  We propose a highly feasible technique with no experimental overhead to
rapidly cool the in-plane degrees of freedom of large two-dimensional ion
crystals in Penning traps. Through simulations, we demonstrate that our
approach enables the in-plane modes to cool down to a temperature of around 1
mK in less than 10 ms. Our technique relies on near-resonant coupling of the
poorly cooled in-plane motions and the efficiently cooled out-of-plane motions,
and is achieved without introducing additional potentials. The rapid cooling
enabled by our approach is in contrast to typical operating conditions, where
our simulations of the laser cooling dynamics suggest that the ion crystal's
in-plane motion cools very slowly on a timescale of several hundreds of
milliseconds, a rate likely slower than experimental heating rates. Our work
sets the stage for sub-Doppler laser cooling of the planar motion, and more
robust and versatile quantum simulation and quantum sensing experiments with
two-dimensional crystals in Penning traps.
