  We derive an analytical approximation of nonlinear force-free magnetic field
solutions (NLFFF) that can efficiently be used for fast forward-fitting to
solar magnetic data, constrained either by observed line-of-sight magnetograms
and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph
data. The derived NLFFF solutions provide the magnetic field components
$B_x({\bf x})$, $B_y({\bf x})$, $B_z({\bf x})$, the force-free parameter
$\alpha({\bf x})$, the electric current density ${\bf j}({\bf x})$, and are
accurate to second-order (of the nonlinear force-free $\alpha$-parameter). The
explicit expressions of a force-free field can easily be applied to modeling or
forward-fitting of many coronal phenomena.
