The Green's function method for a special class of magnetohydrostatic equilibria

We present the Green's function method for a special class of self-consistent three-dimensional solutions of the MHS equations. This allows the construction of MHS solutions with arbitrary Dirichlet or von Neumann boundary conditions. These solutions can be used to extrapolate coronal magnetic fields from known photospheric field data and provide a self-consistent description of magnetic field, plasma pressure, plasma density and plasma temperature. The method therefore allows a much more complete reconstruction of solar coronal structures than is possible by potential or linear force-free field extrapolation. We will demonstrate this property by showing simple examples.