Mathematical Modelling of Solar Plasma Jets

Solar jets have been studied for over 100 years and may hold the key to some of the most long-standing questions in solar physics. Analytical models are well established as a useful tool for examining solar phenomena, many of which exhibit magnetohydrodynamic wave behaviour. In this thesis we investigate a potential mechanism by which solar jets are formed and explore the connection between features such as spicules and magnetic bright points in the lower solar atmosphere. A model is created, utilising a perturbation method and adapting the system of MHD equations in the context of a magnetic flux tube in order to explore the generation of mass flux due to torsional Alfv´en waves. Using the zerobeta approximation to model these intensely magnetic regions, we derive that the presence of such waves can result in field-aligned plasma motion formed non-linearly as a result of the Lorentz force. Comparisons are made with observed properties of spicules. In the next iteration we include a density discontinuity, representing the solar transition region. The initial upward-propagating Alfv´en pulse is reflected from this discontinuity, resulting in a reversal of the flux which may be identified with the behaviour of spicules. The relative mass of plasma lifted by the transmitted and reflected waves is estimated as a ratio, and comparison is made between the relative total mass of spicules and the solar wind. Finally, the model is augmented with a finite transitional layer in which the atmospheric density decreases exponentially. The Alfv´en pulse interacts with and is partially reflected by this layer. We find that the wave transmitted into the upper solar atmosphere results in greater mass flux when compared with the previous model. We examine how varying the parameters of this transitional layer affects the ratio of the flux above and below the layer.