  A phenomenological model of the evolution of an ensemble of interacting
dislocations in an isotropic elastic medium is formulated. The line-defect
microstructure is described in terms of a spatially coarse-grained order
parameter, the dislocation density tensor. The tensor field satisfies a
conservation law that derives from the conservation of Burgers vector.
Dislocation motion is entirely dissipative and is assumed to be locally driven
by the minimization of plastic free energy. We first outline the method and
resulting equations of motion to linear order in the dislocation density
tensor, obtain various stationary solutions, and give their geometric
interpretation. The coupling of the dislocation density to an externally
imposed stress field is also addressed, as well as the impact of the field on
the stationary solutions.
