Equilibrium probability distribution of a conductive sphere's floating charge in a collisionless, drifting Maxwellian plasma

TL;DR

This paper derives analytic charge probability distributions for spherical dust grains in drifting Maxwellian plasmas, extending previous stationary plasma models to include flow and larger sphere sizes, with practical Gaussian approximations.

Contribution

It provides the first analytic expressions for charge distributions of large, drifting plasma-embedded spheres, expanding beyond prior stationary plasma models.

Findings

Distributions are approximately Gaussian with explicit mean and variance.

Analytic formulas are derived for charge probability distributions.

Results apply to large spheres in flowing plasmas.

Abstract

A dust grain in a plasma has a fluctuating electric charge, and past work concludes that spherical grains in a stationary, collisionless plasma have an essentially Gaussian charge probability distribution. This paper extends that work to flowing plasmas and arbitrarily large spheres, deriving analytic charge probability distributions up to normalizing constants. We find that these distributions also have good Gaussian approximations, with analytic expressions for their mean and variance.