We calculate the potential distribution in the neighborhood of a photo-emitting plate immersed in a plasma, and we find that two steady state potential distributions can exist. In one the potential decreases from its plate value to zero monotonically, and in the other it decreases from its plate value to a (negative) minimum and then increases slowly to zero. This second ‘over-shoot’ potential appears to be the stable one. Such over-shoot effects are expected to play an important role for sheaths around satellites in the interplanetary plasma.
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Guernsey et al. (1970) studied this question.