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Sheath-coupled cross-field ion transport in magnetized low-pressure discharges

Summary form only given. Many years ago, Simon (1955) showed that when a plasma is contained within a grounded conducting vessel, it is possible for ions to diffuse across a magnetic field at a rate characterized by the ion Larmor radius and mean free path, while electron currents, which are necessary to maintain quasineutrality, flow along the field lines to the walls. However, one factor that is usually omitted from these calculations is the spatially-dependent sheath potential drop associated with the electron flow. In low-pressure discharges, electric fields arising from this source typically control the ion dynamics, and can strongly inhibit cross-field ion diffusion. The essence of the effect is as follows: suppose that the cross-field flow is such as to increase the number of ions on a particular field line. Then the electron flow from that field line to ground must decrease. In order to suppress the electron flow, the sheath potential must increase on that field line, which increases the plasma potential all along the field line. The resulting electric field pattern repels the net inflow of ions from other field lines. We have developed a quasineutral kinetic formulation for magnetized discharges, which explicitly includes this effect. In linearized analytic calculations, we show that the sheath potential adds a term which is mathematically similar to a viscosity, dissipating non-uniformities in the cross-field ion flux.