  We critically assess limits on the maximum energy of protons accelerated
within superbubbles around massive stellar clusters, considering a number of
different scenarios. In particular, we derive under which circumstances
acceleration of protons above peta-electronvolt (PeV) energies can be expected.
While the external forward shock of the superbubble may account for
acceleration of particles up to 100 TeV, internal primary shocks such as
supernova remnants expanding in the low density medium or the collective wind
termination shock which forms around a young compact cluster provide more
favourable channels to accelerate protons up to 1 PeV, and possibly beyond.
Under reasonable conditions, clustered supernovae launching powerful shocks
into the magnetised wind of a young and compact massive star cluster are found
to be the most promising systems to accelerate protons above 10 PeV. On the
other hand, stochastic re-acceleration in the strongly turbulent plasma is
found to be much less effective than claimed in previous works, with a maximum
proton energy of at most a few hundred TeV.

High Energy Astrophysical Phenomena