The first observations of Jupiter made by the Chandra X‐Ray Observatory revealed a powerful X‐ray aurora located in the polar caps. The X‐ray emission exhibited a 40‐min periodicity. Such 40‐min periodicities have previously been seen in energetic particle fluxes and in Jovian radio emission. This paper develops scenarios in which the X‐ray emission is produced by energetic heavy ion precipitation, either on open field lines connecting to the solar wind or on closed field lines reaching to the outer magnetosphere. In order to produce enough X‐ray power, both scenarios require the existence of field‐aligned electric fields located somewhere between the ionosphere and the magnetosphere, most likely at a radial distance of a few Jovian radii. The potential needed for solar wind ions to produce the observed X‐rays is about 200 kV and the potential needed for the magnetospheric ions is at least 8 MV. Protons and helium ions are also accelerated by the potential and should produce an intense ultraviolet aurora. Downward electrical current is carried by the precipitating ions and also by upwardly accelerated secondary electrons produced by the primary ion precipitation. The estimated downward Birkeland current is about 1000 MA for the solar wind case and is about 10 MA for the magnetospheric case. For the magnetosphere scenario, this observed current represents part of the “return” current portion of the magnetospheric circuit associated with the departure of the mass‐loaded magnetospheric plasma from corotation. The auroral X‐ray emission maps at least part of this return current in the polar cap, whereas the main oval, produced by electron precipitation, is thought to map the region of upward Birkeland currents. The accelerated secondary electrons could be responsible for the periodic radio emission (i.e., QP‐40 bursts).