The Heating of the Solar Corona by Kink Instabilities

The million-degree temperature of the solar corona might be due to the combined effect of barely distinguishable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the high density of nanoflares, implied by this hypothesis, means that conclusive verification is beyond present observational capabilities. Nevertheless, it might be possible to investigate the plausibility of nanoflare heating by constructing a magnetohydrodynamic (MHD) model; one that can derive the energy of nanoflares, based on the assumption that the ideal kink instability of a twisted coronal loop triggers a relaxation to a minimum energy state. The energy release depends on the current profile at the time when the ideal kink instability threshold is crossed. Subsequent to instability onset, fast magnetic reconnection ensues in the non-linear phase. As the flare erupts and declines, the field transitions to a lower energy level, which can be modelled as a helicity-conserving relaxation to a linear force-free state. The aim of this thesis is to determine the implications of such a scheme with respect to coronal heating.Initially, the results of a linear stability analysis for loops that have net current arepresented. There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Photospheric driving is simulated as an entirely random process. Hence, an energy distribution of the nanoflares produced is collated. These results are discussed and unrealistic features of the model are highlighted. Subsequently, confirmation of the plasma relaxation process is sought from a numerical analysis.A sample of marginally unstable and current-neutralised coronal loops are sim-ulated within a non-linear three-dimensional MHD code. Loops that carry zero netcurrent are preferred since the photospheric motions that twist the loop and therebycreate azimuthal field are spatially localised; outside the loop boundary the field ispurely axial. The results of these simulations show the dynamics of the relaxationprocess. A new localised relaxation model is developed which fits the simulation data.The revised relaxation model is combined with a linear stability analysis such that nanoflare energy distributions can be produced from ensembles of loops driven by random photospheric twisting motions. Different loop aspect lengths are considered, as well as the spatial correlation of the twisting motions and the level of radial expansion that may accompany loop relaxation. The range of active-region heat fluxes extracted from all the different scenarios is 0.09–1 × 10^7 erg cm^−2 s^−1 . When the relaxation radius is increased, the flux approaches 10^7 erg cm^−2 s^−1 , regardless of the aspect ratio and of the randomness of the path to instability — this is sufficient for coronal heating. The distribution of energies has a Gaussian form when the twisting motions are correlated across the loop radius. Uncorrelated motions yield power-law distributions with gradients of approximately -2.