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In a plasma at rest, the electrostatic potential around a point charge obeys the well-known Debye shielding law. Modifications, for the ease of a flowing plasma, have been studied in the limiting cases of either long or short distances for subsonic and hypersonic velocities. Only recently this was extended to include all distances, restricted to a two-dimensional case. However, neither of these modifications includes the ionic motions. In this paper, we derive general expressions for the electrostatic potential which are valid for all distances and flow velocities in one-, two- and three-dimensional cases. This is done first with unperturbed ions, and then for the case where ionic motions, which are seen to be important for mesothermic flow velocities, are included. In both cases, the results are discussed and illustrated.

Suggested by numerical simulations, recent experiments have shown that a significant guiding force is exerted by a reduced-density channel on electron beams propagating through initially un-ionized air. A theoretical analysis of this guiding force had been given that assumed uniform beam and channel and small beam-channel offset. From a 2-D model, relative to a beam slice, the guiding force is calculated in this article for arbitrary beamchannel offset and for various smooth beam and channel profiles. This calculation confirms the above-quoted experimental evidence of a guiding force significant with respect to the deflection force exerted by the earth's magnetic field. It also confirms the crucial role played by the secondary electron temperature distribution. Finally, it suggests optimal values for the ratio between channel and beam rms radii.