On the thermophoretic force close to walls in dusty plasma experiments

One observes in radiofrequency-heated vacuum chambers that dust, if present or being produced within the chamber, may float in layers close to both the upper and lower electrodes. Important forces on the dust are the electric force, gravity, plasma drag and the thermophoretic force, which is caused by temperature gradients in the background neutral gas in the vacuum chamber. We here discuss the thermophoretic force and show that the normally adopted formula for this force, which is computed on the assumption of an infinite plasma in all directions from the dust, must be modified when close to the plasma chamber walls. Taking into account the closeness of the plasma walls, we find that the thermophoretic force will be reduced out to many neutral gas molecular collision lengths from the wall, compared with the results from the standard formula. This modification of the thermophoretic force should be of importance for the force equilibrium and stability of dust in the dust layers observed in so many dust levitation experiments.