Abstract
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. First, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Second, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Third, 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.
Highlights
Magnetic fields in plasmas spontaneously self-organize into lower-energy states, for example powering disruptions in laboratory plasma and fusion devices[1,2], or stellar flares[3,4]
The numerical MHD simulations and analytical model in this paper have shown that the field line helicity A can add to understanding of the processes of dynamical relaxation and self organization in highly-conducting plasmas
Even though our simulations are limited to relatively modest Lundquist number ranges, this phenomenon is clearly observed for all Lundquist numbers tested so far
Summary
Magnetic fields in plasmas spontaneously self-organize into lower-energy states, for example powering disruptions in laboratory plasma and fusion devices[1,2], or stellar flares[3,4]. 3D MHD simulations with ever-increasing Lundquist numbers have made it possible to probe turbulent relaxation in detail, at low cost, and for precisely known initial conditions and parameters These numerical experiments have found more counterexamples where the end states are not linear force-free fields[16–20]. In the forty-seven years since Taylor’s original paper, understanding of field line helicities has advanced significantly[28–31], and it has recently been found that they do not evolve arbitrarily during reconnection but instead obey an evolution equation derived by Russell et al.[32] These authors considered how the field line helicities would evolve during localized reconnection in a complex, 3D magnetic field, such as would arise during turbulent evolution of a highly conducting plasma.
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