  The continuous emanation of radon due to trace amounts of uranium and thorium
in detector materials introduces radon to the active detection volume of
low-background rare event search detectors. $^{222}$Rn produces a particularly
problematic background in the physics region of interest by the ``naked'' beta
decay of its $^{214}$Pb daughter nucleus. While charcoal-based adsorption traps
are expected to be effective for radon reduction in auxiliary circulation loops
that service the warm components of current {ton-scale} detectors at slow flow
rates $(0.5-2\;SLPM)$, radon reduction in the entire circulation loop at high
flow rates $\mathcal{O}({100s\;SLPM})$ is necessary to reach high sensitivity
in future generation experiments. In this article we explore radon dynamics
with a charcoal-based radon reduction system in the main circulation loop of
time projection chamber detectors. We find that even for perfect radon traps,
circulation speeds of $2,000\;SLPM$ are needed to reduce radon concentration in
a 10\,ton detector by 90\%. This is faster by a factor of four than the highest
circulation speeds currently achieved in dark matter detectors. We further find
that the effectiveness of vacuum swing adsorption systems, which have been
employed very successfully at reducing atmospheric radon levels in clean-rooms,
is limited by the intrinsic radon activity of the charcoal adsorbent in
ultra-low radon environments. Adsorbents with significantly lower intrinsic
radon activity than in currently available activated charcoals would be
necessary to build effective vacuum swing adsorption systems operated at room
temperature for rare event search experiments. If such VSA systems are cooled
to about $190\,K$, this requirement relaxes drastically.
