Abstract
Predicting the final state of turbulent plasma relaxation is an important challenge, both in astro-physical 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, whereas 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.
Highlights
Self-organization of turbulently relaxing plasma to a predictable minimum-energy state has been observed in laboratory confinement devices including the reversedfield pinch and the spheromak [1,2,3,4]
We identified the presence of an additional constraint beyond the total magnetic flux and helicity: the topological degree of the field line mapping [14,15]
The nature of the final state of the turbulent relaxation is conjectured to be independent of the resistivity. This numerical experiment shows that one must choose the boundary appropriately if one is to correctly predict the end-state topology based on the topological degree of the initial state
Summary
Self-organization of turbulently relaxing plasma to a predictable minimum-energy state has been observed in laboratory confinement devices including the reversedfield pinch and the spheromak [1,2,3,4]. It has been proposed that this Taylor relaxation theory might be applied to predict the energy released by rapid heating events in the solar corona [6], where magnetic energy is believed to be released through relaxation to a lower energy equilibrium In this context, numerical magnetohydrodynamic (MHD) simulations have modelled the dynamic relaxation of various initially unstable equilibria, such as kink-unstable twisted magnetic flux ropes [7,8,9,10,11], or a magnetic field with a braided structure [12,13]. These sub-volumes are separated by a discrete set of irrational flux surfaces that survive even in the presence of the chaotic field lines typical of non-axisymmetric magnetic fields In another application, Gimblett et al [19] have developed a model for edgelocalized modes based on localized Taylor relaxation within only the outer region of the plasma. This complements the particular configurations where this constraint was demonstrated previously [14], which had vanishing magnetic helicity
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