The edge plasma of a tokamak is affected by atomic physics processes and can have density and temperature variations along the magnetic field that strongly modify edge transport. A closed system of equations in the Pfirsch–Schluter regime is presented that can be solved for the radial and poloidal variation of the plasma density, electron and ion temperatures, and the electrostatic potential in the presence of neutrals and a poloidally asymmetric energy radiation sink due to inelastic electron collisions. Neutrals have a large diffusivity so their viscosity and heat flux can become important even when their density is not high, in which case the neutral viscosity alters the electrostatic potential at the edge by introducing strong radial variation. The strong parallel gradient in the electron temperature that can arise in the presence of a localized radiation sink drives a convective flow of particles and heat across the field. This plasma transport mechanism can balance the neutral influx and is particularly strong if multifaceted asymmetric radiation from the edge (MARFE) occurs, since the electron temperature then varies substantially over the flux surface.