Jupiter's main auroral emission is a signature of the current system that transfers angular momentum from the planet to radially outward moving Iogenic plasma. Ray et al. (2010) developed a steady state model of this current system which self-consistently included the effects of a field-aligned potential, and an ionospheric conductance modified by precipitating electrons. The presented parameter space study extends their model to explore how variations in the auroral cavity density and temperature, magnetospheric mass loading rate, and background ionospheric Pedersen conductance affect the current system and resulting auroral emission. We show that while the solutions found by Ray et al. (2010) vary with changes in the system parameters, the gross general trends remain similar to the original solutions. We find that, for an outer constraint of I₁₀₀ = 86 MA, the high-latitude electron temperature and density have a lower limit of ∼1.5 keV and an upper limit of ∼0.01 cm ^-3, respectively, in order for solutions to be consistent with observations of Jupiter's auroral emission. For increases in the radial mass transport rate and an outer constraint of _Max = 75 kV the auroral emission brightness increases.