DE LOS TRABAJADORES (USUARIOS INTERNOS)

η0 2.21 C1– — –C3– — –C5–C6–C7 3 4η0 2.46 C1–C2–C3– — –C5–C6–C7 1 2η0 2.60 C1–C2–C3– — –C5–C6–C7 1 4η0 2.98 C1–C2–C3– — –C5–C6–C7 1 8η0 3.39 C1–C2–C3–C4–C5–C6–C7

Table 4.1: List of total reconnection (RT) and the phases evolved through for the five exper- iments with different constant resistivities (which are given in terms of the reference value,

η0= 5×10−4).

4.7

Discussion

This chapter sought to find the answer to the nature of the reconnection which occurs in the simple numerical experiment we presented in Chapter 3. It has been shown in this chapter that the separators must be the location of reconnection in our model, which we verified by finding the maximum fieldlines of integrated parallel electric field through each diffusion region. As our model has multiple separators, and therefore has hybrid phases where different flux closes and reopens simultaneously, it is obvious that multiple locations of reconnection must concurrently exist in our model.

Since the locations of reconnection are separators, then the reconnection process in our model must beseparator reconnection, which we have confirmed by following particles trans- ported with the plasma flow. These particles each have a single associated fieldline at every point in time and we find that a particle’s fieldline is close to separator 1 just before the particle moves from an open flux domain to either the closed or overlying flux domains. If the particle has a fieldline which is close to either separator 2 or separator 3 then the par- ticle is about to move from either the closed or overlying flux domains to one of the open flux domains. After these fieldlines (which are traced from particles) have reconnected at a separator, they are ejected quickly from that separator. The movement of these particles positively suggests the existence of separator reconnection, as well as recursive reconnection. An estimate of the reconnection rates during this experiment was first given by Parnell and Galsgaard (2004) without any knowledge of the magnetic skeleton. We compare the reconnection rates which they estimated with those found by two new methods, both of which use the magnetic skeleton. The first of these new methods uses the parallel electric field which is integrated along the length of each separator. The second new method uses the known direction of reconnection at each separator and the amounts of flux in each of the flux domains to calculate the reconnection rate at each separator from the transfer of flux. The two new methods, which require the magnetic skeleton, gave self-consistent results and they both estimated far more reconnection than the earlier estimate of Parnell and Galsgaard (2004). Therefore, the knowledge gained from the magnetic skeleton is highly important

CHAPTER 4. SEPARATOR RECONNECTION AND RECIRCULATION when calculating the total amount of reconnection.

Once it is known that more flux has been reconnected in our dynamic model than in the potential model, we conducted some analysis to find (i) the total amount of reconnection and (ii) the number of times that some flux must reconnect. It was found that the total reconnection in our model was 3.6 times the amount of flux through the negative source (i.e. 80% more than the potential model). By a very simple method which minimises the amount of flux reconnecting only twice, then minimises the remaining amount of flux which reconnects only four times, etc., we found that 1₂ of the original open flux reconnects twice,

1

4 four times, 15 six times and 201 eight times. Since these figures assume that all flux must complete a cycle (of closing and then reopening) before the start of the next cycle, it is possible that some flux may reconnect ten, twelve or even more times in the actual model.

Questions arising from the discovery of recursive reconnection include its effects on the energetics in the model, especially the amount of free magnetic energy at the end of the experiment. Using five experiments with different (constant) resistivities, same initial states and driving mechanisms, it was shown that the free magnetic energy at the end of the exper- iment is not related to (i) the resistivity of the model, (ii) the total amount of reconnection during the evolution or (iii) the different evolutions of magnetic skeletons. A higher magnetic Reynold’s number did increase the total amount of reconnection and did increase the flow of magnetic energy through the system. This additional energy entered through the lower boundaries of the experiments as Poynting flux (caused by the driving mechanism) and was dissipated through Joule heating.

This chapter has presented the existence of recursive reconnection, which we found essen- tial for explaining the reconnective processes which occur in the hybrid states of our fly-by model. This has led to far better calculations for the reconnection rates, and has increased the estimates for the amount of reconnection throughout the experiment. We also have seen the existence of multiple reconnection sites, which has allowed for heating to occur over a much larger volume than is possible from a lone separator. Finally, we conclude that changes of magnetic resistivity (which changes the amount of recursive reconnection) do not affect the final free magnetic energy in our constant resistivity models, implying that any additional magnetic energy added to the system in these models must be dissipated as heat energy.

Chapter 5

Generic 2D Interaction of Discrete

Sources

5.1

Introduction

The magnetic flux interactions in the atmosphere above two equal and opposite sources, which are passing one-another in the presence of an overlying field, are similar to many quiet-Sun events. The general structure of these fly-bys was first seen in numeric MHD by Galsgaard et al. (2000a). Further investigations explored the energetics of this model (Galsgaard and Parnell, 2005) and found the complete evolution of the magnetic skeleton (Chapter 3). The previous chapter determined the correct reconnection rates for the interaction using the extra information gained from the magnetic skeleton.

So far all of the above papers and chapters consider only fly-by models with a high level of symmetry (i.e. consider a non-generic setup). One of the most obvious examples of this, is seen in the potential model of Chapter 3. In this model, all originally open flux is closed before any flux is reopened with the bifurcation states between these two phases containing an infinite number of separators. A key question is therefore what happens when a generic interaction is considered? Two simple changes to this model results in the removal of symmetry. The first change is to add or remove flux from one source without changing the flux in the other source. The second change is to vary the physical size and distribution of flux (i.e. geometry) of one source without changing the total amount of flux in the source. In our code the first change would be more difficult to implement as it would involve a flux imbalance within the box. If the upper boundary is closed, then the solenoidal condition (_{∇ ·}B = 0) cannot be satisfied. The second change does not lead to any flux imbalance, which makes it easier to implement

To understand the effects of altering the radii, location and strength of our sources in 3D, it is useful to first step back and understand the similar case for a 2D potential model. In 2D, our model has two discrete magnetic sources at fixed positions on the base (z = 0, i.e.

CHAPTER 5. GENERIC 2D INTERACTION OF DISCRETE SOURCES

photosphere), under a constant overlying magnetic field. In this chapter, we first describe the 2D model in Section 5.2, before examining the effects of changing each parameter separately (Section 5.3). We consider two simple models which investigate the final location of the null point in Section 5.4 before we discuss the results found from this 2D model at the end of this chapter.