Solar force-free magnetic fields on and above the photosphere

If the problem of a magnetic field being force-free with = constant ( 0) is solved by some previously published methods, then the field obtained in the whole exterior of the Sun cannot have a finite energy content and the solution cannot be determined uniquely from only one magnetic field component given at the photosphere. A magnetic field in the volume between two parallel planes has been investigated by us (Chen and Wang, 1986).Based on observational data we present in this paper a suitable physical model for a half-space and adopted an integral transform established by us (Chen, 1980, 1983) to solve this problem. We then obtain a unique analytical solution of the problem from only one magnetic field component (longitudinal field observed) given at the photosphere. Not only the uniqueness of the solution has been proved but also the finiteness of magnetic energy content in the half-space considered has been verified. We have demonstrated that there is no singular point in the solution. It enables us to describe analytically the configurations of magnetic fields on and above the photosphere.