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 groundwater quality through livestock excreta survey based on “Act of the management and use of livestock excreta” was investigated by selecting sampling sites within 1 km of the farmland without considering hydrogeological units. However, these sites can be affected by various pollution sources such as chemical fertilizers and livestock excretions. Additionally, the effects of pollution sources on groundwater quality in the sites cannot be clearly distinguished from naturally occurring backgrounds. In this study, a method was developed to select the sampling sites for groundwater quality through livestock excreta survey in order to understand the effects of pollution sources especially livestock excreta. First, the concentrations of nitrate within the radius of 200 m, 300 m, 500 m and 750 m, respectively, from the farms regarded as pollution sources in hydrogeological units were compared in 2016-2017. All the nitrate concentrations at 200 - 500 m from the farms exceeded a background concentration, 13.3 mg/L. Those at 750 m and the background concentrations measured by the Ministry of Environment were comparable. Therefore, the appropriate radius was suggested as 500 m for livestock excretions survey. In this study, the areas within 500 m from the farms could be considered under the influence of livestock excretions, while those beyond 500 from the pollution sources as background in hydrogeological units. The developed method was validated by applying it to the sites selected based on both administrative divisions and watersheds for livestock excretion survey. The average densities for the developed method were 0.82 and 0.39 points/km2, respectively, which were considered as appropriate levels according to those of the European Environmental Agency.