  Planetary rings are often speculated as being a relatively common attribute
of giant planets, partly based on their prevalence within the Solar System.
However, their formation and sustainability remain a topic of open discussion,
and the most massive planet within our planetary system harbors a very modest
ring system. Here, we present the results of a N-body simulation that explores
dynamical constraints on the presence of substantial ring material for Jupiter.
Our simulations extend from within the rigid satellite Roche limit to 10\% of
the Jupiter Hill radius, and include outcomes from $10^6$ and $10^7$ year
integrations. The results show possible regions of a sustained dense ring
material presence around Jupiter that may comprise the foundation for moon
formation. The results largely demonstrate the truncation of stable orbits
imposed by the Galilean satellites, and dynamical desiccation of dense ring
material within the range $\sim$3--29 Jupiter radii. We discuss the
implications of these results for exoplanets, and the complex relationship
between the simultaneous presence of rings and massive moon systems.
