A two-region model of turbulent transport in the edge and scrape-off layer plasma

3D BOUT simulations of turbulence in diverted tokamak plasmas $\footnote{D.A. Russell, D.A. D’Ippolito, J.R. Myra, W.M. Nevins, X.Q. Xu, Phys. Rev. Lett. \textbf{93}, 265001 (2004).} $ recently demonstrated dramatically enhanced transport by blobs in the scrape-off layer (SOL), correlated with sudden electrical disconnection of the outer-midplane (OM) from the divertor sheath, suggesting that reduced modeling of turbulent transport in the OM ought to include nontrivial ``parallel physics.'' We describe a minimal, ``2-region'' version of the 3D model introduced in [2]: gradient-driven turbulence in the OM is coupled to resistive cross-field transport in the X-point region by a \textit{jump condition} on Ohm’s law applied at the boundary between the two regions. The enhancement of cross-field conductivity by field-line fanning $\footnote{ D. Farina, R. Pozzoli, and D.D. Ryutov, Nucl. Fusion \textbf{33}, 1315 (1993).}$ is modeled by an area-preserving, \textit{stretching-and-squeezing}, coordinate transformation between the two regions. The model's linear, unstable eigenmodes are distinguished by X-point resistivity.$\footnote{ J.R. Myra, D.A. D’Ippolito, X.Q. Xu and R.H. Cohen, Phys Plasmas \textbf{7}, 4622 (2000).}$ Results from numerical simulations of the fully nonlinear model equations in regimes of strong turbulence will be presented.