A non-hollowed-out relativistic electron beam model is considered in which the axial current well exceeds the Alfvén limit when the field-configuration of the beam is highly force free. In this model, the current has an axial as well as an azimuthal component. For a given ratio of these two current components, a family of solutions is obtained in which there is an upper limit on beam radius. Over a large range of the beam radius, the axial current in our model is large compared with the current carried by a beam of the same radius in Hammer and Rostoker's model.
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Kan et al. (1972) studied this question.
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