The boundary layer arising in the radial vicinity of a tokamak limiter is examined, with special reference to the TEXT tokamak [Nucl. Fusion27, 1125 (1987); Phys. Fluids27, 2956 (1984)]. It is shown that sheath structure depends upon the self‐consistent effects of ion guiding‐center orbit modification as well as the radial variation ofE×B‐induced toroidal rotation. Reasonable agreement with experiment is obtained from an idealized model, which, however simplified, preserves such self‐consistent effects. It is argued that the radial sheath, which occurs whenever confining magnetic field lines lie in the plasma boundary surface, is an object of some intrinsic interest. It differs from the more familiar axial sheath because magnetized charges respond very differently to parallel and perpendicular electric fields.