  There are currently no three dimensional numerical models which describe the
magnetic and energetic formation of prominences self-consistently.
Consequently, there has not been significant progress made in understanding the
connection between the dense prominence plasma and the coronal cavity. We have
taken an ad-hoc approach to understanding the energetic implications of the
magnetic models of prominence structure. We extract one dimensional magnetic
field lines from a 3D MHD model of a flux rope and solve for hydrostatic
balance along these field lines incorporating field-aligned thermal conduction,
uniform heating, and radiative losses. The 1D hydrostatic solutions for density
and temperature are then mapped back into three dimensional space, which allows
us to consider the projection of multiple structures. We find that the 3D flux
rope is composed of several distinct field line types. A majority of the flux
rope interior field lines are twisted but not dipped. These field lines are
density-reduced relative to unsheared arcade field lines. We suggest the cavity
may form along these short interior field lines which are surrounded by a
sheath of dipped field lines. This geometric arrangement would create a cavity
on top of a prominence, but the two structures would not share field lines or
plasma
