# Perpendicular Electrical Conductivity in the Topside Ionosphere Derived from Swarm Measurements
## 4 Discussion
The climatological results reported in Figures 1 and 2 agree well with what is known from the literature [105; 114]. For example, parallel Pedersen and Hall conductivities are consistent with the conductivity height profiles in the dayside shown in [PERSON] et al. [115] when fixing the altitude to 450 km, i. e., the Swarm altitude. In the topside ionosphere, the electrical conductivity parallel to the magnetic field is much higher than that perpendicular to the magnetic field, while in the plane perpendicular to the magnetic field, the Pedersen conductivity is higher than the Hall conductivity. Indeed, this behaviour can be explained by the different mechanisms governing the motion of charged particles in the ionosphere. In particular, the parallel conductivity is dominant because charged particles, particularly electrons, can move freely along the magnetic field lines with minimal collisions. As a consequence, this direction offers the least resistance to particle motion, as the magnetic field does not impede movement along its lines. When considering the conductivities perpendicular to the magnetic field, the Pedersen conductivity exceeds the Hall conductivity. The Pedersen conductivity involves particle motion that is influenced by both the electric and magnetic fields, leading to collisions and a moderate level of resistance. However, these collisions are less frequent compared to those in the Hall direction because the Pedersen direction aligns partially with the electric field, allowing for more straightforward movement compared to the purely perpendicular (Hall) direction. The Hall conductivity, which arises due to the Hall effect, is the lowest because charged particles are deflected by the magnetic field, causing them to spiral and experience a higher rate of collisions. These frequent collisions significantly reduce the effective mobility of the particles, resulting in lower conductivity. The dependence of conductivity on seasons and solar activity can be attributed to changes in ionospheric density and composition, which affect collision frequencies. During periods of high solar activity, increased ionisation enhances the number of charged particles, thus influencing the overall conductivity profiles. Furthermore, seasonal changes impact the neutral density and temperature, further modifying the collision rates and conductivities. These characteristics, which delineate the conductivities both parallel and perpendicular to the magnetic field, are readily identifiable in our climatological distributions, as well as in distributions reflecting seasonal and solar activity variations. For instance, we have seen that the equinoctial pattern shown by perpendicular conductivities seems to be strictly connected with the semiannual anomaly characterising the electron density, especially at middle and low latitudes. Concerning the high latitudes, the discussion becomes a little more complicated. The Northern Hemisphere reflects pretty well the semiannual electron density pattern, while the Southern Hemisphere does not. This is a point that deservesfurther in-depth analysis. In any case, our results showed that the assumptions underlying our calculations of conductivities at Swarm altitude are reasonable and provide a scenario that aligns well with the theoretical expectations. As mentioned, this is the first time that statistical maps of Pedersen and Hall conductivities at about 450 km of altitude are shown, with a study of their variation with season and solar activity. This makes it impossible to find studies and models in the literature that calculate these quantities under the same conditions imposed in this work. However, it is possible to show, to some extent, the consistency of our results on the basis of previous works. For example, parallel, Pedersen and Hall conductivities can be retrieved by using the model of the World Data Center (WDC) for Geomagnetism in Kyoto.