Sheath and presheath in a collisionless open-field plasma

Abstract

The plasma–sheath equation for a collisionless plasma with a finite-temperature particle source in a nonuniform open magnetic field is formulated. The plasma equation is solved analytically and the plasma–sheath equation is also solved numerically for various profiles of the magnetic field. The potential formed in the plasma depends considerably on the profile of the magnetic field strength; the potential drop in the presheath increases and the ion distribution function widens as the magnetic field strength decreases in the direction of the plasma flow. Application of the generalized Bohm criterion shows that the solution of the plasma equation always satisfies this criterion when the magnetic field monotonically decreases in the outside direction. The potential drop in the sheath is almost independent of the magnetic field profile, and the ion energy at a wall for a decreasing magnetic field is slightly large when compared with that for a uniform magnetic field.