Unipolar ion sheath

In technical applications, the ion sheath in front of a highly negative wall is frequently described by the well known Child–Langmuir law. Due to inaccurate boundary conditions, however, this yields only a rather poor approximation. The collisionless Child–Langmuir law can be substantially improved by accounting for universal initial conditions following from the Bohm criterion. By a simple analytical ansatz the resulting unipolar ion sheath law is generalized to account for (charge exchange) ion collisions in the sheath.