  The final state of turbulent magnetic relaxation in a reversed field pinch is
well explained by Taylor's hypothesis. However, recent
resistive-magnetohydrodynamic simulations of the relaxation of braided solar
coronal loops have led to relaxed fields far from the Taylor state, despite the
conservation of helicity. We point out the existence of an additional
topological invariant in any flux tube with non-zero field: the topological
degree of the field line mapping. We conjecture that this constrains the
relaxation, explaining why only one of three example simulations reaches the
Taylor state.
