Structure of Plasma Sheaths

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Abstract
A model is given to provide a microscopic description of plasma sheaths, using the Vlasov equation for ions and electrons coupled with Maxwell's equations for the fields. The sheaths considered connect two different constant states of a plasma in a magnetic field. In the charge‐neutral approximation a solution is obtained in closed form in terms of quadratures. The solution depends essentially on three free parameters, related to the differences in density and electric potential between the two end states, and to the value of β, the ratio of the plasma pressure to the magnetic pressure, on one side of the sheath. The scaling law changes considerably from one solution to another. Solutions are obtained which scale according to some representative electron Larmor radius, or ion Larmor radius, or piece‐wise according to both. As a limiting case, when the density is allowed to go to zero on one side of the sheath, one obtains the boundary layer between a plasma and a containing vacuum magnetic field. As a peculiar feature in this limiting situation, the curve for the electric potential appears to be very sensitive to the slightest changes in the distribution functions, in the asymptotic region where the plasma density becomes vanishingly small.