  We consider a generalization of the Nielsen-Olesen ansatz, in an
abelian-Higgs model with externally coupled charge, which describes strings
with twisted magnetic flux lines in the vortex core. The solution does not
possess cylindrical symmetry, which leads to the existence of components of
conserved momentum, both around the core-axis and along the length of the
string. In addition, we consider a model of F-strings with rotating, geodesic
windings in the compact space of the Klebanov-Strassler geometry and determine
matching conditions which ensure energy and momentum conservation when loops
chop off from the long-string network. We find that the expressions for the
constants of motion, which determine the macroscopic string dynamics, can be
made to coincide with those for the twisted flux line string, suggesting that
extra-dimensional effects for F-strings may be mimicked by field- theoretic
structure in topological defects.
