Twisted flux tubes are important features in the Universe and are involved in the storage and release of magnetic energy. Therefore modeling the physical evolution of twisted flux tubes is a
crucial step towards the understanding of basic physical phenomena in the Universe. In order to create a 3D model of twisted flux tubes, we model basic equations of electromagnetism based on a
mathematical description from prescribed boundary conditions: the twisted flux tube is described as a cylinder on which the magnetic field is helically wrapped. The mathematical method is named magnetic field extrapolation. In this research exercise, two different methods were used: the potential
field and nonlinear force-free field. Both methods require prior knowledge of an analytical solution for the magnetic field that will be used as boundary conditions. Two scenarios were created: (i) a
twisted flux tube with a constant radius and an increasing twist, and (ii) a twisted flux tube with a
constant twist and an increasing radius. Within both scenarios, we study how the magnetic energy evolves and how each extrapolation method affects this evolution. Both increasing the twist and increasing the radius produced an exponential increase in magnetic energy: varying the twist producing an increase of 9.5% and varying the radius producing an increase of 7.3%. While these results show that these numerical methods can be used to model twisted flux tubes, several key problems such as the limitations on the boundary conditions, especially the amount of twist which can be injected, must be addressed before further use of these modelling techniques.
Key words: Sun, Corona, Magnetic Fields, Flux Tubes, Numerical Methods, Simulation.
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