Regions of validity for Debye and inverse third-power models for shielding of test charges

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Abstract
The shielding potential for a test charge in a plasma is derived for the case in which the velocity of the charge is much less than the thermal velocity. This potential is an analytical expression valid for any angle in space. The potential contains the Debye term and also a term which is due to the particle's motion. At large distances from the test charge the latter term asymptotically becomes proportional to the inverse third power of the distance. On the other hand, as the distance to the test charge approaches zero, this term vanishes and the potential becomes the Coulomb potential. It is shown that, although the inverse third-power term dominates at very large distances, the Debye term dominates over the very important region out to at least several Debye lengths.

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