Comparison of methods for modelling coronal magnetic fields

E E Goldstraw, A W Hood, Philippa Browning, PJ Cargill

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    Abstract

    Aims. Four dierent approximate approaches used to model the stressing of coronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent agnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements.
    Methods. We consider a simple model problem, comparing the full non-linear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these, magneto-frictional relaxation and a quasi-1D Grad– Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time dependent.
    Results. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements, but has significant errors when the plasma 0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD
    equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes a significant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low 0 plasmas if the viscosity is too high.
    Original languageEnglish
    JournalAstronomy and Astrophysics
    Early online date26 Feb 2018
    DOIs
    Publication statusPublished - Feb 2018

    Keywords

    • Sun: corona
    • Sun: magnetic fields
    • Magnetohydrodynamics (MHD)

    Research Beacons, Institutes and Platforms

    • Manchester Institute for Collaborative Research on Ageing

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