Abstract
A new method for computing potential magnetic field configurations in the solar atmosphere is described. A discrete approximation to Laplace's equation is solved in the domain R ⊙ ≤ r ≤R 1, 0 ≤ θ ≤ π, 0 ≤ φ ≤ 2π (R 1being an arbitrary radial distance from the solar center). The method utilizes the measured line-of-sight magnetic fields directly as the boundary condition at the solar surface and constrains the field to become radial at the outer boundary, R 1. First the differential equation and boundary conditions are reduced to a set of two-dimensional equations in r, θ by Fourier transforming out the periodic φ dependence. Next each transformed boundary condition is converted to a Dirichlet surface condition. Then each two-dimensional equation with standard Dirichlet-Dirichlet boundary conditions is solved for the Fourier coefficient it determines. Finally, the solution of the original three dimensional equation is obtained through inverse Fourier transformation. The primary numerical tools in this technique are the use of a finite fast Fourier transform technique and also a generalized cyclic reduction algorithm developed at NCAR. Any extraneous monopole component present in the data can be removed if so desired.
The code was developed for the HAO solar-interplanetary modeling effort in response to the following specific requirements:
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(1)
High resolution.
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(2)
Speed in computation.
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(3)
Sufficiently accurate solutions of Laplace's equation at all heights.
The spatial resolution of the present code is such that measured surface line-of-sight magnetic fields to a resolution of 2.8° in both latitude and longitude can be adequately treated.
Comparisons with the Altschuler-Newkirk code shows that the two methods are more-or-less equivalent for computing large-scale fields at ≈2R ⊙but that the fixed mesh method is capable of much greater accuracy close to the Sun.
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The National Center for Atmospheric Research is sponsored by the National Science Foundation.
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Adams, J., Pneuman, G.W. A new technique for the determination of coronal magnetic fields: A fixed mesh solution to Laplace's equation using line-of-sight boundary conditions. Sol Phys 46, 185–203 (1976). https://doi.org/10.1007/BF00157566
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DOI: https://doi.org/10.1007/BF00157566