  We identify multiple periodic dusty structures in Saturn's Roche Division, a
faint region spanning the $\sim3000$ km between the A and F rings. The
locations and extent of these features vary over Cassini's tour of the Saturn
system, being visible in 2006 and 2016-2017, but not in 2012-2014. These
changes can be correlated with variations in Saturn's magnetospheric periods.
In 2006 and 2016-2017, one of the drifting magnetospheric periods would produce
a 3:4 resonance within the Roche Division, but in 2012-2014 these resonances
would move into the A ring as the magnetospheric periods converged. A simple
model of magnetic perturbations indicates that the magnetic field oscillations
responsible for these structures have amplitudes of a few nanotesla, comparable
to the magnetic field oscillation amplitudes of planetary period oscillations
measured by the magnetometer onboard Cassini. However, some previously
unnoticed features at higher radii have expected pattern speeds that are much
slower than the magnetospheric periodicities. These structures may reflect an
unexpectedly long-range propagation of resonant perturbations within dusty
rings.
