Generalization of the Heuristic Drift SOL model for finite collisionality and effect on flow shearing rate vs. interchange growth rate

We generalize the low-gas-puff Heuristic Drift (HD) model of the power scrape-off layer width to take into account both the enhanced parallel confinement time in the SOL at high collisionality, due to enhanced thermal resistivity, and the increase of the upstream temperature at very low collisionality, due to finite target temperature. We find a wide range of separatrix densities over which the original HD model is applicable. However, at the region of high separatrix density and collisionality accessible with strong gas puffs the SOL widens, in reasonable agreement with experimental data from ASDEX-Upgrade and JET. We further find that for typical low-gas-puff H-mode conditions, the projected E×B flow shearing rate in the SOL dominates over the interchange growth rate, while at the high separatrix densities at which H-Modes return to L-Mode, the interchange growth rate approximately equals the shearing rate. The result is related to that of Halpern and Ricci with respect to the steep gradient region of the SOL of inner-wall-limiter discharges, which also show HD-like scale lengths. It is also consistent with calculations of shear-flow stabilization of interchange modes by Zhang and Krasheninnikov. Taking ω_s>γ_int as the criterion for retaining H-Mode performance, we use the generalized HD (GHD) model to predict the scaling for the H→L back transition. The power requirements to sustain H-Mode for existing machines and for ITER are in the range of a factor of 2 below the predictions for the L→H transition, consistent with the limited available studies of H-Mode hysteresis. We find reasonable agreement with the scaling of the density at the H→L back transition found by Bernert on ASDEX-Upgrade. Finally, we speculate that the shearing rate in the SOL of H-Mode plasmas contributes to the reduced core turbulence that supports the formation of the H-Mode pedestal and comment on the implications for ITER.