The Earth’s magnetosphere represents a natural plasma laboratory that allows us to study the behavior of particle distribution functions in the absence of Coulomb collisions, typically described by the kappa distributions. We have investigated the properties of these functions for ions and electrons in different magnetospheric regions, thereby making it possible to reveal the κ-parameters for a wide range of plasma beta (β) values (from 10−3 to 102). This was done using simultaneous ion and electron measurements from the five Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft spanning the years 2008–2018. It was found that for a fixed plasma β, the κ-index and core energy (E c ) of the distribution can be modeled by the power law for both species, and the relation between β, κ, and E c is much more complex than earlier reported: both A and γ exhibit systematic dependencies with β. Our results indicate that β ∼ 0.1–0.3 is a range where the plasma is more dynamic, since it is influenced by both the magnetic field and temperature fluctuations, which suggests that the transition between magnetically and kinetically dominated plasmas occurs at these values of β. For β > 1, both A and γ take nearly constant values, a feature that is especially notable for the electrons and might be related to their demagnetization. The relation between β, κ, and E c that we present is an important result that can be used by theoretical models in the future.

Abstract. The study of diurnal and seasonal variations in total electron content (TEC) over Nigeria has been prompted by the recent increase in the number of GPS continuously operating reference stations (CORSs) across Nigeria as well as the reduced costs of microcomputing. The GPS data engaged in this study were recorded in the year 2012 at nine stations in Nigeria located between geomagnetic latitudes -4.33 and 0.72 • N. The GPS data were used to derive GPS TEC, which was analysed for diurnal and seasonal variations. The results obtained were used to produce local GPS TEC maps and bar charts. The derived GPS TEC across all the stations demonstrates consistent minimum diurnal variations during the pre-sunrise hours 04:00 to 06:00 LT, increases with sharp gradient during the sunrise period (∼ 07:00 to 09:00 LT), attains postnoon maximum at about 14:00 LT, and then falls to a minimum just before sunset. Generally, daytime variations are found to be greater than nighttime variations, which range between 0 and 5 TECU. The seasonal variation depicts a semi-annual distribution with higher values (∼ 25-30 TECU) around equinoxes and lower values (∼ 20-25 TECU) around solstices. The December Solstice magnitude is slightly higher than the June Solstice magnitude at all stations, while March Equinox magnitude is also slightly higher than September Equinox magnitude at all stations. Thus, the seasonal variation shows an asymmetry in equinoxes and solstices, with the month of October displaying the highest values of GPS TEC across the latitudes.

The dominant drivers of the large-scale spatial and temporal variability in the upper atmosphere are external forcing by energetic solar radiation (such as extreme ultraviolet) and energy deposition from the magnetosphere, as well as wave forcing from the lower atmosphere. The dynamo process in the E-region ionosphere brings about the solar quiet (Sq) current, which can be inferred from the so-called geomagnetic Sq variations. In the high-latitude ionosphere, the magnetospheric electric fields, which are coupled with the solar wind velocity and interplanetary magnetic field (IMF), are the primary drivers of the electric fields and currents (e.g., Weimer, 2005Weimer, , 2013, while in lower latitude regions, the neutral winds influenced by solar tides play a more active role (e.g., Maute & Richmond, 2016;Richmond & Thayer, 2000). In the equatorial region, a considerable daytime rise in the eastward equatorial electrojet (EEJ) current dominates the

From the very early studies of the Earth's magnetosphere, it became clear that particle flux spectra have energetic tails which are better described by power law distributions instead of exponential tails corresponding to Maxwell distributions. Given that the plasma density in the magnetosphere is very low, we are dealing with a collisionless plasma in which the relaxation of non-Maxwellian distributions toward Maxwellian distribution due to Coulomb collisions can take a long time. However, in spite of the absence of collisions, nearly Maxwellian distribution functions are frequently observed. The process of relaxation of particles to a Maxwell distributions in a collisionless plasma is unknown. The particle population in the Earth's magnetosphere is formed due to the action of several particle and energy sources and sinks. In many cases the observed distribution function for a large energy intervals can be well fitted by a Kappa distribution function, which is composed by a Maxwellian core and a power tail (see Livadiotis & McComas, 2013; Livadiotis, 2017 for a historical review). The formation of Kappa distributions is part of the process of relaxation of nonequilibrium distribution functions to Maxwell distributions. Such functions are often nearly isotropic and have no positive gradients in the velocity space. Such feature makes the process of kappa-type distribution relaxation to the Maxwell distribution function especially interesting. This function has three parameters: The number density of the selected population, the core energy, and the kappa index ( E  ), which describes the spectral slope at energies much larger than thermal ones. The kappa distribution transforms into a Maxwell distribution when E    . Therefore, it is interesting to identify regions with soft spectra(large E  ) to study the processes of relaxation of distribution functions to Maxwell distributions. This process is known as thermalization (see Kirpichev & Antonova, 2020, and references therein), and it is probably connected to diffusion in the velocity space (Collier, 1999).The use of three kappa parameters instead of the two parameters of the Maxwell approximation permits to improve the description of magnetospheric instabilities (

The possible influence of MHD turbulence on the energy distributions of ions in the Earth's plasma sheet was studied using data taken by the THEMIS satellites. Turbulence levels were traced using eddy diffusion coefficients (D), of which we measured one for each Geocentric Solar Magnetospheric (GSM) coordinates every 12 min. Ion fluxes between 1.75 and 210.5 keV during the same time windows that correspond to mainly suprathermal populations were fitted to Kappa distribution functions, which approximate a Maxwellian distribution when the κ-index (κ) is large. We found that the distribution of the eddy diffusion coefficients is bimodal, independently of both the eddy diffusion component and the plasma beta (β) parameter, which is defined as the ratio between plasma and magnetic pressures. The main peak corresponds to turbulent plasma flows with D > 103 km2 s−1. In such cases, the impact of turbulence on the κ index depends on the value of β and also on the direction of the turbulent transport. For eddy diffusion perpendicular to the neutral sheet, the values of κ decrease as Dzz increases for β < 2; while for higher values of β, κ increases with Dzz. For the other two directions, the values of κ decrease as D increases. This last tendency is stronger for β ~ 1 but almost null for β ~ 10. The secondary peak in the distribution of D values might represent quasi-laminar flows forming part of very large vortices, correct detection and description of which is beyond the scope of this study.