128. Self-generated Turbulent Reconnection

Author: Raheem Beg, Alexander Russell and Gunnar Hornig (University of Dundee).

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Over the last 15 years, steady-state reconnection models such as Sweet-Parker and Petschek have been replaced with dynamic ones, encompassing highly nonlinear phenomena such as plasmoids, turbulence and magnetic stochasticity. This work is advancing quickly, enabled by 3D simulations with Lundquist numbers exceeding a critical threshold of 104. These simulations produce self-generated and self-sustaining turbulent reconnection (SGTR) that is fully 3D and fast. Our recent paper [1] has examined the evolution, structure and topology of the SGTR layer. Here we highlight a few key facts about this type of reconnection.

Pathway to Fast Reconnection

Our 3D simulation starts from a 2.5D magnetic field, in which a current layer at y = 0 separates a pair of large twisted flux tubes [1,2]. The simulation shows three major stages:

  1. Laminar phase: The early evolution is 2.5D, laminar and slow. Reconnection is resistive Sweet-Parker. Magnetic islands form due to the tearing instability of the Sweet-Parker layer.
  2. Transition: The 2.5D symmetry breaks as 3D instabilities occur. A significant trigger in our simulation is the helical kink instability of a central flux rope formed by tearing. Magnetic stochasticity develops and spreads.
  3. SGTR phase: The system enters a final stage of self-generated turbulent reconnection that is fully 3D and quasi-stationary. The reconnection rate remains above 0.01.


Figure 1 shows a zoomed horizontal cross-section through the reconnection layer, during the SGTR phase. The magnetic field is stochastic in the region between the white contours. The squashing factor, represented by the colour, reveals “lumpy” structures within the reconnection layer; these are reminiscent of plasmoids in 2.5D reconnection, but they are displaced above and below the centreline and do not form a neat chain.

Figure 1. Cross-section (closeup) of a self-generated turbulent reconnection layer. Colour shows the squashing factor, which has the effect of highlighting flux rope structures. The white contours represent the stochastic layer boundaries.

Oblique Frayed Flux Rope Structures

The 3D magnetic structures can be further explored using field lines. Figure 2 shows that the SGTR layer contains oblique frayed flux rope structures. These magnetic structures are coherent over short distances in z; however, they are made up of stochastic field lines that become highly intermixed over greater distances in z, causing the flux ropes to become “frayed”. This creates a dualism: globally, the magnetic field in the reconnection layer is stochastic, hence one might expect a Lazarian-Vishniac [3,4] type of reconnection; locally, however, reasonably coherent twisted flux ropes divide the reconnection layer into shorter segments by a similar principle to 2.5D plasmoid-mediated reconnection [5-8].

Figure 2. Magnetic field lines in the SGTR layer reveal oblique frayed flux ropes. Each flux rope is coherent over short distances in z, but over longer distances it loses its identity as stochastic field lines wander off.

Mean Profiles and Effective Layer Thickness

Mean profiles provide a valuable top-level view of what is happening. Here, we examine variation in the y-direction across the reconnection layer during SGTR, taking averages over the whole z domain and intervals of t and x.

Figure 3 (left) shows contributions to the mean Ez. The reconnection flow pattern is supported by a fluctuation EMF (electromotive force) inside the reconnection layer, which allows the effective thickness (and hence reconnection rate) to be independent of resistivity and much greater than predicted by Sweet-Parker. Figure 3 (right) further reveals the existence of inner and outer thickness scales: the magnetic field is stochastic in a broad region, whereas the mean current density j, outflow |vx| and the fluctuation EMF have a much narrower peak. It is the inner thickness scale (associated with the main peak of the fluctuation EMF) that determines the reconnection rate.

Figure 3. Mean profiles across the reconnection layer. (left) The convection electric field outside the layer (blue) is balanced by a fluctuation EMF inside the layer (pink). (right) There is an outer thickness scale inside which the magnetic field is stochastic (green curves), and an inner thickness scale associated with current density j (red, dashed), outflow |vx| (yellow, dashed), fluctuation EMF (pink) and other important quantities.


Magnetic reconnection in the Sun is fast, fully 3D, dynamic and triggered. Simulations like the one shown above provide an exciting opportunity to finally address this long-standing and important problem.

How well do existing concepts of fast reconnection match up with simulation results? Two major frameworks are the Lazarian-Vishniac model, which is based on field-line wandering in 3D [3], and the 2D plasmoid-mediated model, which is based on a chain of marginally stable current layers [5-8]. We believe plasmoid-mediated physics is a better guide to this particular simulation, for several reasons. The reconnection rate matches the inner thickness scale, corresponding to the fluctuation EMF produced by the dynamics of flux rope structures, not the larger stochastic thickness. The reconnection rate is consistent with the ~Sc-1/2 of plasmoid-mediated reconnection. And Fig. 2 shows that the flux rope structures are locally coherent, allowing them to subdivide the global current layer into shorter segments.

In future, the plasmoid-mediated framework needs to be updated to address 3D effects, such as replacing plasmoids with oblique frayed flux ropes and incorporating field line stochasticity. New features are being discovered, such as the two thickness scales and the “SGTR wings” (regions where the fluctuation EMF reverses sign, see Fig. 3 right). It is also possible that different behaviour, such as a Lazarian-Vishniac regime, may exist for weaker guide field, so exploring parameter space is important further work.


Figures 2 & 3 in this nugget are reproduced from R. Beg , A. J. B. Russell, and G. Hornig 2022, “Evolution, structure, and topology of self-generated turbulent reconnection layers”, ApJ, 940, 94 https://doi.org/10.3847/1538-4357/ac8eb6 under the Creative Commons Attribution 4.0 licence. They are presented here at reduced resolution so they load quicker.


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