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This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are specified by a distribution on the sphere of projection of the magnetic field vector unto a given direction. It is shown that the solution of this problem exists in the form of a spherical harmonic expansion, and uniqueness of this solution is proved. A conceptual sketch of numerical determination of the harmonic series coefficients is given. The field of application of the method is analyzed having regard to the peculiarities of actual data. Finally, we present differences in results derived from extrapolating the magnetic field from a synoptic map and a full-disk magnetogram.
We have used very high-cadence (sub-minute) observations of the solar mean magnetic field (SMMF) from the Birmingham Solar Oscillations Network (BiSON) to investigate the morphology of the SMMF. The observations span a period from 1992--2012, and the
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Amperes law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this
Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. The field calculations can be improved by preprocessi
The weak-field approximation implying linear relationship between Stokes $V/I$ and longitudinal magnetic field, $B_{Vert}$, often suffers from saturation observed in strong magnetic field regions such as sunspot umbra. In this work, we intend to impr
We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation due to propagation of the polarised emis