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

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.

A treecode to simulate dust–plasma interactions

“…The SOML theory [10] provides a benchmark by The OML-theory prediction [7] is overlaid as a thick dashed line. The region where the charge fluctuations are within 1σ of the equilibrium value, with σ provided by stochastic modelling [2], is shaded grey.…”

“…The region where the charge fluctuations are within 1σ of the equilibrium value, with σ provided by stochastic modelling [2], is shaded grey.…”

“…The central sphere is initialised with no charge and allowed to collect charge from the plasma; the evolution of this charge over the course of the simulation is plotted in figure 4. The charge evolution predicted by OML theory [7] has been added to the plot along with a shaded region to represent the charge's standard deviation s predicted by stochastic modelling [2]. The charge of the sphere as calculated by pot is consistent with both of these theories; applying a c 2 goodness-of-fit test to the variance s 2 from the stochastic model and potʼs results gives a p-value of 0.66, indicating statistically insignificant disagreement.…”

“…This complexity is increased further by the inclusion of dust grains; not only do they represent an additional charged species, but they act as sources and sinks for electrons and ions. Therefore the charge on the dust may fluctuate [2], but this charge depends additionally on nonplasma processes such as thermionic, field-induced and photonic emission of electrons [3]. The shape and size of dust is also variable, as they can grow through aggregation [4] or shrink through evaporation and violent processes such as electrostatic breakup [5].…”

“…The charge q, in units of e, of an absorbing sphere for a pot run with no external fields or plasma flows. The OML-theory prediction[7] is overlaid as a thick dashed line.The region where the charge fluctuations are within 1σ of the equilibrium value, with σ provided by stochastic modelling[2], is shaded grey.Both theoretical predictions agree well with pot's results.…”