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Flux Ropes as Singularities of the Vector Potential

Abstract : A flux rope is a domain where a twisted magnetic field [ B] is concentrated; it can be described as the core of a singularity of the outer field or the outer vector potential [ A] (Kleman and Robbins in Solar Phys. 289, 1173, 2014). This latter case, occurring when the outer field is vanishing, is mathematically analysed for a straight infinite rope. Concepts from condensed-matter physics defect theory are used: the flux [Φ], measured as ∮ C Aṡd s along any loop [ C] surrounding the rope, is a topological constant of the theory. A flux rope with a small outer magnetic field can be treated as a perturbation of the above. This theoretical framework allows for the use of classical configurations inside the core, e.g. the linear force-free field (LFFF) Lundquist model or the nonlinear (NLFFF) Gold-Hoyle model, but restricts the number of stable solutions: they are quantised into strata of increasing energies (an infinite number of strata in the first case, only one stratum in the second case); each stratum is defined by a number 2 πζ= b/ r 0, where b is the periodicity along the axis of the rope and r 0 is its radius, and the rope is made of a continuous set of stable states. We also analyse the merging of identical flux ropes (belonging to the same stratum), with conservation of the relative magnetic helicity: they merge into a unique rope of the first stratum, with a considerable release of energy.
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Submitted on : Friday, February 18, 2022 - 2:00:35 PM
Last modification on : Friday, October 21, 2022 - 3:32:40 PM

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M. Kleman. Flux Ropes as Singularities of the Vector Potential. SOLAR PHYSICS, 2015, 290, pp.707-725. ⟨10.1007/s11207-015-0647-6⟩. ⟨insu-03579987⟩

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