# Perpendicular Electrical Conductivity in the Topside Ionosphere Derived from Swarm Measurements
## 3 Results
### Climatological Behaviour of Electrical Conductivity Perpendicular to the Geomagnetic Field
These elongated structures appear to trace the crests of the Equatorial Ionisation Anomaly (EIA), which are typical electron density features observed on the day side. The EIA consists of a plasma depletion at the magnetic equator due to the \(\mathbf{E}\times\mathbf{B}\) drift. This drift causes plasma to uplift and diffuse poleward along the geomagnetic field lines [89; 90; 91; 92]. Conversely, the relative minima of \(\sigma_{P}\) and \(\sigma_{H}\) are present in the pre-dawn sector at a \(\sim\)\(\pm\)60\({}^{\circ}\) QD magnetic latitude and in correspondence with the morning overshoot. Notably, \(\sigma_{P}\) and \(\sigma_{H}\) exhibit characteristics similar to electron density, \(n_{e}\), in terms of latitudinal and diurnal variations, as can be easily seen by considering Figure 3 in [93]. This indicates that \(n_{e}\), rather than \(T_{e}\) or \(B\), is the dominant physical quantity in driving the \(\sigma_{P}\) and \(\sigma_{H}\) variation. Figure 2 clearly illustrates that the features of \(\sigma_{P}\) and \(\sigma_{H}\) at low latitudes dominate and are orders of magnitude more intense than those at high latitudes. To detect any structures at high latitudes, it is necessary to zoom in on QD magnetic latitudes \(\geq\)60\({}^{\circ}\). For this purpose, Figure 3 presents the results obtained for \(\sigma_{P}\) in a polar stereographic projection using QD-MLT coordinates. At high QD magnetic latitudes, the relative maxima of \(\sigma_{P}\) are \(\sim\)10\({}^{3}\) s\({}^{-1}\), about two orders of magnitude smaller than the same quantity at low QD magnetic latitudes. Moreover, there is also an evident hemispheric asymmetry: in the Northern Hemisphere (left panel in Figure 3), \(\sigma_{P}\) is enhanced around noon between 70\({}^{\circ}\) and 80\({}^{\circ}\) QD magnetic latitude and from 12:00 MLT to 21:00 MLT from 70\({}^{\circ}\) and 80\({}^{\circ}\) QD magnetic latitude and above. Conversely, in the Southern Hemisphere (right panel in Figure 3), \(\sigma_{P}\) is generally smaller, with enhancements localised in the polar cap regions (across almost all MLTs) and within 60-70\({}^{\circ}\), the QD magnetic latitudinal ranges from 06:00 MLT to 16:00 MLT. It should be noted that latitudes above 80\({}^{\circ}\) have the lowest counts, resulting in significantly increased error margins. Nevertheless, below 80\({}^{\circ}\), the results are very robust. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Minimum** & **Maximum** & **Minimum** & **Maximum** & **Maximum** & **Maximum** \\  & **Value (s\({}^{-1}\))** & **Value (s\({}^{-1}\))** & **Uncertainty** & **(\%)** & **(\%)** & **Uncertainty** \\ \hline \(\sigma_{P}\) & 61 & \(7\times 10^{5}\) & 0.6 & 25.5 & 2.4 \\ \(\sigma_{H}\) & \(10^{-2}\) & \(1.3\times 10^{4}\) & 0.8 & 29.3 & 2.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Climatological values of perpendicular electrical conductivities. Figure 3: Climatological maps in QD-MLT coordinates of Pedersen electrical conductivity, \(\sigma_{P}\), in a polar stereographic projection representation in the Northern (**left panel**) and Southern (**right panel**) Hemispheres. Values within each bin are saturated below \(0.5\times 10^{3}\) s\({}^{-1}\) and above \(1\times 10^{3}\) s\({}^{-1}\). Figure 4 displays the results obtained for \(\sigma_{H}\) in a polar stereographic projection in QD-MLT coordinates. At high QD magnetic latitudes, the relative maxima of \(\sigma_{H}\) are around a few s\({}^{-1}\), approximately three orders of magnitude smaller than at low QD magnetic latitudes. The features of \(\sigma_{H}\) at high QD latitudes mirror those of \(\sigma_{P}\), including the hemispheric asymmetry. In the Northern Hemisphere (left panel in Figure 4), \(\sigma_{H}\) is predominantly enhanced around a 80\({}^{\circ}\) QD latitude and between 14:00 MLT and 18:00 MLT. In the Southern Hemisphere (right panel in Figure 4), \(\sigma_{H}\) is weaker, with faint enhancements localised in the polar cap regions between a 75\({}^{\circ}\) and 80\({}^{\circ}\) QD magnetic latitude.