  We construct, within the framework of classical statistical mechanics, a mean
field theory of dilute flux line liquids which goes beyond linear
hydrodynamics. Within our approach, we find that interactions between vortices
produce a massive term in the Hamiltonian of the internal modes of the flux
lines which confines their transverse fluctuations. This suggests that the flux
line liquid, at least in the low density limit considered in this paper, might
very well be in a weakly entangled state, where the average width
$<u^2>^{{1/2}}$ of flux lines can be much larger than the average distance
between the lines but does not diverge with the sample thickness L.
Consequences on the physics of flux line liquids are briefly discussed.

Superconductivity;Statistical Mechanics