The Role of Magnetic Helicity in the Structure and Heating of the Sun's Corona

Two of the most important and interesting features of the solar atmosphere are its hot, smooth coronal loops and the significant concentrations of magnetic shear, known as filament channels, that reside above photospheric polarity inversion lines (PILs; locations where the line-of-sight component of the photospheric magnetic field changes sign). The shear that is inherent in filament channels represents magnetic helicity, a topological quantity describing the amount of linkage in the magnetic field. The smoothness of the coronal loops, on the other hand, indicates an apparent lack of magnetic helicity in the rest of the corona. At the same time, models that attempt to explain the high temperatures observed in these coronal loops require magnetic energy, in the form of twist, to be injected at the photospheric level, after which this energy is converted to heat through the process of magnetic reconnection. In addition to magnetic energy, the twist that is injected at the photospheric level also represents magnetic helicity. Unlike magnetic energy, magnetic helicity is conserved under reconnection, and is consequently expected to accumulate and be observed in the corona. However, filament channels, rather than the coronal loops, are the lo- cations in the corona where magnetic helicity is observed, and it manifests itself in the form of shear, rather than twist. This naturally raises the question: if magnetic helicity needs to be injected to heat coronal loops, why is it only observed in filament channels, with the rest of the corona, and coronal loops in particular, observed to be laminar and smooth? This thesis addresses this question using a series of numerical simulations that explore the effect of helicity injection into the coronal magnetic field. These simulations demonstrate that magnetic helicity is transported throughout the solar corona by magnetic reconnection in such a way that it accumulates above PILs, forming filament channels, and leaving the rest of the corona generally smooth. In the process, it converts magnetic energy into heat throughout the `loop' portion of the corona, accounting for the large observed temperatures. As a result of these sim- ulations, this thesis presents a model for 1) the formation of filament channels in the solar corona and 2) the presence of smooth, hot coronal loops, and shows how the transport of magnetic helicity throughout the solar corona by magnetic reconnection is responsible for both of these phenomena