  Plasma relaxation in the presence of an initially braided magnetic field can
lead to self-organization into relaxed states that retain non-trivial magnetic
structure. These relaxed states may be in conflict with the linear force-free
fields predicted by the classical Taylor theory, and remain to be fully
understood. Here, we study how the individual field line helicities evolve
during such a relaxation, and show that they provide new insights into the
relaxation process. The line helicities are computed for numerical
resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field
with line-tied boundary conditions, where the relaxed state is known to be
non-Taylor. Firstly, our computations confirm recent analytical predictions
that line helicity will be predominantly redistributed within the domain,
rather than annihilated. Secondly, we show that self-organization into a
relaxed state with two discrete flux tubes may be predicted from the initial
line helicity distribution. Thirdly, for this set of line-tied simulations we
observe that the sub-structure within each of the final tubes is a state of
uniform line helicity. This uniformization of line helicity is consistent with
Taylor theory applied to each tube individually. However, it is striking that
the line helicity becomes significantly more uniform than the force-free
parameter.
