The thickness of a resistive sheath in a magnetic separatrix

The formation of an electrostatic double sheath at a magnetic separatrix is described, with particular reference to the polytron. Results are discussed for a collisionless plasma, and for a simple MHD model where the sheath thickness is determined by collisional effects. Expressions are given for the sheath thickness in the polytron. Of more general interest is the result that the formation of a sheath makes the resistance of the plasma to current flow across the separatrix proportional to ωτ, not ω²τ² as expected for a homogenous magnetic field.