Abstract— In this paper, the axial-mode performance features of a non-uniform helix, whose non-uniformity is defined by a logarithmic variation of turns spacing along its axis, is presented. Using the classical vector potential approach, the paper rigorously formulates radiation-zone field integrals for the antenna in terms of an unknown distribution of current. Because the formulation derives from a comprehensive analytical description of this ‘log-helix’ antenna’s geometry, the unknown current distribution is readily determined with the use of the circuitgeometric properties of the Method of Moments (MoM). Subsequently, computational results reveal that – as obtained with other non-uniform helical antennas – the ‘log-helix’ antenna performs significantly better than the corresponding uniform helical antenna of identical axial length. As examples, a 39% increase in power gain was recorded for the log-helix over the corresponding uniform helix; whilst a 25% improvement in radiation field’s axial ratio was achieved. In addition to far-zone fields and their associated performance metrics, antenna input parameters are also computed and discussed in details in this paper. Outcomes of a comparison of the performance of the log-helix with that of an exponential helix of about the same axial profile suggest that whereas the latter has a better power gain performance, the former is superior in terms of axial ratio bandwidth performance.