Externally launched ion Bernstein wave (IBW) experiments have demonstrated localized electron heating, sheared flows and transport barriers in several tokamaks. Experiments in the tokamak fusion test reactor (TFTR) showed that IBW waves launched from low-field side IBW antennas could drive a velocity shear layer in the central plasma, but the power coupled to the IBW was not sufficient to achieve a transport barrier. This experiment raised important questions concerning where the radio-frequency (rf) power went and whether the anomalous loss channels are more important in larger machines. Recently, it was proposed that the power loss was due to a coaxial electron plasma wave (EPW) mode excited in the low density plasma halo near the vessel wall (Myra et al 2000 Phys. Plasmas7 283). This mode could dissipate a significant power fraction by sheath and collisional mechanisms, fits more easily in larger machines like TFTR and has the phasing dependence observed in the experiments. Here we extend that work by demonstrating the existence and phasing dependence of the coaxial mode (CM) in a realistic rf coupling calculation. A three-dimensional finite-element electromagnetic code couples a detailed model of the antenna geometry with a plasma dielectric model that retains CM physics. Quantitative results show the dependence of the CM rf fields and power dissipation on the phasing of the multiple-strap array. Unlike conventional rf coupling codes, this paper enables the antenna limiters to be immersed in tenuous plasma, an important feature for correctly modelling parasitic coupling to the CM.