Solar coronal heating is a long standing problem in astrophysics. One possible explanation is that discrete heating events known as nanoflares heat the solar corona to millions of degrees. However, due to their size, nanoflares are difficult to detect, hence theoretical calculations are required to determine the viability of coronal heating by nanoflares. Relaxation theory ( Taylor , Taylor ) provides a formalism wherein the minimum energy principle (Woltjer ) can be used to calculate energy release from nanoflares. Understanding relaxation theory requires knowledge of magnetohydrodynamics (MHD), includ- ing a quantity known as magnetic helicity. Cylindrical relaxation models have been used to calculate energy release from discrete heating events or nanoflares. Building upon work pre- viously done on cylindrical relaxation models in Browning  (two layers) and Bareford et al.  (three layers), a multi-layer cylindrical model is constructed, valid for an arbitrary number of layers. Cylindrical models allow for a simplified geometry which results in analytic solutions. The model is constructed as embedded concentric cylinders each with a magnetic field which is continuous across the layer boundary. The code is tested and then used to calculate quantities such as helicity transfer and energy. These values are used to verify a process known as hyperdiffusion (Van Ballegooijen and Cran- mer , Bhattacharjee and Hameiri , Boozer ), which offers insight into the process of relaxation. Results from the multi-layer model lend some support to hyperdiffusion being responsible for relaxation in cylindrical flux tubes. More research is needed however to determine if this is the case in the corona and what observable signatures will be present as a result. The model also provides a useful tool for calculating analytical models of force-free magnetic fields, which may be used for a variety of purposes.
|Date of Award
|31 Dec 2019
- The University of Manchester
|Philippa Browning (Supervisor) & Eamonn Kerins (Supervisor)