On the Quasi-Three Dimensional Configuration of Magnetic Clouds.

We develop an optimization approach to model the magnetic field configuration of magnetic clouds, based on a linear force-free formulation in three dimensions. Such a solution, dubbed the Freidberg solution, is kin to the axisymmetric Lundquist solution, but with more general "helical symmetry." The merit of our approach is demonstrated via its application to two case studies of in situ measured magnetic clouds. Both yield results of reduced  ≈ 1. Case 1 shows a winding flux rope configuration with one major polarity. Case 2 exhibits a double-helix configuration with two flux bundles winding around each other and rooted on regions of mixed polarities. This study demonstrates the three-dimensional complexity of the magnetic cloud structures.