  High luminosity accretion onto a strongly magnetized neutron star results in
a radiation pressure dominated, magnetically confined accretion column. We
investigate the dynamics of these columns using two-dimensional radiative
relativistic magnetohydrodynamic simulations, restricting consideration to
modest accretion rates where the height of the column is low enough that
Cartesian geometry can be employed. The column structure is dynamically
maintained through high-frequency oscillations of the accretion shock at
$\simeq 10-25$~kHz. These oscillations arise because it is necessary to
redistribute the power released at the accretion shock through bulk vertical
motions, both to balance the cooling and to provide vertical pressure support
against gravity. Sideways cooling always dominates the loss of internal energy.
In addition to the vertical oscillations, photon bubbles form in our
simulations and add additional spatial complexity to the column structure. They
are not themselves responsible for the oscillations, and they do not appear to
affect the oscillation period. However, they enhance the vertical transport of
radiation and increase the oscillation amplitude in luminosity. The
time-averaged column structure in our simulations resembles the trends in
standard 1D stationary models, the main difference being that the time-averaged
height of the shock front is lower because of the higher cooling efficiency of
the 2D column shape.
