In an effort to understand the cause of the apparent depletion in the number density of radio-loud AGNs at $z>3$, this work investigates the viability of the so-called Cosmic Microwave Background (CMB) quenching mechanism of intrinsically jetted, high-z AGNs, whereby Inverse Compton scattering of CMB photons off electrons within the extended lobes results in a substantial dimming of the lobe synchrotron emission at GHz frequencies, while simultaneously boosting their diffuse X-ray signal. We focus on five $z>3.5$ radio galaxies that have sufficiently deep Chandra exposure (> 50 ks) to warrant a meaningful investigation of any extended X-ray emission. For those objects with evidence for statistically significant extended X-ray lobes (4C 41.17 and 4C 03.24), we combine the Chandra measurements with literature data at lower frequencies to assemble the systems Spectral Energy Distributions (SEDs), and utilize state-of-the-art SED modelling (Ghisellini et al. 2015) -- including emission from the disk, torus, jet, hotspots, and lobes -- to infer their physical parameters. For both radio galaxies, the magnetic energy density in the hotspots is found to exceed the energy density in CMB photons, wheres the opposite is true for the lobes. This implies that any extended synchrotron emission likely originates from the hotspots themselves, rather than the lobes. Conversely, Inverse Compton scattering of CMB photons dominates the extended X-ray emission from the lobes, which are effectively radio-quenched. As a result, CMB quenching is effective in these systems in spite of the fact that the observed X-ray to radio luminosity ratio does not bear the signature $(1+z)^4$ dependence of the CMB energy density.
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