Optimal Fitting of the Freidberg Solution to In Situ Spacecraft Measurements of Magnetic Clouds
Abstract
We report, in detail, an optimization approach for fitting a three-dimensional (3D) magnetic cloud (MC) model to in situ spacecraft measurements. The model, dubbed the Freidberg solution, encompasses 3D spatial variations in a generally cylindrical geometry, as derived from a linear force-free formulation. The approach involves a least-squares minimization implementation with uncertainty estimates from magnetic field measurements. We present one case study of the MC event on 22 May 2007 to illustrate the method and demonstrate the satisfying result of the minimum reduced 2 1, obtained from the STEREO B (STB) spacecraft measurements. In addition, since the ACE spacecraft at Earth crossed the STB solution domain with an appropriate separation distance, the result from the optimally fitted Freidberg solution along the ACE spacecraft path is compared with the actual measurements of magnetic field components. A correlation coefficient of 0.89 is obtained between the two sets of data.