Kelvin–Helmholtz vortex formation and particle transport in a cross-field plasma sheath. II. Steady state

The steady-state behavior of the magnetized plasma–wall sheath has been studied through two-dimensional particle simulations, which have shown that the sheath maintains itself in a strongly nonlinear, turbulent equilibrium, continuously driven by the edge Kelvin–Helmholtz instability. The sheath assumes a thickness of order lx∼5ρi, and maintains large, long-lived vortices, with amplitudes δφ∼2.5Ti/e, which drift parallel to the wall at half the ion thermal velocity. The sheath also maintains a large, spatially averaged potential drop from the wall to the plasma with Δφ≊−2Ti/e, opposite in sign to that of the unmagnetized sheath. Accompanying the long-wavelength vortices are shorter-wavelength fluctuations, which induce an anomalous cross-field transport, scaling in accordance to Bohm diffusion when ωpi≥2ωci. At lower densities, ωpi<2ωci, the diffusion coefficient has an additional factor, proportional to the density. These results permit the modeling of the cross-field sheath by a simple effective boundary condition.