Sheath formation in low-pressure discharges

Sheath formation is studied for slightly ionized plasmas, i.e. for many typical low-pressure discharges. A sheath adjacent to an insulating wall is a space charge region where the electron flux to the wall is reduced to the corresponding ion flux. Numerical and analytical results show that no lower bound of the ion drift speed upsilon (i) exists to form a sheath under collisional conditions. The product of the ambipolar ion speed v(B) and the square root of the ratio of the number density of the ions to that of the electrons occurs as a characteristic ion drift speed upsilon (c) for the sheath formation. In the interval 0 < <upsilon>(i) < <upsilon>(c) the collisions promote the sheath formation, whereas the electric field inhibits it. The effect of the collisions dominates. In the interval upsilon (i) > upsilon (c) both the electric field and the collisions support the sheath formation. The effect of the electric field alone can form the sheath. When the electron density is relatively small under collision-dominated conditions the space charge density can become relatively large in the neighbourhood of the point when upsilon (i) = upsilon (B), and then the difference between upsilon (c) and upsilon (B) is significant. It is also possible that such a point does not exist. At low collisionality, in the centre of the plasma and close to the wall upsilon (i) < <upsilon>(c) can hold, whereas in an intermediate region upsilon (i) > upsilon (c) can be satisfied. When the collisionality is high upsilon (i) < <upsilon>(c) everywhere. This relation can also hold when upsilon (i) > upsilon (B) occurs close to the wall. The sheath formation can be dominated by collisions in a larger range of parameters than recognized to date. The application of the Bohm criterion is inappropriate when the collisionality is high and the electron density is relative low. Multi-component plasmas are discussed briefly. The concept of a sheath edge is examined critically.