  Predicting the final state of turbulent plasma relaxation is an important
challenge, both in astrophysical plasmas such as the Sun's corona and in
controlled thermonuclear fusion. Recent numerical simulations of plasma
relaxation with braided magnetic fields identified the possibility of a novel
constraint, arising from the topological degree of the magnetic field-line
mapping. This constraint implies that the final relaxed state is drastically
different for an initial configuration with topological degree 1 (which allows
a Taylor relaxation) and one with degree 2 (which does not reach a Taylor
state). Here we test this transition in numerical resistive-magnetohydrodynamic
simulations, by embedding a braided magnetic field in a linear force-free
background. Varying the background force-free field parameter generates a
sequence of initial conditions with a transition between topological degree 1
and 2. For degree 1, the relaxation produces a single twisted flux tube, while
for degree 2 we obtain two flux tubes. For predicting the exact point of
transition, it is not the topological degree of the whole domain that is
relevant, but only that of the turbulent region.
