Assuming a fixed ion density, adiabatic electron motion, and quasi-neutrality, we use the stationary Vlasov equation to derive the self-consistent potential in an auroral flux tube that carries downward current. Our model predicts downward electric fields ~5 mV/m at an altitude near 2000 km, and around 4000 km the potential reaches ~2.5 kV. A weak upward electric field at high altitudes reduces the potential, and the potential difference between the ionosphere and magnetosphere is much smaller.