On the computation of constant α force-free magnetic field

We present solutions of the boundary value problem of constant α, force-free magnetic field in plane geometry, in terms of Fourier transforms. These solutions are easily adaptable to computations far from the center of the solar disk. We find that the large scale (larger than 2π vertical stroke α vertical stroke) components of the solutions involve a quasi-periodic variation of the field and the current with height, contain infinite energy in the upper half-plane and that their complete specification requires observations of a transverse component of the field at the boundary; this behaviour makes them unphysical. We also discuss the numerical computation of the field with fast Fourier transforms, which make the computation about 100 times faster compared to computations using Green's functions; in particular we discuss the effects of aliasing. (orig.)