  At proposed future hadron colliders and in the coming years at the LHC, top
quarks will be produced at genuinely multi-TeV energies. Top-tagging at such
high energies forces us to confront several new issues in terms of detector
capabilities and jet physics. Here, we explore these issues in the context of
some simple JHU/CMS-type declustering algorithms and the N-subjettiness
jet-shape variable tau_32. We first highlight the complementarity between the
two tagging approaches at particle-level with respect to discriminating
top-jets against gluons and quarks, using multivariate optimization scans. We
then introduce a basic fast detector simulation, including electromagnetic
calorimeter showering patterns determined from GEANT. We consider a number of
tricks for processing the fast detector output back to an approximate
particle-level picture. Re-optimizing the tagger parameters, we demonstrate
that the inevitable losses in discrimination power at very high energies can
typically be ameliorated. For example, percent-scale mistag rates might be
maintained even in extreme cases where an entire top decay would sit inside of
one hadronic calorimeter cell and tracking information is completely absent. We
then study three novel physics effects that will come up in the multi-TeV
energy regime: gluon radiation off of boosted top quarks, mistags originating
from g -> tt, and mistags originating from q -> (W/Z)q collinear electroweak
splittings with subsequent hadronic decays. The first effect, while nominally a
nuisance, can actually be harnessed to slightly improve discrimination against
gluons. The second effect can lead to effective O(1) enhancements of gluon
mistag rates for tight working points. And the third effect, while conceptually
interesting, we show to be of highly subleading importance at all energies.
