# Polar Cap Patches Scaling Properties: Insights from Swarm Data
## 4 Discussion and Conclusions  
The high-latitude ionosphere is characterized by the presence of multi-scale structures that becomes clear when studying the dynamic processes that occur on mesoscales, which means on spatial scales ranging from tens to hundreds of kilometers. These structures are created by different types of plasma instabilities and other processes that are essentially responsible for variations in plasma density and electric fields. Transient and localized structures can often be observed in regions such as the cusp, polar cap, and auroral oval, whose properties, propagation, and coupling processes are not yet fully understood, although they represent a critical element in the development of realistic numerical models. The results just presented fall within this scope and aim to shed new light on the properties of a particular type of plasma irregularity, the polar cap patch, which can be analyzed using electron density data measured by a low-altitude polar-orbiting satellite belonging to the ESA Swarm constellation. The analysis of the scale properties of electron density fluctuations shows that there is some difference between what is found within these irregularities and the surrounding environment. Indeed, electron density fluctuations corresponding to PCPs are associated with higher average values of RODI and have a less antipersistent character than those not corresponding to PCPs. This difference with the surrounding environment can be observed during both quiet and disturbed conditions. Concerning the second-order scaling exponent, which indirectly provides information on the values of the slope of the fluctuations' energy spectrum, the PCPs are characterized by higher values compared to the external environment. Inside the PCPs, the second-order scaling exponent is between 0.8 and 0.9, which means a slope \(\beta\) of the energy spectrum of between 1.8 and 1.9. The electron density fluctuations outside the PCPs have a second-order scaling exponent of about 0.7 and therefore an energy spectrum slope value of \(\beta\simeq 1.7\). Thus, we can infer a distinct electron density fluctuation dynamics from the difference in the second-order scaling exponent values inside and outside the irregular structures analyzed. Additionally, the power spectral indices obtained indirectly can aid in identifying instabilities responsible for low-frequency turbulence [47]. These findings are consistent with previous research that utilized data from other satellites and demonstrated that the power spectra of increased plasma density fluctuations typically follow a power law with a spectral index \(\beta\simeq 1.8\)[48; 49; 50] for scales ranging from several kilometers to tens of meters. These spectra were linked to the gradient drift instability (e.g., [51]), which arises from the differential drifts of ions and electrons on a plasma density gradient, and to the Kelvin-Helmholtz instability, which occurs in the presence of flow shears (e.g., [5; 49]). In conclusion, the statistical analysis of PCPs conducted on approximately 3.5 years of data clearly shows that these structures, with respect to the surrounding environment, are characterized by electron density fluctuations with higher values of \(\gamma(1)\) and a steeper energy spectrum that can be associated with the occurrence of gradient drift instability and Kelvin-Helmholtz instability, and higher RODI values, meaning they are characterized by larger density fluctuations. These characteristics are independent of the hemisphere in which the PCPs develop. Beyond what resulting considering the whole set of PCPs that allowed us to obtain their average characterization and, at the same time, provided us with a tool to distinguish them from the surrounding environment, the results reported in Figures 7 and 9 are certainly very interesting. These results show how the scaling properties of PCPs tend to vary according to their spatial location within the analyzed region, which corresponds to magnetic latitudes greater than \(|75^{\circ}|\).