Kinetic analysis of the collisional layer

To understand plasma behaviour in the scrape-off layer, we need to know the boundary conditions for the plasma and electromagnetic fields near a divertor. At the plasma-wall boundary, in the direction normal to the wall, there are four length scales of interest: the Debye length λ_D, the ion gyroradius ρ_i, the projection of the collisional mean free path in the direction normal to the wall λ_⊥ and the device size L. If λ_D << ρ_i << λ_⊥<< L, we can split the plasma-wall boundary into three layers, the Debye sheath, the magnetic presheath and the collisional layer of width λ_⊥, this is the layer we analyse.  At distances much greater than λ_⊥ from the wall collisionality is high and Braginskii fluid equations are usually used to model the plasma behaviour, here the ions are approximately Mawellian. The collisional layer connects this region with the collisionless magnetic presheath. We have found that at the entrance of the collisional layer the flow of ions is supersonic.  The distribution function at the entrance of the magnetic presheath is far from Maxwellian and must satisfy the Chodura condition. We use a Galerkin method to solve the drift kinetic equation in one spatial dimension with the full Fokker-Planck collision operator, the quasineutrality equation and adiabatic electrons.