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As the principal design driver, the emphasis in the paper will be on steady state power flux densities in the deuterium-tritium (DT) phases (Section 3), drawing heavily on the "carbon-free" SOLPS-4. 3 plasma boundary simulation code database first introduced in  [3] , itself a more extensive repeat of earlier studies with metal walls but with an older divertor geometry  [7]. In addition to discussing some of the key results with regard to divertor performance, the analysis in  [3]  focused on core-edge integration to examine the impact on the burning plasma operation window of the switch to non-carbon plasma-facing components (PFC) and extrinsic radiators for power flux control. Here, the simulation database is revisited with divertor performance in mind and, in particular the issue of the peak divertor target stationary power flux density, q ⊥,pk , where the symbol "⊥" refers here, and subsequently throughout the paper, to the quantity on the real target surface (hence the quantity most important to those designing the divertor PFCs).
It was found that restricting q ⊥,pk to 10 MW m -2 yields a reasonable operational window (the range of viable input parameters which result in acceptable performance of ITER as a fusion device) for most of the assumptions made on the transport properties of the core and boundary plasmas. The value of target loading in ITER is not therefore a prediction of SOLPS modelling, but rather the constraint imposed to restrict the acceptable range of core plasma performance. Although this paper focuses on divertor performance and not on the details of the integrated core-edge modelling, it should be clear that all the simulations from the ITER SOLPS database used here have been performed with core compatibility in view. In reality, it is technology which places the limit on the tolerable q ⊥,pk. At the time of the very first ITER designs, well before formation of the IO, when CFC was also still envisaged as an option for nuclear operation  [8] , CFC and W monoblock (MB) technology was under development and neutron irradiated samples were later shown to be able to withstand several thousand stationary cycles at 10 MW m -2 and hundreds more at twice this value without failure of the cooling channel (see e.
The fact that burning plasmas dominate the integral fluence which will be intercepted by the divertor over its lifetime, justifies the focus of the divertor simulation database on conditions appropriate to FPO. In fact, the FPO-1 phase is largely focused on discharges of shorter flattop duration (e. g. ∼50 s), with substantial time dedicated to DD operation, including L-mode development to high current, DD then DT H-mode plasmas at 7. 5 MA/2. 65 T and finally optimization of DT fusion performance towards Q DT = 10 at 15 MA/5. 3 T. In FPO-2, approximately half of the programmatic time is foreseen for expansion of operation to full ITER baseline inductive performance (Q DT = 10 for durations of 300-500 s). During the latter stages of FPO-2 and throughout FPO-3, emphasis is expected to turn to non-inductive operation at lower plasma current (I p ), lower Q DT and longer pulse length (target is Q DT ∼ 5 for 3000 s), for which plasma boundary simulations at  ITER  have not yet begun.
These fully integrated simulations have the advantage of being able to capture important time dependent features such as ELMs and confinement transitions, but, in the interests of computational time, generally deploy the plasma boundary code in a less intensive manner than for stationary (time independent) simulations (for example launching typically much lower numbers of particles in the Eirene neutral kinetic modelling and ignoring neutral-neutral collisions). This section now focuses on the database of stationary SOLPS simulations which have been used to scope the ITER divertor operational window and refine details of the design, leaving aside the question of core-SOL integration. Emphasis will be largely on q ⊥,pk and its dependence on p n since both are key controlling parameters. They are strongly linked.
The ITER SOLPS simulation database Presented for the first time in  [3] , the existing ITER divertor plasma boundary simulation database for the metallic PFC environment in baseline burning plasma conditions (Q DT = 10) and the final divertor geometry consists of ∼125 validated cases with Ne seeding and a much lower number for N-injection, for which more expanded studies are now ongoing. This database of SOLPS-4. 3 code (comprising the twodimensional B2 fluid plasma and the three-dimensional Eirene Monte Carlo kinetic neutral codes) runs is now being fully transferred into the ITER Integrated Modelling Analysis Suite (IMAS)  [46]  and each run is associated with a unique case number, as is the case henceforth for all new simulations. The latter are now mostly being produced with the SOLPS-ITER code (B2.
5 fluid plasma and Eirene Monte Carlo kinetic neutral codes), the most up-to-date version of the SOLPS suite, launched by the IO in 2015  [47, 48]. Beginning with a description of the most important code inputs for the main (SOLPS-4. 3) database (Section 3. 1. 1), the following sub-sections describe a selection of key findings which can be derived from the simulations.
Code inputs and definitions To-date, the "carbon-free" SOLPS simulation database uses exclusively the baseline ITER inductive magnetic equilibrium at q 95 = 3, and assumes Type I ELMing H-mode operation, the regime of the discharges constituting the multi-machine database used to derive the IPB98(y,2) scaling for the ITER thermal energy confinement time  [49]. For Q DT = 10 burning plasmas (the main concern here), q 95 = 3 is obtained at plasma current and toroidal magnetic field of I p = 15 MA, B φ = 5. 3 T respectively, but equally at one half and one third values (5 MA/1. 8 T and 7. 5 MA/2. 65 T), both of which figure prominently in the new IRP  [6]  to progressively approach full performance. The equilibrium features high upper triangularity (δ ∼ 0. 5) and outer midplane separation between the first and second separatrices of Δr sep ∼ 9 cm.
3 , both for the pure cylindrically symmetric case assumed in SOLPS (which is a 2D model) and the (higher) value obtained when component surface shaping is taken into account For the ITER divertor, the final shaping decision (see Section 3. 2. 1 and  [36] ) increases the strike point angle by 1. 5°compared to a perfect, toroidally symmetric target. There are several key input specifications and general characteristics of the main database simulations which are of importance for this paper (see also Fig. 3 ): 1) Since the B2 code contains no drift terms in the fluid equations, SOLPS-4. 3 simulations do not include drifts and currents. 2) Simulations are steady state: ELMs are included only implicitly in that it is assumed that they will carry some fraction of P SOL (typically in the range 20-40% for Type I ELMs  [2] ).
This is a reasonable approach from the point of view of global power balance, but does not of course take into account any possible modifications of the target power load profiles during the ELM. The latter aspect has in fact been investigated at the IO in an unpublished study in which a series of SOLPS-4. 3 stationary IT and OT profiles for varying p n have been combined with simulations of ITER Type I ELM target heat flux profiles  [51]  obtained with the 3D non-linear MHD code JOREK (for the specific case of a relatively low ELM plasma energy loss of 4 MJ). Normalizing the peak power flux density to a fixed value determined by an average stationary load consistent with the combined inter-ELM and ELM power fluxes (the sum of which must equal P SOL ), the study found that including the ELMs led to only very minor variations in the SOLPS stationary power flux density profile.
Almost all current entries in the simulation database use D ⊥ = 0. 3 m 2 s -1 and χ ⊥ = 1. 0 m 2 s -1 (fixed at all radial and poloidal cells in the numerical grid) for both main ions, impurities and electrons, with the power injected across the inner core boundary of the numerical grid, split equally between ions and electrons. As discussed in more detail below, this leads to a fixed value of the radial decrease of heat flow parallel to the magnetic field in the near SOL (λ q ). No radial pinch velocity is specified. At the outer edge of the plasma grid, radial decay lengths of 3 cm for all densities and temperatures are set as boundary conditions at all poloidal locations. Note that the power entering the inner core boundary is denoted here by P SOL , even though this is not strictly the power crossing the separatrix in the simulations.
The assumption of a fully Be coated IT is consistent with WALLDYN simulations for ITER burning plasmas conducted in  [52] , but is not supported by these same calculations at the OT, where, depending on the operating point, the surface temperature would be too high for Be to remain. This may not be the case if the divertor is operated at high neutral pressures, when the surface temperature at both IT and OT will be low (see Section 4 and Fig. 17 ). 7) The impurity and fuel ions are injected in the simulations across a poloidally extended low field side region of the main chamber corresponding to the location of the upper lateral ports. This choice is somewhat historical since the real gas puff locations were not fully decided at the time the simulation database was being constituted. Out of the 10 gas lines which will be installed in ITER  [53] , 4 will enter through the upper ports.
It is currently expected that these lines will in fact be the primary vehicle for divertor detachment control through impurity and fuel gas injection. New simulations  [54]  are now ongoing with SOLPS-ITER to examine the influence of divertor versus main chamber injection. First results confirm the expectation of a rather weak influence in these steady state simulations: once ionized, the injected gas components will rapidly distribute in the boundary plasma on SOL transport timescales (ms), though main chamber injection (and this is seen in both the SOLPS-4. 3 and SOLPS-ITER simulations) does have a strong local effect on the SOL density at the injection point. 8) Along with the fuel throughput, the impurity concentration, c imp = n imp /n e is the principle variable in the P SOL = 100 MW database.
Here, the average of c imp in all cells of the first poloidal ring outside the main chamber separatrix, from X-point to X-point is used as the metric to classify the simulation cases. Although the impurity level could be characterized by different quantities, this separatrix-averaged, relative ion impurity concentration is most convenient for coupling to a core model and this has been the keypoint in all SOLPS-4. 3 modelling for ITER since 2003  [3, 7, [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]. The first SOL ring outside the separatrix is used in the definition to avoid uncertainties due to the lack of a proper core model in the simulations. In practice, to generate the scans of c imp for various p n in the database, the ratio of fuel to impurity puffing is controlled through the use of feedback loops in the simulations.
9) The key parameter p n is defined as the average of the neutral pressures (computed in Eirene) over the parts of the PFR boundary which face the dome support openings (see Fig. 3  and  [20] ). This choice is historical and was made in an early stage of development of the Eirene code when neutral-neutral collisions were not modelled and neutral gas parameters were calculated only on the B2 plasma grid. The definition was maintained for backwards compatibility: although the absolute value of p n is not so important, the definition must be maintained for meaningful comparisons. Note that the Eirene simulations present in the ITER database employ the "Kotov model"  [55]  for collisions between fuel atoms and molecules (in this case D/D 2 neutrals and charged species). The impact of molecular vibrationally excited states is included in the quasi-static approximation in which the timescale for equilibration of the vibrational state population is faster than transport times.
Additional experimental measurements performed since the multi-machine work in  [56]  was published show that the empirical scaling is followed also on COMPASS  [59]  and Globus-M  [60] , much smaller devices than those comprising the initial study, and on the C-Mod tokamak, operating at much higher B θ than any point in the existing database  [61]. This latter study is particularly significant given that it extends the scaling to values of B θ even beyond the ITER value at 15 MA. In contrast to these extremely narrow predicted heat flux widths, a key result from state-of-the-art simulations of attached divertor conditions on ITER with the 3D particle-in-cell based edge (electrostatic) gyrokinetic code XGC1 is that at high current on ITER, the contribution of cross-field electron turbulence (radial streamers) dominates over the neoclassical magnetic ion drifts, yielding λ q ∼ 6 mm  [62].
The code finds λ q ∼ 5 mm for I p = 15 MA operation at Q DT = 10. This is remarkably similar to the XGC1 result, but occurs for different reasons (due to peeling-ballooning turbulence). In common with XGC1, BOUT++ simulations also find good agreement with present machines, with the predicted λ q following the experimental 1/B θ scaling, even for the newest results from C-Mod  [61]  at ITER-relevant B θ. To overcome the problem of timescales (the large disparity between electron and ion SOL transit times (∼100 μs vs. ∼10 ms) precludes reaching saturation of the divertor ion heat flux during the turbulence simulation), a separate "transport" model has been developed inside the BOUT++ framework. The model includes electric and magnetic drifts, with the same flux-limited parallel thermal SOL transport as in the full turbulence model, but with SOL cross-field transport specified rather than evolving self-consistently from the turbulence (transport coefficients in the pedestal are computed from experimentally measured or prescribed pedestal profiles of n e , T e , T i ).
As a consequence, turbulence dominates over magnetic drifts and the empirical scaling  [56]  is broken for ITER. It is thus not yet possible to state with confidence what the burning plasma, 15 MA heat flux width should be on ITER, but a choice of anomalous cross-field transport coefficients must be made for the divertor plasma simulations. The values fixed for the simulation database (D ⊥ = 0. 3 m 2 s -1 and χ ⊥ = 1. 0 m 2 s -1 , see point 4) above) are in fact retained from earlier studies with carbon targets, where the choice was made based on simple ballooning stability arguments  [65]  which indicated λ q ∼ few mm, long before the recent experimental scalings and theoretical work were available. Fig. 4  uses the approach first introduced in  [28]  to characterize the upstream near SOL parallel heat transport in the ITER SOLPS-4.
3 Ne-seeding simulation database. The symbols represent the poloidally averaged Ne concentrations as defined in Point 7) above (see also Fig. 5 ) and points from all 53 simulation cases selected from the database (used throughout the rest of this section) are plotted. These cases cover a wide range of fuel and impurity throughput, giving n e,sep = 3-6 × 10 19 m -3 (see also Fig. 15a ). All have P SOL = 100 MW. Illustrated by the inset in Fig. 4 , the procedure is to extract the radial profile of parallel heat flux density, q || just above the entrance to the outer divertor (Step 1) and then (Step 2) map this to the OT, Fig. 4. Outer target perpendicular heat flux density profiles mapped to the omp for the 53 cases in the SOLPS-4. 3 simulation database sorted by Ne concentration (P SOL = 100 MW).
The average of all these fitted values gives λ q ∼ 3. 4 ± 0. 5 mm. What is important to note from Fig. 4  is that despite the very wide variation in divertor parameters found in the database (as shown in the following sub-sections), the upstream λ q is essentially unchanged. Similarly, at fixed impurity concentration, n e,sep is relatively insensitive to fuel throughput (see Section 3. 2. 2). This can be taken as evidence that within the range of fuel and impurity throughputs included in the database, the divertor is efficient at screening the main SOL. A value of λ q ∼ 3. 4 mm is clearly significantly higher than the ∼1 mm widths predicted by the empirical scaling (and the neoclassical ion drift model) discussed above, but is less than a factor ∼2 lower than found in the XGC1 or BOUT++ simulations.
Since q || = const/λ q for fixed q 95 , R and P SOL , it is clear that a factor 3 lower λ q will yield q || at the divertor entrance higher by the same factor, requiring stronger dissipation to achieve detachment. The consequences for divertor power loading under dissipative conditions of a much lower λ q than the characteristic value for the simulation database will be discussed further in Section 3. 2. 2.
Operating window in peak power flux density Fig. 5  summarizes the divertor target response at both targets, in terms of peak perpendicular power load, q pk sym , (Fig. 5a ), peak ion flux density, pk sym , (Fig. 5b ) and integral ion flux to the plate (Fig. 5c ) for a selection (comprising 53 cases) of the Ne-seeded simulation database sorted by c Ne and plotted against the averaged divertor neutral pressure defined in Section 3. 1. 1. Here, as defined in Section 1, the superscript "sym" now denotes the standard cylindrically symmetric quantity provided by SOLPS, thus assuming a perfect toroidal target with no shaping. A few selected points for N seeding at c N = 0. 8% (P SOL = 100 MW) have been added for comparison (the database is currently much more restricted for nitrogen impurity). The peak power density includes all contributions to the target heat load: thermal plasma, energy due to recombination at the plate, charge exchange (CX) and photon loads, but does not account for divertor target shaping, of which the CX neutral and photon loads are independent.
This was seen clearly in the early ITER divertor simulations studies with carbon targets (see e. g. Fig. 2b  in  [12] ). The same behaviour is recovered in the "carbon-free" database discussed here, for which the scalings for core-edge integration developed in  [3]  show a reduction in upstream separatrix He ion density and He neutral influx to the core with increase of p n. The issue of at what point (i. e. which level of detachment) this trend fails, has not yet been systematically studied. Fundamentally, He exhaust improves at higher p n , because the plasma temperature in the divertor is lower and the ionisation mean-free path for the He atoms recycling off the target increases, so more He reaches the PFR where the pumping duct is located. At the lowest values of p n in the scan (≲ 3 Pa), where thermal plasma loading dominates the total heat load (Section 3.
Fig. 5c  illustrates one of the features of the simulation database in the context of detachment. In all studies of the ITER divertor performance thus far, an "edge-based density limit" (at which point neutral escape to the main chamber would be excessive) has been fixed at the point corresponding to full detachment of the inner target, which usually detaches earlier than the outer for given fuel/impurity throughput. Simulations have not yet been strongly pursued beyond this point. For the purposes of core-SOL integration  [3] , (partial) detachment is defined, rather arbitrarily, as the value of p n at which the integral OT ion flux falls to 80% of its maximum value, corresponding to p n ∼ 10 Pa in Fig. 5c. At the IT, the detachment degree is higher for given p n and the turnover in total ion flux is less marked.
Steps are being taken to improve this situation with the recent development (under contract to the IO) of the AMMONX database describing nitrogen chemistry for inclusion into Eirene  [72]. The possible impact on the IRP of using N-seeding has thus not yet been assessed, but Ne is likely to be the preferred alternative if it is found to perform similarly with regard to plasma performance, with the added benefit that its property as a fully recycling gas may extend the timescales for avoidance of divertor MB overheating in the event of loss of seeding or other divertor reattachment events. The very extensive experiments performed in recent years in the full-tungsten ASDEX Upgrade with ITER-relevant divertor geometry (see e. g. [73] ) have clearly demonstrated that N is sufficiently compressed to provide high levels of divertor radiation whilst maintaining good plasma performance, but that for Ne, the impurity is not well retained in the divertor and plasma performance is impaired, due in large part to its effect on the pedestal and the consequent changes in seeded impurity and tungsten transport.
These results may be contrasted with those found on radiative divertor experiments on Alcator C-Mod with molybdenum PFCs at high magnetic field in which, for both N and Ne seeding in the ELM-free "EDA" mode, partially detached divertor conditions at normalized confinement (H 98 ∼1) with edge power flows only marginally above the H-mode threshold power (by factors of 1-1. 4), as in ITER, were achieved  [75]. Here, as in the JET and ASDEX Upgrade experiments, at high radiative fractions, the radiation is observed to occur mostly in the X-point region, with some incursion onto flux surfaces just inside the separatrix. Apparently, in C-Mod, this was insufficient to strongly affect the pedestal top, even in the case of Ne. In ITER, the SOLPS-4. 3 simulation database, though still sparse for N, indicates that for both N and Ne, the impurity radiation is well confined to the divertor across the operating range in p n and c imp explored thus far.
Fig. 8  provides the dependence on p n of the fractions f rad,tot = P rad,tot /P SOL and f rad,div = P rad,div /P rad,tot for the Ne-seeded database and for a single N series with c N = 0. 8%. Here P rad,tot is the total power radiated in the simulation domain and P rad,div the power radiated in all computational cells below the vertical position of the X-point. These radiated powers include all contributors: impurity ions, neutrals (impurities and fuel, including molecules) and even Bremsstrahlung. Several key observations may be drawn from Fig. 8 : • for all c imp , f rad,tot increases monotonically with p n , reaching ∼0. 70 (70 MW since P SOL = 100 MW) at the highest p n ; • f rad,tot increases with increasing c imp at fixed p n ; • f rad,div decreases with increasing c imp (Ne only since database too restricted in N) and remains approximately constant with increasing p n ; • f rad,div is within 0.
The radiation is also very symmetric in both inner and outer divertors for both species, as might be anticipated from the rather symmetric target power loading seen at high p n (see Fig. 5a ). As a crude measure of impurity compression, the ratio n imp,osp /n imp,omp of the impurity ion densities at the outer strike point and the outer midplane in the two cases is ∼100 for N and ∼30 for Ne. In fact, for the Neseeded cases, which represent the majority of the simulation database, this value of n imp,osp /n imp,omp ∼30 for run #2317 in Fig. 9  at p n ∼10 Pa is about as high as it gets. Except at very low p n , where the compression is very poor, n imp,osp /n imp,omp is generally in the range 10-20. Regarding the ratio of impurity concentrations from downstream to upstream (the enrichment), c imp,osp /c imp,omp, this ranges from near zero to near unity with increasing p n and is thus inconsistent with simple models (e.