Electric sheath and presheath in a collisionless, finite ion temperature plasma

TLDR

The authors formulate and numerically solve the plasma‑sheath equation for a collisionless plasma with arbitrary ion temperature, deriving an analytic potential solution outside the sheath and validating it against numerical results. An analytic potential solution is obtained outside the sheath, the ion distribution, wall potential, and sheath fluxes are calculated, and numerical results agree with the analytic solution for small Debye lengths.

Abstract

The plasma-sheath equation for a collisionless plasma with arbitrary ion temperature in plane geometry is formulated. Outside the sheath, this equation is approximated by the plasma equation, for which an analytic solution for the electrostatic potential is obtained. In addition, the ion distribution function, the wall potential, and the ion energy and particle flux into the sheath are explicitly calculated. The plasma-sheath equation is also solved numerically with no approximation of the Debye length. The numerical results compare well with the analytical results when the Debye length is small.