Abstract
Magnetic reconnection is a fundamental phenomenon in magnetised plasmas where magnetic field lines rearrange their topology, responsible for explosive dynamic events in astrophysical environments such as solar flares and coronal heating. Recent computational advancements in magnetohydrodynamic (MHD) simulations have produced compelling evidence that astrophysical reconnection is intrinsically 3D and turbulent, due to the development of 3D nonlinear instabilities and stochastic field lines. A crucial topic for illuminating the complex interaction between magnetic reconnection and MHD turbulence is the process of self-generated (and self-sustaining) turbulent reconnection (SGTR). This thesis examines the evolution, structure and magnetic topology of a 3D SGTR layer— properties which have not yet been fully explored for Sweet-Parker-type configurations. Advances are made on outstanding challenges regarding the role of field line stochasticity and flux rope structures in driving SGTR, and what ultimately sets the global reconnection rate for quasi-stationary turbulent dynamics.In our main study, we analyse a 3D MHD simulation of two merging flux ropes exhibiting SGTR that is fully 3D and “fast”, within a Sweet-Parker-type global magnetic topology (borrowed from Huang & Bhattacharjee, 2016, The Astrophysical Journal 818 (1), 20). The simulation proceeds from 2.5D Sweet-Parker reconnection to 2.5D nonlinear tearing, followed by a dynamic transition to a final SGTR phase that is globally quasi-stationary. The transition phase is dominated by a kink instability of a large “cat-eye” flux rope and the proliferation of a broad stochastic layer.
Within the SGTR layer, the fully-developed reconnection-generated turbulence is highly inhomogeneous and displays an energy cascade steeper than the Kolmogorov scaling, consistent with plasmoid-mediated models of strong MHD turbulence over Goldreich-Sridhar theory, with approximately scale-independent local eddy anisotropy. The mature field line diffusion spectra within the stochastic layer exhibit Richardson-type superdiffusion followed by ordinary Brownian-type diffusion for increasing trace distances, which agrees with the theoretical scalings for field line wandering in the Lazarian-Vishniac model.
The global reconnection layer has two general characteristic thickness scales, which correlate with the global reconnection rate and differ by a factor of approximately six: an inner scale corresponding with current and vorticity densities, outflow jets, and turbulent fluctuations; and an outer scale associated with field line stochasticity. The effective thickness of the global SGTR layer, facilitating “fast” reconnection, is the inner scale of the effective reconnection electric field produced by turbulent fluctuations, i.e., the turbulent electromotive force (EMF), not the stochastic thickness. While the volumetric and diffusive components of the field line stochasticity correlate with the global reconnection rate over time, it is uncertain whether the stochastic layer directly influences the governing inner scale.
From a mean-field perspective, the SGTR layer displays a “core and wings” structure. Within the “SGTR core” associated with the inner scale, strong turbulent fluctuations and reconnection activity are concentrated, and the turbulent EMF dominates over resistive diffusion in Ohm’s law. Within the distinctive intermediate regions between the SGTR core and stochastic separatrices (“SGTR wings”), the MHD turbulence is weaker and characteristically different from the SGTR core. The dynamics inside the SGTR layer are commanded by flux rope structures analogous with 2D plasmoids. However, these structures are topologically complicated: they appear to lack well-defined axes, are only locally coherent, and the stochastic field lines they are composed of become highly intermixed over large trace distances and eventually exit into the broader stochastic region. Future explorations of the flux rope structures and SGTR wings, and their connections, are potentially key to understanding SGTR.
The 3D study concludes with discussions on the apparent dualism between the plasmoid-mediated and Lazarian-Vishniac model perspectives on SGTR. Overall, the plasmoid-mediated paradigm appears to be a stronger description of the reconnection behaviour in our particular simulation.
Finally, two supplementary studies using analogous 2.5D MHD simulations are presented: a global Lundquist number scaling study and a novel simulation ensemble study. These 2.5D investigations provide valuable insights into the plasmoid-mediated component of SGTR and possible numerical effects in the main 3D simulation.
The characteristic “fast” global reconnection rates in 2.5D are consistent with the canonical plasmoid-mediated magnitude and have excellent agreement with the characteristic rate in 3D. The statistically-averaged global reconnection layer displays a “core and wings” structure similar to our 3D results. The effective layer thickness corresponds with the core of the fluctuation EMF (and other inner variables), which is unambiguously attributed to plasmoid dynamics, and shown to match the thickness of the “typical” largest plasmoid, in line with theoretical predictions. These findings strongly support that the SGTR dynamics in the main 3D simulation are predominantly plasmoid-mediated; they also signify that the SGTR core is comparable with a 2.5D plasmoid-mediated statistical baseline, with flux rope structures playing an instrumental role in inducing the turbulent EMF. The wing regions, however, are fundamentally different between the 2.5D and 3D cases, indicating that fully 3D plasma effects are significant within the SGTR wings.
The influence of the grid resolution on the reconnection properties in 2.5D MHD simulations was inspected, both numerically and analytically. In principle, there exists a maximum global Lundquist number for a given grid scale, above which the simulation cannot sufficiently resolve critical small scales during the “fast” plasmoid-mediated regime, leading to artificial enhancements in the global reconnection rate and effective layer thickness. While comparison tests with 2.5D suggest that the main 3D simulation was somewhat under-resolved, numerical effects on the SGTR properties are not likely to be major. Moreover, the “collisionless-like” grid effects in “under-resolved” MHD simulations may closely capture reconnection behaviour found in real coronal plasmas where kinetic scales are pertinent.
| Date of Award | 2023 |
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| Original language | English |
| Awarding Institution |
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| Sponsors | Science and Technology Facilities Council |
| Supervisor | Alexander Russell (Supervisor) & Gunnar Hornig (Supervisor) |