  We study several aspects of the structure of vortices in conventional s-wave
Type $II$ superconductors. It is well-known that there are low energy
quasiparticles bound to the core of a vortex. We show that under certain
conditions, these quasiparticles form a degenerate Fermi gas with a finite
density of states at the Fermi energy. In three dimensional superconductors,
the result is a one dimensional Fermi gas of quasiparticles bound to the core
of a vortex line. As is usual in one dimensional systems, interactions between
the quasiparticles lead to Luttinger liquid behaviour. This may be probed
through STM tunneling into the vortex core. We further suggest that a novel
Peierls-type instability in the shape of the vortex line may develop due to
interactions between the quasiparticle gas and fluctuations in the vortex line
shape.
