Solar coronal loops

In the past few years it has been realised that loop structures are an important feature of the solar corona. Presumably, these structures outline the local magnetic field and in this thesis some theoretical aspects of solar coronal loops are considered. The starting point is to model the static equilibrium, in a 1 - D structure, and determine the temperature and density by solving the energy balance equation. The basic state is determined by two dimensionless parameters, namely the ratio of optically thin radiation to thermal conduction, and the ratio of mechanical heating to radiation, An important result is that when critical values of the parameters are exceeded thermal non-equilibrium- ensues and the loop rapidly cools from coronal temperatures 10. 6K to below10. 5K. A simple 2 - D model extends this work and results provide a possibleexplanation for several loop features. The thermal stability of coronal .loops is investigated by developing two simple methods which apply to a wide class of equilibria. Stability is found to depend on the boundary conditions adopted but not critically on the form of the heating. A loop is shown to be stable if its conductive flux is large enough that it lies on the upper- of two equilibrium branches. Solar coronal loops are observed to be remarkably stable structures. A magneto hydrodynamic stability analysis of a model loop by the energy method suggests that the main reason for stability is the fact that the ends of the loop are anchored in the dense photosphere. Two-ribbon flares follow the eruption of an active region filament, which may lie along a magnetic flux tube. It is suggested that the eruption is caused by the kink instability, which sets in when the amount of magnetic twist in the flux tube exceeds a critical value. Occasionally active region loops may become unstable and give rise to small loop flares, which may also be a result of the kink instability. A more realistic model of an active region filament, that takes account of the overlying magnetic field, shows that instability may occur if either the twist or the height of the filament exceed critical values. Finally, the possibility that a solar flare is triggered by thermal non-equilibrium, instead of by magnetic instability, is investigated. This is demonstrated by solving approximately the energy equation for a loop under a balance between thermal conduction, optically thin radiation and a heating source. It is found that, if one starts with a cool equilibrium at a temperature about 10. 4K and gradually increases theheating or decreases the loop pressure (or decreases the loop length), ultimately critical conditions are reached beyond which no cool equilibrium exists. The plasma rapidly heats up to a new quasi-equilibrium at typically 10. 7 K. Duringsuch a thermal flaring, any magnetic disruption or particle acceleration is of secondary importance.