion accumulation near the midplane separatrix; the model provides simple analytic expressions for estimating the divertor leakage rate (ions/m2/s) and impurity density peaking/accumulation (ions/m3). A subsequent paper will report comparisons of results from the 1DImpFM and from SOLPS-ITER modeling of some ITER cases with neon impurities.