Comparison of dust charging between Orbital-Motion-Limited theory and Particle-In-Cell simulations

The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [Tang and Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with Particle-In-Cell simulations that retain the absorption radius effect. It is found that for large dust grain radius $r_d$ relative to the plasma Debye length $\lambda_D$, the revised OML theory remains a very good approximation as, for the parameters considered ($r_d/\lambda_D\le10$, equal electron and ion temperatures), it yields the dust charge to within $20\%$ accuracy. This is a substantial improvement over the Whipple approximation. The dust collected currents and energy fluxes, which remain the same in the revised and standard OML theories, are accurate to within $15-30\%$.