Sheath collapse at critical shallow angle due to kinetic effects

TL;DR

This paper investigates the conditions under which the Debye sheath vanishes in magnetised plasmas, revealing that kinetic effects and finite ion orbit widths cause sheath collapse at much smaller angles than previously estimated.

Contribution

The study provides a kinetic analysis showing the sheath collapse angle scales with the electron-ion mass ratio, highlighting effects not captured by fluid models.

Findings

Sheath collapse occurs at smaller angles than previously predicted.

The collapse angle scales with the electron-ion mass ratio.

Potential for sheath inversion above the collapse potential.

Abstract

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.