Does Magnetic Reconnection Change Topology?

Abstract

We employ well-known concepts from statistical physics, quantum field theories and general topology to study magnetic reconnection, topology-change and their connection in incompressible flows in the context of an effective field theory without appealing to magnetic field lines. We consider the dynamical system corresponding to wave-packets moving with Alfven velocity dx/dt=V_A whose trajectories x(t) define path lines, which naturally provides a mathematical way to estimate the rate of magnetic topology-change. In laminar and even chaotic flows, the separation of path lines at all times remains proportional to their initial separation, argued to correspond to slow reconnection, and topology changes by dissipation with a rate proportional to resistivity. In turbulence, path lines diverge super-linearly with time independent of their initial separation, i.e., fast reconnection, and magnetic topology changes by turbulent dissipation with a rate independent of small-scale plasma effects. In fact, due to the loss of Lipschitz continuity of magnetic field in turbulence, path lines separate super-linearly even if their initial separation tends to vanish, unlike deterministic chaos. This super-chaotic behavior is an example of spontaneous stochasticity in statistical physics, sometimes called the real butterfly effect in chaos theory to distinguish it from the butterfly effect in which trajectories can diverge exponentially only if initial separation remains finite. If 3D reconnection is defined as magnetic topology-change, it can be fast only in turbulence where both reconnection and topology-change are driven by spontaneous stochasticity, independent of any plasma effects. Our results strongly support the Lazarian-Vishniac theory of turbulent reconnection.