A reduced model for the ITER divertor based on SOLPS solutions for ITER Q = 10 baseline conditions: A. identifying options for the control parameters*

Abstract

Edge codes such as SOLPS coupled to neutral codes such as EIRENE have become so comprehensive and sophisticated that they now constitute, in effect, ‘code-experiments’ that, as for actual experiments, can benefit from interpretation using simple models and conceptual frameworks, i.e. reduced models. The first task is the identification of options for the reduced model control parameters that are best suited for control of the action of the divertor, i.e. for control of target power loading and sputter-erosion, primarily. A strong correlation between the electron temperature at the divertor target, Te,t, and the neutral deuterium D2 density at the target, nD2,t, flux-tube resolved, has recently been reported for a number of code studies including SOLPS-4.3 modeling of a set of ~ 50 ITER baseline cases: QDT = 10, q95 = 3, PSOL¬ = 100 MW, metallic walls, and Ne seeding [1]. This Part A of the present study reports new results for largely the same ITER cases, confirming the strong correlations reported earlier between local values of T¬¬e,t, and (i) n¬D2,t, and (ii) normalized volumetric losses of power and pressure in the divertor. Strong correlations have now also been found, and are reported here for the first time, between Te,t and all of the divertor target quantities of practical interest. A physical explanation for this surprising result has not been fully identified; nevertheless it has encouraging implications for reduced modeling of the ITER divertor. For such ITER conditions, (i) the global Ne injection rate, Inj_Ne [Ne/s], and (ii) the electron temperature at the location on the target where the peak power deposition occurs, T_(e,t)@q_(⊥,pk) [eV], are found to be promising reduced model control parameters. In the companion report, Part B, a Reduced Model for the ITER divertor is developed and described in detail, based on reversed-direction 2 Point Modelling, Rev2PM. The input to the Reduced Model is a value of the variable pair (T_(e,t)@q_(⊥,pk),Inj_Ne ) and the output are values of the various target as well as divertor-entrance quantities of practical interest, e.g. q_(⊥,pk), n_(e,Xpt) (the electron density at the poloidal location of the X-point), etc. In Part B the Reduced Model is quantitatively characterized using one half of the code cases; it is then used to successfully predict (replicate) the code values of e.g. n_(e,Xpt) for the other half of the cases.

Reversed-direction 2-point modelling applied to divertor conditions in DIII-D *

“…However, it has recently been found that in almost all cases (both experimental and computational), these can be represented by functions that depend primarily on the target electron temperature, T e,t [6,14,15]. In this work, we make use of volumetric loss terms that are fit to the aforementioned large database of SOLPS-ITER simulations of the ITER divertor [12], fitting to the electron temperature in the last cell in front of the target on the computational grid used in the modeling. These fits take the form of a 4th-order log-log polynomial:…”

“…These fit functions are plotted versus T e,t in figure 1. The fit functions are clamped to their maximum for T e,t values above the range used to define these fits in [12] (about 13 eV), though this assumption has negligible effect on any of the results presented in this paper.…”

“…We may now combine equation (12) at the target and upstream, plug into equation (2), and make use of the T e,tdependent fit for (1-f mom ) (figure 1) to derive the following Rev2PM prediction for the upstream electron pressure:…”

“…Figure 9 shows the ratio of measured electron pressure at the target to that at the Xpoint, versus measured target electron temperature. Overlaid is the volumetric momentum loss function (1-f mom ) that was extracted from the ITER Q = 10 SOLPS-ITER database [12] (see also figure 1).…”

“…The Reverse 2-Point Model (described in section 2) shows promise as such a reduced model. Recent analysis of a large database of SOLPS-ITER simulations for Q = 10 operation in ITER (spanning a wide range of detachment states) have shown very strong correlations between the divertor target electron temperature (and to a lesser extent the impurity seeding rate) and almost all quantities of interest for divertor physics [12]. In [13], a Reverse 2-Point Model for the ITER divertor (taking the SOLPS-calculated divertor target plasma conditions as input) was developed, and it was found that the reduced model could replicate with excellent accuracy the upstream plasma parameters calculated by SOLPS.…”