Inductively coupled plasmas with antennas wrapped around the radial surface of a cylinder are known to produce uniform plasma density profiles even though the skin depth is smaller than the discharge radius. The penetration of rf energy into interior regions has been attributed to the anomalous skin effect, in which thermal motions carry ionizing electrons past the skin layer,@footnote 1@ or to the nonlinear generation of 2nd harmonic currents.@footnote 2@ We have computed the orbits of electrons starting at arbitrary positions as they are accelerated and decelerated at different rf phases. Elastic and inelastic collisions are taken into account, and electrons are reflected when they strike the wall sheath unless they have sufficient energy to penetrate it, in which case they are lost and replaced by a slow electron elsewhere. The nonlinear Lorentz force preferentially pushes fast current-carrying electrons toward the axis. This effect, coupled with reflections from the curved wall, generates a population of fast, ionizing electrons distributed throughout the discharge. This dominant mechanism eliminates the need to place antenna elements at small radii. @FootnoteText@ @footnote 1@V.A. Godyak and V.I. Kolobov, Phys. Rev. Lett. 81, 369 (1998). @footnote 2@R.B. Piejak and V.A. Godyak, Appl. Phys. Lett. 76, 2188 (2000).