# Interplanetary Magnetic Field Bx Effect on Field-Aligned Currents in Different Local Times
## 2 Materials and Methods  
The Swarm satellite constellation was launched by the European Space Agency (ESA, Paris, France) on 22 November 2013. It consists of three nearly identical spacecraft: Swarm A, Swarm B, and Swarm C. The primary goal of this mission is to conduct an in-depth study of the Earth's geomagnetic environment, which includes the main geomagnetic field, the crustal magnetic field, and the currents in the ionosphere and magnetosphere. Swarm A and Swarm C orbit together at approximately 450 km above the Earth's surface, maintaininga longitudinal separation of about 1.4\({}^{\circ}\), while Swarm B operates independently at a higher altitude of around 510 km. The three satellites share a nearly identical orbital inclination of 87.4\({}^{\circ}\). By utilizing polar orbits, the Swarm satellites provide comprehensive coverage of the auroral regions, enabling them to collect global data on FACs every 133 days. This study utilized vector magnetic field data from the Swarm A and C satellites to invert FACs. Based on the geometric relationship between the two Swarm satellites, FACs can be derived using [PERSON]'s integral law, defined as \(\mathbf{j}_{\parallel}=\frac{1}{\mu_{0}\alpha\sin(i)}\oint Bdl\), where \(\mu_{0}\) is the vacuum permeability, \(i\) is the magnetic field inclination, and \(B\) is the horizontal perturbation magnetic field generated by the FACs [18]. To compute the perturbation magnetic field \(B\), the CHAOS-6 model (developed by DTU Space, Kongens Lyngby, Denmark) was utilized to remove the internal geomagnetic field. The integral is performed along the closed quadrilateral, which is constructed from four consecutive positions of the two satellites and includes the orbit segments of Swarm A and C, as well as the connecting lines between them (see Figure 1 of [PERSON] et al., 2013 [19]). Here, \(dl\) represents a line element along the integration path, while \(A\) denotes the area of the closed quadrilateral formed by the four observation points. Considering the radial distance between the Swarm A and C satellites, a 20 s low-pass filter was applied to the FACs, effectively suppressing Alfven waves and other small-scale current structures. This filtering process allowed for extracting large-scale FACs (spatial scale > 150 km). In the following analysis, FACs emanating from the ionosphere were considered positive, while those moving inward toward the ionosphere were considered negative. FACs with absolute values below 50 A/m\({}^{2}\) were excluded from the analysis. The Polar Electrojet (PEJ) refers to intense horizontal currents flowing in the ionospheric E-layer (-110 km altitude) within the auroral zones, oriented perpendicular to both the electric and magnetic fields. In the dusk sector, the PEJ flows eastward along the auroral belt, while in the dawn sector, it flows westward. These currents are driven by the convection electric field and are closely linked to FACs and auroral activity. In this study, PEJ intensity is derived from Swarm scalar magnetic field data. The PEJ is modeled as a series of infinite line currents spaced 1\({}^{\circ}\) apart in the ionospheric E-layer (110 km). The observed total field residuals are then inverted using an iterative least-squares fitting approach to determine the strength of each line current [20]. In this study, we used the polar electrojet (PEJ) to organize FACs. Swarm A scalar magnetic field data were utilized to derive the PEJ, conceptualized as an ensemble of linear currents extending infinitely within the ionospheric E-layer, spaced 1\({}^{\circ}\) apart. Using the least-squares fitting method, the residuals of the measured total magnetic field were processed to determine the intensity of each individual linear current. The calculation formula was defined as follows: I = (G\({}^{\mathrm{T}}\)AG)\({}^{-1}\) GAF. In this formula, \(A\) is a weighting matrix used to prevent oscillatory results caused by adjacent line currents, while \(G\) is a matrix composed of known parameters such as satellite positions and the magnetic field model.