  The effect of the dipole-dipole interaction on the far-off-resonance optical
dipole trapping scheme is calculated by a mean-field approach. The trapping
laser field polarizes the atoms and the accompanying dipole-dipole energy shift
deepens the attractive potential minimum in a pancake-shaped cloud. At high
density the thermal motion cannot stabilize the gas against self-contraction
and an instability occurs. We calculate the boundary of the stable and unstable
equilibrium regions on a two-dimensional phase diagram of the atom number and
the ratio of the trap depth to the temperature. We discuss the limitations
imposed by the dipole-dipole instability on the parameters needed to reach
Bose-Einstein condensation in an optical dipole trap.
