Fitting a toroidal force‐free field to multispacecraft observations of a magnetic cloud

Abstract

A torus‐type flux rope model with an arbitrary aspect ratio was applied to an interplanetary magnetic cloud observed by ACE and Nozomi on 16–18 April 1999, when Nozomi was 0.2 AU downstream of ACE in the solar wind within 3° of heliocentric longitude. The large and small radii of the torus, the direction of the symmetric axis, and the crossing points of the spacecraft were determined so that they would minimize the sum of the square of the difference between the model field and the hourly averages of the observed field. Self‐similar expansion of the flux rope was assumed in proportion with the heliocentric distance. The best fit model had large and small radii of 0.16 and 0.09 AU, respectively. Both spacecraft passed through the northern part of the torus. Difference in the magnetic field observed by the two spacecraft was explained by the difference in their paths through the magnetic cloud. The model fit was consistent with the direction of the vector normal to the preceding planar magnetic structures. The chirality of the flux rope was positive (left handed), suggesting that the solar source was on the Northern Hemisphere. Assuming a probable association with the filament disappearance observed on 13 April 1999 at N16 E00, it is inferred that the filament had traveled in interplanetary space across the ecliptic plane. It was also found that nearly the same fitting result was obtained using a single‐spacecraft observation in the case of a torus‐shaped magnetic cloud with a small aspect ratio.