The boundary value problem of the solar force-free magnetic field with constant α and its analytical solution
In this paper we present a physical model which uses boundary conditions which seem to correspond more appropriately to actual situations. A boundary value problem of solar force-free magnetic field with constant α has been specified to represent the discretely concentrated characteristics of the longitudinal magnetic field on the photosphere. A unique analytical solution for the problem is obtained by a more strict method in mathematical physics. The most distinctive feature of our method is to make the solution be the superposition of the fields of single sources which are described by the physical parameters of corresponding sunspots on the photosphere, such as their position, strength, decay rates and the extent of the same polarity. The solution enables us to make an analytical description of the configuration of the magnetic field in the chromosphere and corona, and to investigate more conveniently its development as the foot points on the photosphere evolve.