On the Relation between Kappa Distribution Functions and the Plasma Beta Parameter in the Earth’s Magnetosphere: THEMIS Observations

The Earth's magnetosphere represents a natural plasma laboratory that allows us to study the behavior of particle distribution functions in absence Coulomb collisions, typically described by Kappa distributions. We have investigated properties these for ions and electrons different magnetospheric regions, thereby making it possible reveal $\kappa$-parameters wide range beta ($\beta$) values (from $10^{-3}$ $10^{2}$). This was done using simultaneous ion electron measurements from five Time History Events Macroscale Interactions during Substorms (THEMIS) spacecraft spanning years 2008 2018. It found fixed $\beta$, $\kappa$-index core energy ($E_c$) can be modeled power-law $\kappa=AE_c^\gamma$ both species, relation between $\kappa$, $E_c$ is much more complex than earlier reported: $A$ $\gamma$ exhibit systematic dependencies with $\beta$. Our results indicate $\beta \sim 0.1-0.3$ where dynamic since influenced magnetic field temperature fluctuations, which suggests transition magnetically dominated plasmas kinetically occurs at For > 1 $, take nearly constant values, feature especially notable might related their demagnetization. we present an important result used theoretical models future.