A simple model is given adequate to describe the limiting mechanism and the bound on injected current is estimated. The smallness of the bound is due in large part to the strong electrostatic defocussing of a cylindrical electron layer, as compared to linear electron beams. Consequences of ionized background gas and of resistor layers are described. An appendix clarifies the different roles of electric and magnetic field energies in axial motion of the E layer.
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Langdon et al. (1973) studied this question.
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