Limiting boundary conditions of a plasma fluid at an absorbing target

An absorbing boundary (e.g., a material wall or a target) in contact along magnetic field lines with a plasma induces a loss flow of charged particles. An ideal fluid model of this flow does not match the onset condition of the sheath. In order to meet this condition the fluid model is to include transport processes, e.g., parallel ion viscosity. A fluid-transport model in the Braginskii form of parabolic transport equations needs boundary conditions which are not available at an absorbing target. Different to the Braginskii model, in the present paper the inertial terms in the ion transport equations are retained. Thereby the system of ion fluid equations remains hyperbolic. The characteristics of this system are used to derive limiting conditions of the ion fluids at the absorbing boundary. The limiting boundary conditions are derived for the complete set of fluid equations as well as for a set in which the inertial terms in the equations for the flow components perpendicular to the magnetic field are neglected (drift approximation). It is shown that the limiting boundary conditions derived in these two cases coincide with the onset conditions of the magnetoacoustic and the ionacoustic (Debye) part of the sheath. Numerical results from the one-dimensional fluid model, using the limiting boundary conditions in front of the target in different external situations, are checked against results from a kinetic particle model which imposes boundary conditions directly at the target. The results of the fluid model and the kinetic model agree well in case of frequent collisions in the bulk and only few collisions in the sheath. They agree less well in case of few collisions in the bulk and no collisions in the sheath