Plasma and sheath

In the analysis of a finite plasma system in contact with an absorbing wall separate model zones of a quasi-neutral plasma body and a thin space charge sheath may be distinguished. This subdivision goes back to Langmuir and is based on a small ratio of the Debye length λD and the plasma dimension L. It is strictly valid only in the asymptotic limit λD/L → 0. In this limit the plasma–sheath interface, the 'sheath edge', is characterized by a formal singularity of the plasma solution and closely related to the Bohm criterion. For finite λD, in contrast, there are difficulties in the interpretation of the plasma–sheath transition, in the application of the Bohm criterion, and in a reasonable definition of the plasma–sheath boundary. These difficulties are discussed both in the framework of a fluid and of a kinetic analysis on the basis of an 'intermediate scale' analysis. Special emphasis is given to the matching problem and its relation to the eigenvalue problem caused by the plasma balance.