Long Chen
On the Sun’s surface, many of the observed features such as solar flares, result from the interaction between the magnetic field and surrounding plasmas. A highly tangled bundle of magnetic field lines may spontaneously reconnect, release energy and relax to a simpler state, as if it knows how to self-organize. Recent research has shown that we can use a proxy named the field line helicity(FLH) to trace such structural changes in the magnetic field. In an effort to better understand the magnetic relaxation similar to that found on the solar surface, we then construct an effective model to study what is the dominant behaviour of FLH during relaxation. We find that in the examples we tested the dominant topological evolution is equivalent to advection by an effective flow. We are currently developing other effective models to see how the overall topology can be related to local reconnection events.
In the first page, we show an image of the coronal loops on the solar surface. We see many twisted lines that look like a bundle of very fine threads. These are actually magnetic field lines illuminated by particles spinning along them. As time evolves these structures change, often end up in a much simpler state. We are interested in studying how these structures self-organise. On the same page, we then show one example of numerical simulation with magnetic field lines plotted throughout the volume in a Cartesian box, and a topological measure called the field line helicity (FLH) plotted at the bottom plane. The end state is a very simple two-tube structure compared to a highly entangle initial braided pattern.
In the second page, we briefly explain the physical effects involved, and give the main equations in the original 3D simulations, the quantity that links the 3D to 2D reduced model, and the equations in our reduced 2D model. The basic idea is that we do not need all the physical effects in the 3D model in order to study the evolution of topology. In our reduced model we have simply advection by an effective flow. This effective flow is coupled to the complexity of the magnetic field that we want to relax. In this way, not only we are saving computational resources, we can also test which physical effect is important.
In the last page, we show the result in our 2D model matches with the main features in the original 3D model. We also give a brief discussion about the next step. We hope our method can be applied more broadly not only to study resistive magnetic relaxation but also fluid mechanics in general.