UV radiation from white dwarfs can efficiently clear Galactic globular clusters (GCs) of their intra-cluster medium (ICM). This solves the problem of the missing ICM in clusters, which is otherwise expected to build up to easily observable quantities. To show this, we recreate the ionizing flux in 47 Tuc, following randomly generated stars through their AGB, post-AGB and white dwarf evolution. Each white dwarf can ionize all the material injected into the cluster by stellar winds for ∼3 Myr of its evolution: ∼40 such white dwarfs exist at any point. Every GC's ICM should be ionized. The neutral cloud in M15 should be caused by a temporary overdensity. A pressure-supported ICM will expand over the cluster's tidal radius, where it will be truncated, allowing Jeans escape. The modelled Jeans mass-loss rate approximates the total stellar mass-loss rate, allowing efficient clearing of ICM. Any cluster's ICM mass should equal the mass injected by its stars over the sound-travel time between the cluster core and tidal radius. We predict ∼11.3 M ⊙ of ICM within 47 Tuc, cleared over ∼4 Myr, compared to a dynamical timescale of 4.3 Myr. We present a new mass hierarchy, discussing the transition between globular clusters dwarf galaxies.