Image potential for stepped and corrugated surfaces

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Abstract
The classical image potential is derived for a nonplanar conducting surface. A general formulation is given for first-order deformations of an arbitrary shape. Detailed formulas are presented for a variety of rectangular step and terrace configurations including corrugations. It is shown that ions and electrons are always attracted to the elevated part of the surface. Potential-energy minima and hence bound states parallel to the surface can exist on a track or terrace. Classical trajectories are calculated in some special cases and compared to the plane conductor. The effects produced by these nonplanar surfaces on ion angular distributions are also discussed.