  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.
