On asymptotic matching and the sheath edge

The position of the sheath edge and the value of the electric field at the sheath edge are found using asymptotic matching techniques for collisionless plasma-wall systems. It is demonstrated that specifying the position of the sheath edge by the Bohm criterion or by Riemann's weak electric field is inconsistent with the asymptotic matching theory and contradicts the commonly accepted definition of the sheath as a region where ionization can be neglected. It is shown that the sheath found using the asymptotic matching theory is the ion sheath, characterized by negligible electron density, and that the value of the electric field at the sheath edge practically coincides with the value of Godyak's electric field. In addition, analytical expressions are given for the position of the wall, the sheath width, and sheath characteristics for arbitrary potentials at the wall.