Multi-machine scaling of the main SOL parallel heat flux width in tokamak limiter plasmas

As in many of today's tokamaks, plasma start-up in ITER will be performed in limiter configuration on either the inner or outer midplane first wall (FW). The massive, beryllium armored ITER FW panels are toroidally shaped to protect panel-to-panel misalignments, increasing the deposited power flux density compared with a purely cylindrical surface. The chosen shaping should thus be optimized for a given radial profile of parallel heat flux, ${{q}_{||}}$ in the scrape-off layer (SOL) to ensure optimal power spreading. For plasmas limited on the outer wall in tokamaks, this profile is commonly observed to decay exponentially as ${{q}_{||}}={{q}_{0}}\text{exp} ~\left(-r/\lambda _{q}^{\text{omp}}\right)$ , or, for inner wall limiter plasmas with the double exponential decay comprising a sharp near-SOL feature and a broader main SOL width, $\lambda _{q}^{\text{omp}}$ . The initial choice of $\lambda _{q}^{\text{omp}}$ , which is critical in ensuring that current ramp-up or down will be possible as planned in the ITER scenario design, was made on the basis of an extremely restricted L-mode divertor dataset, using infra-red thermography measurements on the outer divertor target to extrapolate to a heat flux width at the main plasma midplane. This unsatisfactory situation has now been significantly improved by a dedicated multi-machine ohmic and L-mode limiter plasma study, conducted under the auspices of the International Tokamak Physics Activity, involving 11 tokamaks covering a wide parameter range with $R=\text{0}\text{.4--2}\text{.8}\,\text{m},\,{{B}_{0}}=\text{1}\text{.2--7}\text{.5}\,\text{T},\,{{I}_{\text{p}}}=\text{9--2500}\,\text{kA}.$ Measurements of $\lambda _{q}^{\text{omp}}$ in the database are made exclusively on all devices using a variety of fast reciprocating Langmuir probes entering the plasma at a variety of poloidal locations, but with the majority being on the low field side. Statistical analysis of the database reveals nine reasonable engineering and dimensionless scalings. All yield, however, similar predicted values of $\lambda _{q}^{\text{omp}}$ mapped to the outside midplane. The engineering scaling with the highest statistical significance, $\lambda _{q}^{\text{omp}}=10{{\left({{P}_{\text{tot}}}/V\,\left(\text{W}\,{{\text{m}}^{-3}}\right)\right)}^{-0.38}}{{\left(a/R/\kappa \right)}^{1.3}}$ , dependent on input power density, aspect ratio and elongation, yields $\lambda _{q}^{\text{omp}}$ = [7, 4, 5] cm for ${{I}_{\text{p}}}$ = [2.5, 5.0, 7.5] MA, the three reference limiter plasma currents specified in the ITER heat and nuclear load specifications. Mapped to the inboard midplane, the worst case (7.5 MA) corresponds to $\lambda _{q}^{\text{imp}}\sim 57\pm 14$ mm, thus consolidating the 50 mm width used to optimize the FW panel toroidal shape.