(1) a current sheet is formed at the interface between different flux domains interacting each other. Multiple flux domains might be formed via the emergence of a partially split flux tube (Figure 25).
(2) a current sheet is formed inside a single flux domain where sheared magnetic field develops (development of magnetic shear)
A simple model for interacting flux domains is given by the emerging magnetic field that touches the preexisting magnetic field (Rust, 1972; Heyvaerts et al., 1977). Figure 29 illustrates this model in which a current sheet is formed at the interface between these two magnetic domains, leading to magnetic reconnection there.
The dynamic process of interacting flux domains has been studied extensively using numerical simulations (Forbes and Priest, 1984; Shibata et al., 1989b, 1992b; Yokoyama and Shibata, 1994, 1995, 1996). Figure 30 shows a result from a two-dimensional MHD simulation where emerging bipolar field interacts with the preexisting oblique field (Yokoyama and Shibata, 1996). This simulation clearly demonstrates how a current sheet develops via the interaction of flux domains, followed by fast magnetic reconnection producing a high-speed, collimated plasma flow (i.e., ‘jet’).
Recently, numerical simulations analyze the interaction of flux domains in various three-dimensional configurations, revealing more complicated dynamic processes than in two-dimensional configurations (Archontis et al., 2004; Isobe et al., 2005, 2006; Galsgaard et al., 2007; Moreno-Insertis et al., 2008). Figures 31 – 33 present several prominent results obtained from these three-dimensional simulations.
Those works mentioned above are basically focused on the local dynamics produced by interacting flux domains, while it is also important to investigate the global magnetic configuration of multiple flux domains observed in real active regions. In particular, such a global approach permits to understand where current sheets are able to form, so where they locate flare ribbons/loops and how they evolve. It also permits a detailed comparison between modeling and observations (Aulanier et al., 2006; Masson et al., 2009, and references therein).
The so-called Minimum Current Corona (MCC) estimates the free energy stored in those multiple flux domains (see Longcope, 2005, for details). The original MCC assumes a configuration in which the magnetic field is in a potential state inside each flux domain, while it allows nonzero electric current flowing at the interface between flux domains. This gives a minimum excess of magnetic energy over the potential field energy in multiple flux domains. The MCC tells where current sheets form and how much electric current flows, so it can be used to investigate where flares might occur and how much energy will be released (Longcope, 1998). Later MCC was extended to enable the magnetic field to deviate from a potential state inside each flux domain (Longcope and Magara, 2004). While the MCC assumes a current sheet of infinitesimal thickness, there is also a model using a current sheet of finite thickness, which is called the quasi-separatrix layer (QSL) (Priest and Démoulin, 1995; Démoulin et al., 1996). Longcope (2005) is one of the comprehensive reviews on magnetic topology on the Sun.
The formation of a current sheet in a flux domain could be a direct consequence of the emergence of a twisted flux tube, as shown in Figure 22. A key process here is the development of magnetic shear inside a magnetic structure. This process has extensively been studied using the so-called shear-induced model in which shear and/or converging flows are imposed on the footpoints of coronal loops to increase magnetic shear (Mikić et al., 1988; Biskamp and Welter, 1989; DeVore and Antiochos, 2000; Inhester et al., 1992; Aly, 1995; Amari et al., 1996, 2003; Choe and Lee, 1996). An important suggestion from these works is that a current sheet tends to form as magnetic shear develops, followed by magnetic reconnection in the current sheet, leading to the onset of a flare (see Figure 34).
Later, the origin of these shear and converging flows assumed in the shear-induced model as photospheric boundary conditions has been investigated from the viewpoint of flux emergence. It has been demonstrated that the shear flows are self-consistently driven via the emergence of sheared magnetic structure, such as a twisted flux tube (Manchester IV, 2001; Fan, 2001; Magara and Longcope, 2001; Manchester IV et al., 2004; Manchester IV, 2007) (see Figure 35).
Regarding the converging flows, Magara (2011) demonstrates that the emergence of U-loops composing a twisted flux tube causes the convergence of photospheric footpoints of these loops, but the plasma actually shows a diverging motion on those loops which is opposite to the apparent converging motion of magnetic polarities at the surface (see Figure 36).
Manchester IV et al. (2004) show that a twisted flux tube forms a flux rope above the surface, which tends to keep floating in the corona (the rising velocity of the flux rope decreases toward zero with time). This suggests that a mechanism to eject a flux rope from the corona to the interplanetary space is needed.
Living Rev. Solar Phys. 8, (2011), 6
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