Infrared and ultraviolet images have established that auroral emissions at Jupiter caused by the electromagnetic interaction with Io not only produce a bright spot, but an emission trail that extends in longitude from Io's magnetic footprint. Electron acceleration that produces the bright spot is believed to be dominated by Alfvén waves whereas we argue that the trail or wake aurora results from quasi-static parallel electric fields associated with large-scale, field-aligned currents between the Io torus and Jupiter's ionosphere. These currents ultimately transfer angular momentum from Jupiter to the Io torus. We examine the generation and the impact of the quasi-static parallel electric fields in the Io trail aurora. A critical component to our analysis is a current-voltage relation that accounts for the low-density plasma along the magnetic flux tubes that connect the Io torus and Jupiter. This low-density region, ∼2 R_j from Jupiter's center, can significantly limit the field-aligned current, essentially acting as a "high-latitude current choke." Once parallel electric fields are introduced, the governing equations that couple Jupiter's ionosphere to the Io torus become nonlinear and, while the large-scale behavior is similar to that expected with no parallel electric field, there are substantial deviations on smaller scales. The solutions, bound by properties of the Io torus and Jupiter's ionosphere, indicate that the parallel potentials are on the order of 1 kV when constrained by peak energy fluxes of a few milliwatts per square meter. The parallel potentials that we predict are significantly lower than earlier reports.