Three dimensional MHD simulations of the dynamics and energetics of coronal flux tubes

In this thesis we present the results of three-dimensional MHD simulations of the evolution of magnetic flux tubes within the solar atmosphere. We consider the dynamics and energetics of coronal loops that are perturbed from an equilibrium state by wave motions or driven continuously by an imposed velocity field. In each case, we investigate the dissipation of magnetic and kinetic energy and evaluate the implications for the heating of coronal plasma. We present models of transversely oscillating flux tubes which experience rapid damping as kink mode energy is transferred into azimuthal Alfvén modes. This mode conversion is typically associated with a density enhancement within the flux tube, however, we demonstrate that it can also proceed with an increased internal magnetic field strength. In either regime, the azimuthal wave modes are subject to dissipation through phase mixing and may promote the development of the magnetic KelvinHelmholtz instability. This is associated with the generation of further small scales in the magnetic and velocity fields and, in a non-ideal regime, will enhance the rate of wave dissipation. We show that the growth rate of the instability is sensitive to the implemented transport coefficients and the presence of helical magnetic field. Additionally, we consider the effects of thermal conduction and optically thin radiation on the evolution of a flux tube tectonics model. We present the results of simulations in which two magnetic flux tubes are twisted around each other by the action of rotational drivers imposed at the loop foot points. Large currents develop at the interface of the flux tubes and magnetic reconnection is triggered as the braiding progresses. The inclusion of conduction and optically thin radiation reduces the high temperatures and gas pressures observed in the centre of the numerical domain. As a result, these processes modify the reconnection outflows, distribution of plasma and the evolution of the magnetic field. Candidate’s declaration I, Thomas Alexander Howson, do hereby certify that this thesis, submitted for the degree of PhD, which is approximately 50,000 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for any degree. I was admitted as a research student at the University of St Andrews in August 2015. I received funding from an organisation or institution and have acknowledged the funders in the full text of my thesis. Date: . Signature of candidate: . Supervisor’s declaration I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of PhD in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. Date: . Signature of supervisor: . Permission for publication In submitting this thesis to the University of St Andrews we understand that we are giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. We also understand, unless exempt by an award of an embargo as requested below, that the title and the abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that this thesis will be electronically accessible for personal or research use and that the library has the right to migrate this thesis into new electronic forms as required to ensure continued access to the thesis. I, Thomas Alexander Howson, confirm that my thesis does not contain any third-party material that requires copyright clearance. The following is an agreed request by candidate and supervisor regarding the publication of this thesis: Printed copy No embargo on print copy. Electric copy No embargo on electronic copy. Date: . Signature of candidate: . Date: . Signature of supervisor: . Underpinning Research Data or Digital Outputs Candidate’s declaration I, Thomas Alexander Howson, hereby certify that no requirements to deposit original research data or digital outputs apply to this thesis and that, where appropriate, secondary data used have been referenced in the full text of my thesis. Date: . Signature of candidate: .