# Polar Cap Patches Scaling Properties: Insights from Swarm Data
## 3 Results  
After estimating the first- and second-order scaling exponents from Swarm A \(N_{\text{e}}\) time series for the entire period under investigation, we divided values of \(\gamma(1)\), \(\gamma(2)\), intermittency and RODI into two subsets characterized by: (1) the presence of PCPs; (2) the absence of PCPs. Actually, when PCP flag values are equal to 4 or to 1, the first subset is obtained, while when they are equal to 0, the second subset is obtained. A further selection criterion was applied to these subsets based on the AE index to distinguish between quiet and disturbed geomagnetic conditions. The entire analysis was performed separately for each hemisphere. The idea of introducing RODI into our analysis arises from recent studies [19; 46] that have highlighted how plasma bubbles, which are ionospheric irregularities occurring in equatorial regions, have a turbulent nature and are characterized by very high values of RODI. In that case, the analysis of the joint distribution between the scaling exponents inside the plasma bubbles and RODI has shown how the properties of this class of irregularities are completely different from the surrounding environment. Similarly, we examined the joint distribution between the scaling exponents and intermittency, and RODI, to investigate whether the properties of PCPs differ from the surrounding ionospheric environment. This investigation was carried out for both quiet and disturbed geomagnetic conditions in both polar regions. By doing so, we aimed to gain further insights into the distinctive characteristics and behavior of PCPs. Joint probability distributions for the Northern hemisphere are shown in Figure 6. In detail, the upper plots show the results for quiet conditions for \(\gamma(1)\) (left side), \(\gamma(2)\) (center), and intermittency (right side), while the lower plots refer to disturbed conditions. Dotted lines represent joint probabilities distributions obtained for the absence of PCPs, while solid lines represent distributions obtained when PCPs are present. Figure 6 shows that the two distributions are shifted, on both axes, one with respect to the other. The shift of the isolines corresponding to the presence of PCPs on the vertical axis, i.e., towards higher values of log(RODI) can be explained in terms of the intrinsic meaning of RODI. Indeed, RODI is a measure of the presence of ionosphere irregularities, and PCPs are one among them. Therefore RODI values related to the presence of PCP are expected to be higher than those related to the absence of PCPs. The shift of the isolines corresponding to the presence of PCPs on the horizontal axes, for both \(\gamma(1)\), \(\gamma(2)\), and intermittency in the direction of higher values should instead be interpreted in terms of the different dynamical properties of PCPs with respect to the surrounding plasma. It is interesting to note that these distributions appear to be practically independent of the level of geomagnetic activity for both scaling exponents and intermittency. Figure 6: Northern hemisphere: joint probability distributions between RODI and \(\gamma(1)\) (**left side**), \(\gamma(2)\) (**center**), and intermittency (**right side**) separately for data with (solid contours) and without (dashed contours) PCPs, for two levels of geomagnetic activity, i.e., quiet (**top**) and disturbed (**bottom**). The situation changes if we represent the values of the two scaling exponents as a function of QD-latitude and MLT separately for the two levels of geomagnetic activity as shown by Figure 7. Bins in Figure 7 represent, for the Northern hemisphere and both levels of geomagnetic activity, the average values of \(\gamma(1)\) (left side), \(\gamma(2)\) (center), and intermittency (right side) when the presence of PCP is recorded. Focusing on \(\gamma(1)\), we see that under quiet geomagnetic conditions, only PCPs in the area corresponding to MLTs in the range 13:00-17:00 and to QD-latitudes between 75\({}^{\circ}\) and 80\({}^{\circ}\), exhibit a weak persistent behavior with \(\gamma(1)>0.5\).