Heuristic Drift-Based Model for the Power Scrape-off Width in H-Mode Tokamaks at Low Gas Puff

An heuristic model for the plasma scrape-off width in H-mode plasmas is presented, in which magnetic drifts into the SOL are balanced against c$_{s}$/2 parallel flows to the divertor plates. The overall particle flow pattern is a modification for open field lines of Pfirsch-Shl\"{u}ter flows, including sinks to the divertors. This model results in an estimated SOL width of $\sim $2a$\rho $/R. It also results in a first-principles calculation of the particle loss rate from low-gas-puff H-mode plasmas, given n$_{sep}$ and T$_{sep}$, and thus the global particle confinement time. Using measured values of n$_{sep}$ and T$_{sep}$, these are in reasonable agreement with experiment. It is next assumed that anomalous perpendicular electron thermal diffusivity is the dominant source of heat flux across the separatrix, investing the SOL particle width derived above with heat from the main plasma. The separatrix temperature is then calculated self-consistently, based on a two-point model balancing power input to the SOL against Spitzer-H\"{a}rm parallel thermal conduction losses to the divertor. This results in a closed-form prediction for the power scrape-off width that is in reasonable quantitative agreement both in absolute magnitude and scaling with recent experimental data.