A topological analysis of the magnetic breakout model for an eruptive solar flare

Abstract. We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two currents sheets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution due either to changes at the boundary or to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current sheet model a reconnection electric field in one current sheet causes the current in that sheet to increase rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away.

Section: Structure Of Equilibrium Spacementioning

confidence: 99%

Breakout and Tether-Cutting Eruption Models Are Both Catastrophic (Sometimes)

Longcope¹,

Forbes²

2014

“…A global spine-fan bifurcation (β 1 ) between B1 and B2 takes the topology to the configuration seen in Figure 5. Maclean et al (2005) explain why, if S is the set of all the separators of the null (S) whose spine is involved in the bifurcation, and T is the separator set of the null (T ) whose separatrix is involved in the bifurcation, the global spine-fan bifurcation changes the separators in the topology such that, afterwards, the set of separators connected to null T is everything that was connected to T , but not S before, plus everything that was connected to S, but not T before. In set notation, the set of separators connected to null T after the bifurcation is U = {T \S } ∪ {S \T }.…”

Section: Figurementioning

confidence: 97%

Topological Aspects of Global Magnetic Field Reversal in the Solar Corona

Maclean

Priest

2007

Every eleven years on average, the dipolar component of the Sun's global coronal magnetic field reverses in sign -a consequence of the sunspot cycle. In this paper we begin to investigate the complex changes in coronal structure during the reversal. We present a simplified model of the solar cycle containing six time-varying photospheric sources of magnetic field and analyse the evolution of the global coronal field using the technique of magnetic charge topology. Surprisingly, a sequence of seventeen topological changes takes place in the model between one solar minimum state and the next; many of the resultant topological configurations correspond to observable magnetic field structures in the real corona. We also show how descriptions of all the six-source topological states from the model can be built up in terms of combinations of simpler four-source states, providing a framework for future descriptions of even more complicated topological states.

“…To see this in action, consider the Topological Magnetic Breakout configuration (Maclean et al, 2005b), schematically represented in Figure 5. It consists of three positive sources denoted by plusses and four negative sources (including one at infinity) marked by crosses.…”

Section: Spine Graph Analysismentioning

confidence: 99%

A New Method for Finding Topological Separators in a Magnetic Field

Beveridge

2006

Magnetic topology is a powerful tool for constraining certain physical properties of a given magnetic configuration, including the strengths and locations of current sheets, relative helicity and the magnetic free energy available for reconnection. A critical feature of magnetic topology is the separator, a field line bordering several different regions of connectivity. With existing methods, these field lines are at best computationally expensive and at worst impossible to find. A new method is presented for finding the Minimal Separator Set, all of the separators that necessarily exist in a configuration, and to use this information in combination with the optical analogy and a simulated annealing method to 'cool' an initial guess for each separator into a good approximation.