Ion Kappa Distribution Parameters in the Magnetosphere of the Earth at Geocentric Distances Smaller Than 20 R_E During Quiet Geomagnetic Conditions

Abstract

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 (

RCM Modeling of Bubble Injections Into the Inner Magnetosphere: Spectral Properties of Plasma Sheet Particles

“…We were also able to capture the crescent-like region (near 𝐴𝐴 𝐴𝐴∼ 10𝐴𝐴e ), as described by Kirpichev et al (2021), who showed its existence in the dusk, midnight, and dawn sectors where the protons are thermalized, and the kappa index can reach values of ∼10 (see Figure 4 of their paper). However, deviations are also found at some locations, especially in the averaged 𝐴𝐴 𝐴𝐴 values, which could be explained by (a) spatio-temporal averaging of 𝐴𝐴 𝐴𝐴RCM , (b) fitting the protons' spectrum with a two-functional form (i.e., Maxwellian plus kappa), (c) using Geotail data as the RCM boundary particle distribution, (d) different complex processes (e.g., wave-particle/wave interactions and loss), and (e) different temporal averaging.…”

“…By fitting THEMIS satellite data during geomagnetically quiet conditions to a single kappa distribution function, Kirpichev et al. (2021) obtained the equatorial distribution of proton kappa parameters ($${\kappa }_{\mathrm{p}}$$) to elucidate plasma heating and acceleration processes. They discovered that $${\kappa }_{\mathrm{p}}$$ peaks in an arc‐like region between $$8$$ and $$10{R}_{\mathrm{e}}$$ in the dawn, night, and dusk, presumably due to insignificant impact of injections.…”

“…It would be very interesting and informative to use controlled numerical experiments to see how different mechanisms maintain the kappa-like state or pull it toward thermodynamic equilibrium. When geomagnetic activity is low, the spectra of plasma sheet particles are statistically dominated by a single kappa functional form (Christon et al, 1989;Kirpichev et al, 2021), but this is not the case during active periods (Christon et al, 1991). Christon et al (1991) indicated that the kappa values for protons and electrons in active central plasma sheet samples are ∼4-15 and ∼3-10, respectively.…”

“…Christon et al (1991) indicated that the kappa values for protons and electrons in active central plasma sheet samples are ∼4-15 and ∼3-10, respectively. By fitting THEMIS satellite data during geomagnetically quiet conditions to a single kappa distribution function, Kirpichev et al (2021) obtained the equatorial distribution of proton kappa parameters ( 𝐴𝐴 𝐴𝐴p ) to elucidate plasma heating and acceleration processes. They discovered that 𝐴𝐴 𝐴𝐴p peaks in an arc-like region between 𝐴𝐴 8 and 𝐴𝐴 10𝑅𝑅e in the dawn, night, and dusk, presumably due to insignificant impact of injections.…”

The Influence of Extreme Levels of the Solar Wind Dynamic Pressure on the Structure of Nightside Auroral Precipitation

“…In our study, we used a modified version of that method, which was proposed by Stepanova et al (2006). The ion pressure is calculated under the assumption of a Maxwellian energy distribution of particles, which, despite the recorded non Maxwellian energetic tails of the distribution functions, does not lead to significant errors in calculating the pressure in the considered regions (Kirpichev et al, 2021). To avoid a significant effect of substorm processes on the results of the study, an important criterion in selecting the data and study intervals was the low level of magnetic activity in the auroral zone, AL > -200 nT.…”