There are also methods of extrapolation available to reconstruct non-force-free fields although these may require additional data ( Wiegelmann 2004). Various methods of extrapolation are used to reconstruct potential fields, linear force-free fields ( Gary 1989), and non-linear force-free fields ( Wiegelmann 2008). These cases correspond to potential, linear, and non-linear force-free fields, respectively ( Aschwanden 2004). ( 1) where α can be either zero, a constant, or a variable that is constant along field lines. Another way of expressing this condition is given below in Eq. This defines a force-free field ( Wiegelmann & Sakurai 2012). For magnetostatic equilibrium the magnetic Lorentz force must then be zero J × B = 0. Most commonly non-magnetic forces such as pressure gradients and gravity are neglected this is well justified in the solar corona because of the low plasma beta ( Wiegelmann 2008) and when considering scales smaller than the hydrostatic scale height ( Peter et al. The commonly used methods rely on various assumptions ( Neukirch 2005). There are many methods for extrapolating the structure of the magnetic field from surface measurements. Extrapolation of the photospheric magnetic field is currently the primary tool for modelling the coronal magnetic fields ( Tadesse et al. Fortunately the photospheric magnetic field can be used to reconstruct the coronal field by means of extrapolation. It is however much more difficult to measure directly the magnetic field in the solar corona ( Ruan et al. the splitting of spectral lines in the presence of a magnetic field ( Beckers 1971). Maps of the line-of-sight and vector magnetograms from the photosphere can be measured by means of spectropolarimetric methods such as the Zeeman effect, i.e. For more detailed magnetic structures we need information from solar observations. In the case of a static equilibrium both the velocity vector v and its time derivative ∂ v/∂ t must equal zero.Īnalytic expressions exist for a number of structures that describe magnetostatic equilibria in both 2D and 3D for example ( Smith et al. For many problems, primarily those concerning MHD waves, it is useful to have a static equilibrium on which to impose perturbations to the velocity and magnetic fields ( Goossens 2003). Computational 3D magnetohydrodynamic (MHD) models are often used to address the coronal heating problem ( Klimchuk 2015).Ĭomputational MHD models require an initial magnetic field to be specified. Researchers agree that energy is transported to the corona by non-thermal transport of energy through the Sun’s magnetic field ( Arregui 2015), although the dominant mechanism for coronal heating is under debate ( Parnell & De Moortel 2012). The coronal heating problem, the question of why the Sun’s corona is much hotter (∼1 MK) than photosphere (∼6000 K), is an ongoing problem in solar physics. Key words: Sun: magnetic fields / methods: numerical / magnetohydrodynamics (MHD) #Physics calculator codeThe code and supporting description are provided in the appendices. The program can be parallelised to run quickly over multiple computing cores. The program is a FORTRAN 90 code that can be used to generate potential magnetic field inputs for Lare3d and other MHD solvers that use a staggered grid for magnetic field components. It is also shown that extending the region over which normal photospheric field is specified can improve the accuracy of the potential field produced. A new finite differencing formula was derived which accounts for grid staggering it is shown that this formula gives a numerical approximation that is closest to the real potential field. The code first calculates a magnetic potential using the Green’s function method and then uses a finite differencing scheme to calculate the magnetic field from the potential. Jones Building, 327 Mile End Road, London E1 4NS, UKĮ-mail: program has been designed to generate accurately a potential magnetic field on a staggered grid by extrapolating the magnetic field normal to the photospheric surface. School of Physics and Astronomy, Queen Mary University of London, G.O. Astronomical objects: linking to databases.Including author names using non-Roman alphabets.Suggested resources for more tips on language editing in the sciences Punctuation and style concerns regarding equations, figures, tables, and footnotes
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