In this paper a sheath near the wall whose surface is ''rough,'' conta
ining random bumps with a height comparable to the distance between th
em is considered. The magnetic held is assumed to form a shallow angle
with the wall (as in a tokamak divertor) and the scale of nonuniformi
ties is assumed greater than the ion gyroradius. The following new eff
ects caused by surface roughness are identified: (1) The fraction of t
he surface ''wetted'' by the plasma becomes much smaller than for a fl
at wall. (2) The ion subsheath is broadened and the diamagnetic curren
t in it acquires a complex three-dimensional structure. (3) Cross-held
nonuniformities of the plasma potential appear in the bulk plasma. [S
1070-664X(98)02006-0]