Sj. Chapman et G. Richardson, MOTION AND HOMOGENIZATION OF VORTICES IN ANISOTROPIC TYPE-II SUPERCONDUCTORS, SIAM journal on applied mathematics, 58(2), 1998, pp. 587-606
The motion of vortices in an anisotropic superconductor is considered.
For a system of well-separated vortices, each vortex is found to obey
a law of motion analogous to the local induction approximation, in wh
ich velocity of the vortex depends upon the local curvature and orient
ation. A system of closely packed vortices is then considered, and a m
ean field model is formulated in which the individual vortex lines are
replaced by a vortex density.