A Dirichlet problem with applications to solar prominences

Abstract

Abstract. Convective motions in the photosphere and sub-photosphere may be responsible for generating the magnetic fields that support long-lived quiescent solar prominences. The connection is explored here by solving a Dirichlet problem on a semi-infinite strip where the base of the strip is the photosphere, and the strip extends into a current free corona. Even though the convection is simulated only by a one-dimensional potential prescribed at the photosphere it is found that both Kippenhahn-Schlüter and Kuperus-Raadu type fields are possible.

Solar prominence magnetic configurations derived numerically from convection

“…The field lines in the models by KS and KR are line tied to the photosphere (see McKaig 2001). In a previous paper (McKaig 2001) photospheric motions were simulated by a one-dimensional boundary condition and KS/KR type fields were obtained in the corona.…”

Numerical solution of the Helmholtz equation in an infinite strip by Wiener‐Hopf factorization

“…Other interesting applications are the analysis of efficient ducts for acoustic noise suppression (see [3] for an interesting introduction to the problem), as well as the study of unbounded waveguides in electromagnetics or other fields of interest [4]. In [5] the Laplace equation on the semi-infinite strip is applied to the study of solar prominences. Finally, the Helmholtz equation on a strip can fruitfully describe fluid/solid problems (see [6]) frequently encountered in applications.…”