The relation between upstream radial widths of $n_e$ and $T_e$ and outer target power width for H-mode discharges in DIII-D*

For H mode discharges in DIII-D, the relation between the power width at the outer target, $\lambda_{q_{target}}$, and the radial profiles near the outside midplane is in somewhat better agreement with flux-limited (weak collisionality) electron parallel heat conduction, $q_\parallel \propto n_e T_e^{3/2}$, i.e. $\lambda_{q_{target}}^{flux-lim} = [3/(2\lambda_{T_e}^{up}) + 1/ \lambda_{n_e}^{up}]^{-1}$, than Spitzer (collisional) electron parallel heat conduction, $\lambda_{q_{target}}^{Spitzer} = (2/7) \lambda_{T_{e}}^{up}$. It appears that cross-field transport is the basic controlling process of SOL widths, manifesting itself most directly in upstream widths, with parallel transport and volumetric losses in the SOL/divertor then controlling the relation between upstream and target widths. For an initial data set of three discharges it was found that $\lambda_{q_{target}}^{measured}/ \lambda_{q_{target}}^{flux-lim} = 0.93$, 0.90, 1.00 while $\lambda_{q_{target}}^{measured}/ \lambda_{q_{target}}^{Spitzer} = 1.32$, 0.71, 1.21. Further results will be reported for discharges in upcoming experiments. We find that for DIII-D H-mode shots, the strongest dependence for $\lambda_{q_{target}}^{measured}$ is $I_p^{-1}$. The separate contributions of $\lambda_{n_e}^{up}$, $\lambda_{T_e}^{up}$ to the observed $I_p$ scaling is assessed.