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.

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