We present deep MUSE integral-field unit (IFU) spectroscopic observations of the giant (~150 x 80 kpc) Ly-alpha halo around the z=4.1 radio galaxy TNJ J1338-1942. This 9-hr observation maps the two-dimensional kinematics of the Ly-alpha emission across the halo. We identify two HI absorbers which are seen against the Ly-alpha emission, both of which cover the full 150 x 80 kpc extent of the halo and so have covering fractions ~1. The stronger and more blue-shifted absorber (dv~1200 km/s) has dynamics that mirror that of the underlying halo emission and we suggest that this high column material (n(HI) ~ 10^19.4 /cm^2), which is also seen in CIV absorption, represents an out-flowing shell that has been driven by the AGN (or star formation) within the galaxy. The weaker (n(HI)~10^14 /cm^2) and less blue shifted (dv~500 km/s) absorber most likely represents material in the cavity between the out-flowing shell and the Ly-alpha halo. We estimate that the mass in the shell must be of order 10^10 Msol -- a significant fraction of the ISM from a galaxy at z=4. The large scales of these coherent structures illustrate the potentially powerful influence of AGN feedback on the distribution and energetics of material in their surroundings. Indeed, the discovery of high-velocity (~1000 km/s), group-halo-scale (i.e. >150 kpc) and mass-loaded winds in the vicinity of the central radio source are broadly in agreement with the requirements of models that invoke AGN-driven outflows to regulate star formation and black-hole growth in massive galaxies at early times.
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