Orbital-motion-limited theory of dust charging and plasma response

TL;DR

This paper revises the orbital motion limited (OML) theory to accurately predict dust charge and plasma response in dusty plasmas, especially for larger dust particles in tokamak environments.

Contribution

A new formulation of the OML theory that can predict dust charge and plasma response, extending its applicability to larger dust particles.

Findings

Revised OML theory predicts dust charge for larger particles.

Whipple approximation agrees with OML for small dust, deviates for larger dust.

Application relevance to tokamak plasma dust particles.

Abstract

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely-used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma.