  Although debris disks may be common in exoplanet systems, only a few systems
are known in which debris disks and planets coexist. Planets and the
surrounding stellar population can have a significant impact on debris disk
evolution. Here we study the dynamical evolution of debris structures around
stars embedded in star clusters, aiming to determine how the presence of a
planet affects the evolution of such structures. We combine NBODY6++GPU and
REBOUND to carry out N-body simulations of planetary systems in star clusters
(N=8000; Rh=0.78 pc) for a period of 100 Myr, in which 100 solar-type stars are
assigned 200 test particles. Simulations are carried out with and without a
Jupiter-mass planet at 50 au. We find that the planet destabilizes test
particles and speeds up their evolution. The planet expels most particles in
nearby and resonant orbits. Remaining test particles tend to retain small
inclinations when the planet is present, and fewer test particles obtain
retrograde orbits. Most escaping test particles with speeds smaller than the
star cluster's escape speed originate from cold regions of the planetary system
or from regions near the planet. We identify three regions within planetary
systems in star clusters: (i) the private region of the planet, where few
debris particles remain (40 - 60 au), (ii) the reach of the planet, in which
particles are affected by the planet (0 - 400 au), and (iii) the territory of
the planetary system, most particles outside which will eventually escape (0 -
700 au).
