Revisiting the plasma sheath - dust in plasma sheath

In this work, we have considered the formation of warm plasma sheath in the vicinity of a wall in a plasma with considerable presence of dust particles. As an example, we have used the parameters relevant in case of lunar plasma sheath, though the results obtained in this work could be applied to any other physical situation such as laboratory plasma. In the ion-acoustic time scale, we neglect the dust dynamics. The dust particles affect the sheath dynamics by affecting the Poisson equation which determines the plasma potential in the sheath region. We have assumed the current to a dust particle to be balanced throughout the analysis. This makes the grain potential dependent on plasma potential, which is then incorporated into the Poisson equation. The resultant numerical model becomes an initial value problem, which is described by a 1-D integro-differential equation, which is then solved self-consistently by incorporating the change in plasma potential caused by inclusion of the dust potential in the Poisson equation.