Abstract
In a number of papers dating back to the 1970s, Parker has hypothesized that, in a perfectly ideal environment, complex photospheric motions acting on a continuous magnetic field will result in the formation of tangential discontinuities corresponding to singular currents. I review direct numerical simulations of the problem and find that the evidence points to a tendency for thin but finite-thickness current layers to form, with thickness exponentially decreasing in time. Given a finite resistivity, these layers will eventually become important and cause the dynamical process of energy release. Accordingly, a body of work focuses on evolution under continual boundary driving. The coronal volume evolves into a highly dynamic but statistically steady state where quantities have a temporally and spatially intermittent nature and where the Poynting flux and dissipation are decoupled on short time scales. Although magnetic braiding is found to be a promising coronal heating mechanism, much work remains to determine its true viability. Some suggestions for future study are offered.
Highlights
The notion that solar coronal loops are heated as an end result of magnetic braiding dates back to the 1970s and Parker’s notion of topological dissipation [1,2,3]
Loops themselves are subject to photospheric motions at their footpoint, and slow footpoint motions will lead to the quasi-static evolution of loops through sequences of force-free equilibria
The notion of footpoint motions acting on the complex coronal field with all of its topological features has been formalized into the theory of coronal tectonics [9]
Summary
The notion that solar coronal loops are heated as an end result of magnetic braiding dates back to the 1970s and Parker’s notion of topological dissipation [1,2,3]. In a real corona, as soon as sufficiently small length scales develop, diffusion will locally become appreciable and a change in the magnetic topology can occur, releasing energy This release of magnetic energy, built up through braiding, could, under the Parker hypothesis, explain the observed high temperatures of coronal loops. The notion of footpoint motions acting on the complex coronal field with all of its topological features has been formalized into the theory of coronal tectonics [9] Simulations addressing this relevant scenario are so far rare, with just a very few examining the basic effect [10,11,12,13]. The resolution of these large-scale simulations is not sufficient to provide an understanding of exactly where or how the dissipation is occurring, the broad comparisons to observed loops are encouraging.
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