  We introduce a framework to study the occurrence of vortex filament
concentration in $3D$ Ginzburg-Landau theory. We derive a functional that
describes the free-energy of a collection of nearly-parallel quantized vortex
filaments in a cylindrical $3$-dimensional domain, in certain scaling limits;
it is shown to arise as the $\Gamma$-limit of a sequence of scaled
Ginzburg-Landau functionals. Our main result establishes for the first time a
long believed connection between the Ginzburg-Landau functional and the energy
of nearly parallel filaments that applies to many mathematically and physically
relevant situations where clustering of filaments is expected. In this setting
it also constitutes a higher-order asymptotic expansion of the Ginzburg-Landau
energy, a refinement over the arclength functional approximation. Our
description of the vorticity region significantly improves on previous studies
and enables us to rigorously distinguish a collection of multiplicity one
vortex filaments from an ensemble of fewer higher multiplicity ones. As an
application, we prove the existence of solutions of the Ginzburg-Landau
equation that exhibit clusters of vortex filaments whose small-scale structure
is governed by the limiting free-energy functional.
