Title: Kinetic treatment of ions in the magnetic presheath
Abstract: Boundary layers are present in the thin region of a tokamak where the Scrape-Off Layer plasma reaches the divertor or limiter target. If the magnetic field impinges with an oblique angle on the target surface, there is a small region - called the "magnetic presheath" or "Chodura sheath" - of size a typical ion Larmor radius, in which ions may intersect the wall during an orbit. Typically this region is quasineutral and collisionless to a good approximation. In this region, ions feel electric forces (directed towards the wall) that compete with the magnetic forces, therefore the approximately periodic ion orbits are distorted. An expression for the ion density in terms of the electrostatic potential profile is obtained by exploiting an asymptotic expansion of the ion trajectories in the small angle between magnetic field and wall. The full distortion of the lowest order periodic orbits is retained. The electron density is assumed to be a Boltzmann distribution. By using an iteration scheme to impose the quasineutrality equation, the self-consistent electrostatic potential, ion density and ion flow across the magnetic presheath are numerically found with some prescribed distribution functions at the magnetic presheath entrance. The numerical solution can be obtained for any distribution function that satisfies a solvability condition at the magnetic presheath entrance. This condition is the kinetic generalization of the fluid Chodura condition, which states that the ion flow at the magnetic presheath entrance must be supersonic in the direction parallel to the wall. With our kinetic treatment, we obtain the velocity distribution function of ions entering the thin non-neutral Debye sheath. Moreover, the dependence on the ratio of ion temperature to electron temperature is studied and the results of Chodura's fluid equations (valid when the ion temperature is zero) are recovered.