The plasma on an auroral field line is simulated using a Vlasov model. In the initial state, the acceleration region extends from one to three Earth radii in altitude with about half of the acceleration voltage concentrated in a stationary double layer at the bottom of this region. A population of electrons is trapped between the double layer and their magnetic mirror points at lower altitudes. A simulation study is carried out to examine the effects of fluctuations in the total accelerating voltage, which may be due to changes in the generator or the load of the auroral current circuit. The electron distribution function on the high potential side of the double layer changes significantly depending on whether the perturbation is toward higher or lower voltages, and therefore measurements of electron distribution functions provide information about the recent history of the voltage. Electron phase space holes are seen as a result of the induced fluctuations. Most of the voltage perturbation is assumed by the double layer. Hysteresis effects in the position of the double layer are observed when the voltage first is lowered and then brought back to its initial value.