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.

The Sun-Earth Lagrange point L4 is considered as one of the unique places where the solar activity and heliospheric environment can be observed in a continuous and comprehensive manner. The L4 mission affords a clear and wide-angle view of the Sun-Earth line for the study of the Sun-Earth and Sun-Moon connections from he perspective of remote-sensing observations. In-situ measurements of the solar radiation, solar wind, and heliospheric magnetic field are critical components necessary for monitoring and forecasting the radiation environment as it relates to the issue of safe human exploration of the Moon and Mars. A dust detector on the ram side of the spacecraft allows for an unprecedented detection of local dust and its interactions with the heliosphere. The purpose of the present paper is to emphasize the importance of L4 observations as well as to outline a strategy for the planned L4 mission with remote and in-situ payloads onboard a Korean spacecraft. It is expected that the Korean L4 mission can significantly contribute to improving the space weather forecasting capability by enhancing the understanding of heliosphere through comprehensive and coordinated observations of the heliosphere at multi-points with other existing or planned L1 and L5 missions.

We examine the observations of large-scale magnetic fields in the Universe. We begin at the largest scale with clusters of galaxies and work our way down through galaxies and finally to the Milky Way. on which we concentrate in detail. We examine the observations of the Galactic magnetic field, and their interpretation, under the philosophy that the Galactic magnetic field is like that in other spiral galaxies. We use pulsar data. diffuse Galactic synchrotron emission, and starlight polarization data to discuss the Galaxy's global magnetic configuration and the uniform (Bu), random (Br), and total (Bt) components of the field strength. We find disagreement among conclusions derived from the various data sets and argue that the pulsar data are not the best indicator for large-scale Galactic field. Near the Solar circle, we find that the azimuthal average of Bt is 4.2 μG and we adopt Bu ~2.2 and Br ~3.6 μG. Bt is higher in spiral arms, reaching ~5.9 μG. Bt is higher for smaller RGal, reaching ~8.0 μG for RGal = 4.0 kpc. The pattern of field lines is not concentric circles but spirals. The inclination of the magnetic spiral may be smaller than that of the Galaxy's spiral arms if our sample, which refers primarily to the interarm region near the Sun, is representative. However, it is not inconceivable that the local field lines follow the Galaxy's spiral pattern, as is observed in external galaxies.