# Unveiling the Core Patterns of High-Latitude Electron Density Distribution at Swarm Altitude
## 1 Introduction  
The ionosphere, a layer of Earth's atmosphere, extends from about 60 km above the surface to a height of about 1000 km. It is made up of charged particles such as electrons and ions that form as a result of the ionization of neutral particles caused by solar radiation and energetic particles from the magnetosphere [1]. Aided by technological advances in observation techniques and numerical modeling, researchers have extensively studied the ionosphere over the last century, leading to continuous advances in our understanding of its dynamics. Solar flares, geomagnetic storms, atmospheric tides, and atmospheric waves all influence the behaviour of the ionosphere, resulting in distinct characteristics under varying solar and geomagnetic conditions. These dynamics have immediate consequences for radio communication and satellite navigation systems [2, 3, 4]. Despite significant progress in recent decades, certain aspects of the ionosphere, particularly during geomagnetic storms, remain unresolved due to the complex interplay within the interconnected magnetosphere-ionosphere-thermosphere system. Over the course of the last decade, the Swarm satellite constellation [5] launched by the European Space Agency (ESA) has consistently surveyed the highest-altitude layer of the ionosphere, known as the F layer. This constellation, which consists of three identicalsatellites orbiting in a polar trajectory at altitudes ranging from 450 and 500 km, collects crucial data on electron density and other physical parameters. This information has created a valuable database, providing new insights into the F layer region. The processes occurring in the ionosphere at middle and high latitudes, particularly in regions directly influenced by interactions with the magnetosphere and solar wind, are of particular interest [6]. At these latitudes, the ionosphere responds to the velocity field transmitted by the solar wind-magnetosphere interaction, exhibiting distinctive planetary-scale patterns [7]. However, the specific pattern observed at any particular time is highly dependent on the prevailing conditions in the interplanetary medium, including the orientation and magnitude of the interplanetary magnetic field (IMF). In addition to large-scale plasma motions that contribute to electron density distribution at high latitudes, the ionosphere is subject to other latitude-independent processes [8]. Photoionization is a notable process that occurs as a result of the ionizing impact of sunlight on the ionospheric plasma. This photoionized plasma can travel long distances, even through dark regions, before significant recombination occurs. The interaction with sunlight shapes the plasma content in the ionosphere, making it an important consideration in understanding the dynamic behavior of the system. Other processes, such as particle precipitation, frictional heating, particle and heat exchange with the plasmasphere, and interaction with thermospheric winds [9], all have significant impact on the polar ionosphere, contributing to the considerable complexity of this region. In recent years, ionospheric modeling has grown in popularity as a means of reproducing and predicting ionospheric behavior at various temporal and spatial scales. These models are critical in assisting advanced technological systems that rely heavily on applications such as radio signal propagation. Furthermore, they help to improve our understanding of the ionosphere and the near-space environment. By conducting numerical experiments with these models, researchers can study various ionospheric processes without the need to take direct measurements. Ionospheric models are primarily concerned with describing the behavior of electron density in the ionosphere over space and time; however, certain models can account for additional parameters such as ion and electron temperatures, ion densities, and ionospheric drift. The advancement of ionospheric models results from high-quality observations, model improvements, and enhanced computing power.