The active magnetized plasma-sheath over a wide range of collisionality

Recent work by Sternberg and Poggie (2004 IEEE Trans. Plasma Sci. 32 2217), concerned with the structure of an active collisionless magnetized plasma-sheath, is extended to include the effect of collisions on the ion motion. In the collisionless case an expression for the eigenvalue of the problem analogous to that obtained by Franklin and Ockendon (1970 J. Plasma Phys. 4 371) for an active unmagnetized plasma is obtained. As is to be expected with increasing collisionality, increased transport of ions across the magnetic field lines means that the effect of the magnetic field is diminished. Special attention is given to the case when the magnetic field is nearly parallel to the wall.