A method is described to model the magnetic field in the vicinity of
constellations of multiple satellites using field and plasma current
measurements. This quadratic model has the properties that the divergence is
zero everywhere and matches the measured values of the magnetic field and its
curl (current) at each spacecraft, and thus extends the linear curlometer
method to second order. It is able to predict the topology of the field lines
near magnetic structures, such as near reconnecting regions or flux ropes, and
allows a tracking of the motion of these structures relative to the spacecraft
constellation. Comparisons to PIC simulations estimate the model accuracy.
Reconstruction of two electron diffusion regions show the expected field line
structure. The model can be applied to other small-scale phenomena (bow shock,
waves of commensurate wavelength), and can be modified to reconstruct also the
electric field, allowing tracing of particle trajectories.