A force-free field (FFF) is determined solely by the normal components of magnetic field and current density on the entire boundary of the domain. Methods employing three components of magnetic field suffer from overspecification of boundary conditions and/or a nonzero divergence-B problem. A vector potential formulation eliminates the latter issue, but introduces difficulties in imposing the normal component of current density at the boundary. This paper proposes four different boundary treatment methods within the vector potential formulation. We conduct a comparative analysis of the vector potential FFF solvers that we have developed incorporating these methods against other FFF codes in different magnetic field representations. Although the vector potential solvers with the new boundary treatments do not outperform our poloidal-toroidal formulation code, they demonstrate comparable or superior performance compared to the optimization code in SolarSoftWare. The methods developed here are expected to be readily applied not only to force-free field computations but also to time-dependent data-driven simulations.

A method of estimating the lower bound of coronal magnetic field strength in the neighborhood of an ejecting plasmoid is presented. Based on the assumption that the plasma ejecta is within a magnetic island, an analytical expression for the force acting on the ejecta is derived. The method is applied to a limb coronal mass ejection event, and a lower bound of the magnetic field strength just below the CME core is estimated. The method is expected to provide useful information on the strength of reconnecting magnetic field if applied to X-ray plasma ejecta.

Recently, Choe & Cheng (2002) have demonstrated that multiple magnetic flux systems with closed configurations can have more magnetic energy than the corresponding open magnetic fields. In relation to this issue, we have addressed two questions: (1) how much fraction of eruptive solar active regions shows multiple flux system features, and (2) what winding angle could be an eruption threshold. For this investigation, we have taken a sample of 105 front-side halo CMEs, which occurred from 1996 to 2001, and whose source regions were located near the disk center, for which magnetic polarities in SOHO/MDI magnetograms are clearly discernible. Examining their soft X-ray images taken by Yohkoh SXT in pre-eruption stages, we have classified these events into two groups: multiple flux system events and single flux system events. It is found that 74% (78/105) of the sample events show multiple flux system features. Comparing the field configuration of an active region with a numerical model, we have also found that the winding angle of the eruptive flux system is slightly above 1.5π.