  Atmospheric xenon is strongly mass fractionated, the result of a process that
apparently continued through the Archean and perhaps beyond. Previous models
that explain Xe fractionation by hydrodynamic hydrogen escape cannot gracefully
explain how Xe escaped when Ar and Kr did not, nor allow Xe to escape in the
Archean. Here we show that Xe is the only noble gas that can escape as an ion
in a photo-ionized hydrogen wind, possible in the absence of a geomagnetic
field or along polar magnetic field lines that open into interplanetary space.
To quantify the hypothesis we construct new 1-D models of hydrodynamic
diffusion-limited hydrogen escape from highly-irradiated CO$_2$-H$_2$-H
atmospheres. The models reveal three minimum requirements for Xe escape: solar
EUV irradiation needs to exceed $10\times$ that of the modern Sun; the total
hydrogen mixing ratio in the atmosphere needs to exceed 1% (equiv. to 0.5%
CH$_4$); and transport amongst the ions in the lower ionosphere needs to lift
the Xe ions to the base of the outflowing hydrogen corona. The long duration of
Xe escape implies that, if a constant process, Earth lost the hydrogen from at
least one ocean of water, roughly evenly split between the Hadean and the
Archean. However, to account for both Xe's fractionation and also its depletion
with respect to Kr and primordial $^{244}$Pu, Xe escape must have been limited
to small apertures or short episodes, which suggests that Xe escape was
restricted to polar windows by a geomagnetic field, or dominated by outbursts
of high solar activity, or limited to transient episodes of abundant hydrogen,
or a combination of these. Xenon escape stopped when the hydrogen (or methane)
mixing ratio became too small, or EUV radiation from the aging Sun became too
weak, or charge exchange between Xe$^+$ and O$_2$ rendered Xe neutral.
