A model of a neutralized electron beam in which the electrons make helical orbits about the axis is described. This differs from previous models in that there is no longitudinal field or azimuthal current. Three particular cases, corresponding to (1) uniform charge density in a solid beam, (2) uniform current density in a solid beam, and (3) uniform charge density in a hollow beam are analyzed. In none of these configurations is there a current limit, and all the electrons move in the forward direction.