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 boundary, in the direction normal to the wall, there are four length scales of interest, the Debye length $\lambda_D$, the ion gyroradius $\rho_i$, the projection of the collisional mean free path in the direction normal to the wall $L_N$ and the device size $L$. Assuming that the plasma near the divertor satisfies $\lambda_D\ll\rho_i\ll L_N\ll L$, we can split the plasma-wall boundary into three layers\footnote{K-U Riemann, \textbf{J. Phys. D: Appl. Phys.} 24:493, 1991}. At distances of order $\rho_i$ from the wall the plasma is collisionless and the distribution is far from Maxwellian. At distances much greater than $L_N$ from the wall, Braginskii fluid equations are used to model the plasma, since collisionality is high and the distribution is close to Maxwellian\footnote{P Ricci et al., \textbf{PPCF} 54:124047, 2012}. We focus on the collisional layer of width $L_N$ that connects these two regions. We use a Galerkin method to numerically solve the ion drift kinetic equation in one spatial dimension, with the full Fokker-Planck collision operator, and the quasineutrality equation with adiabatic electrons.