  We investigate the evolution of field line helicity for magnetic fields that
connect two boundaries without null points, with emphasis on localized finite-B
magnetic reconnection. Total (relative) magnetic helicity is already recognized
as an important topological constraint on magnetohydrodynamic processes. Field
line helicity offers further advantages because it preserves all topological
information and can distinguish between different magnetic fields with the same
total helicity. Magnetic reconnection changes field connectivity and field line
helicity reflects these changes; the goal of this paper is to characterize that
evolution. We start by deriving the evolution equation for field line helicity
and examining its terms, also obtaining a simplified form for cases where
dynamics are localized within the domain. The main result, which we support
using kinematic examples, is that during localized reconnection in a complex
magnetic field, the evolution of field line helicity is dominated by a
work-like term that is evaluated at the field line endpoints, namely the scalar
product of the generalized field line velocity and the vector potential.
Furthermore, the flux integral of this term over certain areas is very small
compared to the integral of the unsigned quantity, which indicates that changes
of field line helicity happen in a well-organized pairwise manner. It follows
that reconnection is very efficient at redistributing helicity in complex
magnetic fields despite having little effect on the total helicity.
